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<?xml version="1.0" encoding="utf-8"?>
<search>
<entry>
<title>机试第11章</title>
<url>/2023/03/08/%E6%9C%BA%E8%AF%95%E7%AC%AC11%E7%AB%A0/</url>
<content><![CDATA[<h2 id="并查集"><a href="#并查集" class="headerlink" title="并查集"></a>并查集</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">1000</span>;</span><br><span class="line"><span class="type">int</span> fa[MAXN], h[MAXN];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">init</span><span class="params">(<span class="type">int</span> n)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < n; ++i)</span><br><span class="line"> fa[i] = i, h[i] = <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">find</span><span class="params">(<span class="type">int</span> x)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (x != fa[x])</span><br><span class="line"> fa[x] = <span class="built_in">find</span>(fa[x]);</span><br><span class="line"> <span class="keyword">return</span> fa[x];</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">uni</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> y)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> x = <span class="built_in">find</span>(x), y = <span class="built_in">find</span>(y);</span><br><span class="line"> <span class="keyword">if</span> (x != y)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (h[x] < h[y])</span><br><span class="line"> fa[x] = y;</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (h[x] > h[y])</span><br><span class="line"> fa[y] = x;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> {</span><br><span class="line"> h[x]++;</span><br><span class="line"> fa[y] = x;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="判断无向图是否连通"><a href="#判断无向图是否连通" class="headerlink" title="判断无向图是否连通"></a>判断无向图是否连通</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">bool</span> <span class="title">isConnected</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> cnt = <span class="number">0</span>; <span class="comment">// 连通分量个数</span></span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i < n; ++i)</span><br><span class="line"> <span class="keyword">if</span> (<span class="built_in">find</span>(i) == i)</span><br><span class="line"> cnt++;</span><br><span class="line"> <span class="keyword">return</span> cnt == <span class="number">1</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="判断有向图是否为树"><a href="#判断有向图是否为树" class="headerlink" title="判断有向图是否为树"></a>判断有向图是否为树</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">int</span> degree[MAXN]; <span class="comment">// 入度，在union时改变</span></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">init</span><span class="params">(<span class="type">int</span> n)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < n; ++i)</span><br><span class="line"> degree[i] = <span class="number">0</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">bool</span> <span class="title">isTree</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">bool</span> flag = <span class="literal">true</span>;</span><br><span class="line"> <span class="type">int</span> cnt = <span class="number">0</span>;</span><br><span class="line"> <span class="type">int</span> root = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < MAXN; ++i)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (fa[i] == i)</span><br><span class="line"> cnt++;</span><br><span class="line"> <span class="keyword">if</span> (degree[i] == <span class="number">0</span>)</span><br><span class="line"> root++;</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (degree[i] > <span class="number">1</span>)</span><br><span class="line"> {</span><br><span class="line"> flag = <span class="literal">false</span>;</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> (cnt != <span class="number">1</span> || root != <span class="number">1</span>)</span><br><span class="line"> flag = <span class="literal">false</span>;</span><br><span class="line"> <span class="keyword">if</span> (cnt == <span class="number">0</span> || root == <span class="number">0</span>)</span><br><span class="line"> flag = <span class="literal">true</span>;</span><br><span class="line"> <span class="keyword">return</span> flag;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="最小生成树Kruskal算法"><a href="#最小生成树Kruskal算法" class="headerlink" title="最小生成树Kruskal算法"></a>最小生成树Kruskal算法</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="keyword">struct</span> <span class="title class_">edge</span></span><br><span class="line">{</span><br><span class="line"> <span class="type">int</span> s, e, w;</span><br><span class="line"> <span class="type">bool</span> <span class="keyword">operator</span><(<span class="type">const</span> edge &e) <span class="type">const</span></span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">return</span> w < e.w;</span><br><span class="line"> }</span><br><span class="line">};</span><br><span class="line">edge edges[MAXN * MAXN];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">kruskal</span><span class="params">(<span class="type">int</span> n, <span class="type">int</span> len)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="built_in">init</span>(n); <span class="comment">// 初始化并查集</span></span><br><span class="line"> <span class="built_in">sort</span>(edges, edges + len);</span><br><span class="line"> <span class="type">int</span> res = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < len; ++i)</span><br><span class="line"> {</span><br><span class="line"> edge cur = edges[i];</span><br><span class="line"> <span class="keyword">if</span> (<span class="built_in">find</span>(cur.s) != <span class="built_in">find</span>(cur.e))</span><br><span class="line"> {</span><br><span class="line"> <span class="built_in">uni</span>(cur.s, cur.e);</span><br><span class="line"> res += cur.w;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="最短路"><a href="#最短路" class="headerlink" title="最短路"></a>最短路</h2><h3 id="单源最短路Dijkstra算法"><a href="#单源最短路Dijkstra算法" class="headerlink" title="单源最短路Dijkstra算法"></a>单源最短路Dijkstra算法</h3><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><bits/stdc++.h></span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">1000</span>;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> INF = INT_MAX;</span><br><span class="line"></span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">edge</span></span><br><span class="line">{</span><br><span class="line"> <span class="type">int</span> to, length;</span><br><span class="line"> <span class="built_in">edge</span>(<span class="type">int</span> to, <span class="type">int</span> length) : <span class="built_in">to</span>(to), <span class="built_in">length</span>(length) {}</span><br><span class="line">};</span><br><span class="line"></span><br><span class="line"><span class="keyword">struct</span> <span class="title class_">point</span></span><br><span class="line">{</span><br><span class="line"> <span class="type">int</span> num, dis;</span><br><span class="line"> <span class="built_in">point</span>(<span class="type">int</span> num, <span class="type">int</span> dis) : <span class="built_in">num</span>(num), <span class="built_in">dis</span>(dis) {}</span><br><span class="line"> <span class="type">bool</span> <span class="keyword">operator</span><(<span class="type">const</span> point &x) <span class="type">const</span></span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">return</span> dis > x.dis;</span><br><span class="line"> }</span><br><span class="line">};</span><br><span class="line"></span><br><span class="line">vector<edge> graph[MAXN];</span><br><span class="line"><span class="type">int</span> dis[MAXN];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">dijkstra</span><span class="params">(<span class="type">int</span> s)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> priority_queue<point> q;</span><br><span class="line"> q.<span class="built_in">push</span>({s, <span class="number">0</span>});</span><br><span class="line"> <span class="keyword">while</span> (!q.<span class="built_in">empty</span>())</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> u = q.<span class="built_in">top</span>().num;</span><br><span class="line"> q.<span class="built_in">pop</span>();</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < graph[u].<span class="built_in">size</span>(); ++i)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> v = graph[u][i].to, d = graph[u][i].length;</span><br><span class="line"> <span class="keyword">if</span> (dis[v] > dis[u] + d)</span><br><span class="line"> {</span><br><span class="line"> dis[v] = dis[u] + d;</span><br><span class="line"> q.<span class="built_in">push</span>({v, dis[v]});</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> n, m;</span><br><span class="line"> cin >> n >> m;</span><br><span class="line"> <span class="built_in">memset</span>(graph, <span class="number">0</span>, <span class="built_in">sizeof</span>(graph));</span><br><span class="line"> <span class="built_in">fill</span>(dis, dis + n, INF);</span><br><span class="line"> <span class="keyword">while</span> (m--)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> from, to, length;</span><br><span class="line"> cin >> from >> to >> length;</span><br><span class="line"> graph[from].<span class="built_in">push_back</span>({to, length});</span><br><span class="line"> graph[to].<span class="built_in">push_back</span>({from, length});</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="type">int</span> s, t;</span><br><span class="line"> cin >> s >> t;</span><br><span class="line"> <span class="keyword">if</span> (dis[t] == INF)</span><br><span class="line"> dis[t] = <span class="number">-1</span>;</span><br><span class="line"> cout << dis[t] << <span class="string">"\n"</span>;</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h3 id="多源最短路Floyd算法"><a href="#多源最短路Floyd算法" class="headerlink" title="多源最短路Floyd算法"></a>多源最短路Floyd算法</h3><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string"><bits/stdc++.h></span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> INF = INT_MAX;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> n, target;</span><br><span class="line"> cin >> n >> target;</span><br><span class="line"> vector<vector<<span class="type">int</span>>> <span class="built_in">g</span>(n + <span class="number">1</span>, <span class="built_in">vector</span><<span class="type">int</span>>(n + <span class="number">1</span>, INF));</span><br><span class="line"> vector<vector<<span class="type">int</span>>> <span class="built_in">next</span>(n + <span class="number">1</span>, <span class="built_in">vector</span><<span class="type">int</span>>(n + <span class="number">1</span>));</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < n; ++i)</span><br><span class="line"> {</span><br><span class="line"> g[i][i] = <span class="number">0</span>;</span><br><span class="line"> next[i][i] = i;</span><br><span class="line"> }</span><br><span class="line"> <span class="type">int</span> src, dst, dis;</span><br><span class="line"> <span class="keyword">while</span> (cin >> src >> dst >> dis)</span><br><span class="line"> {</span><br><span class="line"> g[src][dst] = dis;</span><br><span class="line"> next[src][dst] = dst;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> k = <span class="number">0</span>; k < n; ++k)</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < n; ++i)</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = <span class="number">0</span>; j < n; ++j)</span><br><span class="line"> <span class="keyword">if</span> (g[i][k] == INF || g[k][j] == INF)</span><br><span class="line"> <span class="keyword">continue</span>;</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (g[i][k] + g[k][j] < g[i][j])</span><br><span class="line"> {</span><br><span class="line"> g[i][j] = g[i][k] + g[k][j];</span><br><span class="line"> next[i][j] = k;</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="type">int</span> cur = <span class="number">1</span>;</span><br><span class="line"> cout << cur;</span><br><span class="line"> <span class="keyword">while</span>(cur!=target)</span><br><span class="line"> {</span><br><span class="line"> cur = next[cur][target];</span><br><span class="line"> cout << <span class="string">" "</span> << cur;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="拓扑排序"><a href="#拓扑排序" class="headerlink" title="拓扑排序"></a>拓扑排序</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">500</span>;</span><br><span class="line">vector<<span class="type">int</span>> graph[MAXN];</span><br><span class="line"><span class="type">int</span> inDegree[MAXN];</span><br><span class="line"></span><br><span class="line"><span class="function">vector<<span class="type">int</span>> <span class="title">TopologicalSort</span><span class="params">(<span class="type">int</span> n)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> vector<<span class="type">int</span>> res;</span><br><span class="line"> priority_queue<<span class="type">int</span>, vector<<span class="type">int</span>>, greater<<span class="type">int</span>>> q;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i <= n; ++i)</span><br><span class="line"> <span class="keyword">if</span> (inDegree[i] == <span class="number">0</span>)</span><br><span class="line"> q.<span class="built_in">push</span>(i);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">while</span> (!q.<span class="built_in">empty</span>())</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> u = q.<span class="built_in">top</span>();</span><br><span class="line"> q.<span class="built_in">pop</span>();</span><br><span class="line"> res.<span class="built_in">push_back</span>(u);</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < graph[u].<span class="built_in">size</span>(); ++i)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> v = graph[u][i];</span><br><span class="line"> inDegree[v]--;</span><br><span class="line"> <span class="keyword">if</span> (inDegree[v] == <span class="number">0</span>)</span><br><span class="line"> q.<span class="built_in">push</span>(v);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="关键路径"><a href="#关键路径" class="headerlink" title="关键路径"></a>关键路径</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">1e5</span>;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> INF = INT_MAX;</span><br><span class="line">vector<<span class="type">int</span>> graph[MAXN];</span><br><span class="line"><span class="type">int</span> inDegree[MAXN];</span><br><span class="line"><span class="type">int</span> earliest[MAXN], latest[MAXN], time[MAXN];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">CriticalPath</span><span class="params">(<span class="type">int</span> n)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> vector<<span class="type">int</span>> topology;</span><br><span class="line"> queue<<span class="type">int</span>> q;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i <= n; ++i)</span><br><span class="line"> <span class="keyword">if</span> (inDegree[i] == <span class="number">0</span>)</span><br><span class="line"> q.<span class="built_in">push</span>(i);</span><br><span class="line"></span><br><span class="line"> <span class="type">int</span> total = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">while</span> (!q.<span class="built_in">empty</span>())</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> u = q.<span class="built_in">front</span>();</span><br><span class="line"> q.<span class="built_in">pop</span>();</span><br><span class="line"> topology.<span class="built_in">push_back</span>(u);</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < graph[u].<span class="built_in">size</span>(); ++i)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> v = graph[u][i];</span><br><span class="line"> earliest[v] = <span class="built_in">max</span>(earliest[v], earliest[u] + time[u]);</span><br><span class="line"> inDegree[v]--;</span><br><span class="line"> <span class="keyword">if</span> (inDegree[v] == <span class="number">0</span>)</span><br><span class="line"> {</span><br><span class="line"> q.<span class="built_in">push</span>(v);</span><br><span class="line"> total = <span class="built_in">max</span>(total, earliest[v] + time[v]);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = topology.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; --i)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> u = topology[i];</span><br><span class="line"> <span class="keyword">if</span> (graph[u].<span class="built_in">size</span>() == <span class="number">0</span>) <span class="comment">// 无后继的节点</span></span><br><span class="line"> latest[u] = total - time[u];</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> latest[u] = INF;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = <span class="number">0</span>; j < graph[u].<span class="built_in">size</span>(); ++j)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> v = graph[u][j];</span><br><span class="line"> latest[u] = <span class="built_in">min</span>(latest[u], latest[v] - time[u]);</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> total;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
]]></content>
<tags>
<tag>机试</tag>
<tag>图论</tag>
</tags>
</entry>
<entry>
<title>cs专业单词</title>
<url>/2023/03/12/cs%E4%B8%93%E4%B8%9A%E5%8D%95%E8%AF%8D/</url>
<content><![CDATA[<h3 id="ChatGPT-Prompt"><a href="#ChatGPT-Prompt" class="headerlink" title="ChatGPT Prompt"></a>ChatGPT Prompt</h3><p>将输入的文本逐行按单词，词性，释义，发音分列，输出为markdown格式的表格，忽略小括号及其中的内容</p>
<h3 id="单词"><a href="#单词" class="headerlink" title="单词"></a>单词</h3><p>prompt,n.&,v.提示 [prɑmpt]</p>
<p>execute,v.实行，实施 [ˈɛksɪˌkjut]</p>
<p>argument,n.变元，自变量 [ˈɑrgjumənt]</p>
<p>macro,n.宏，宏功能，宏指令 [ˈmækroʊ]</p>
<p>restore,vt.恢复，复原 [rɪˈstɔr, -ˈstor]</p>
<p>decimal,n.&,a.十进制 [ˈdɛsəməl]</p>
<p>attribute,n.属性，标志，表征 [əˈtrɪbjut]</p>
<p>scope,n.范围，显示器 [skoʊp]</p>
<p>toggle,n.&,v.触发器；系紧 [ˈtɑgl]</p>
<p>reflow,v.&,n.回流，逆流 [ˈrifloʊ]</p>
<p>assign,vt.赋值，指定，分派 [əˈsaɪn]</p>
<p>abbreviate,vt.缩写，省略 [əˈbriːvɪeɪt]</p>
<p>delimiter,n.定界符，分界符 [dɪ’lɪmɪtə]</p>
<p>omit,vt.省略，删去，遗漏(ao,mai,te) [oˈmɪt</p>
<p>coprocessor,n.协同处理器(kou,pa,sei,se) [‘koʊˌproʊsesə]</p>
<p>overlay,v.覆盖，重叠(ou,wei,chi) [ˌoʊvərˈleɪ]</p>
<p>recall,vt.撤消，复活，检索(rui,kao,l) [rɪˈkɔl]</p>
<p>wildcard,n.通配符 [‘waɪldkɑd]</p>
<p>spill,v.漏出，溢出，漏失 [spɪl]</p>
<p>even,a.&,ad.偶数的 [ˈivən]</p>
<p>syntax,n.语法，文法，句法 [ˈsɪnˌtæks]</p>
<p>utility,n.&,a.实用程序；实用性,(,yo,u,t,i,li,t,i) [juˈtɪləti]</p>
<p>eject,n.弹出 [ɪ’dʒekt]</p>
<p>term,n.项，条款，术语 [tɜrm]</p>
<p>invoke,vt.调用，请求,,(in,wou,te) [ɪnˈvoʊk]</p>
<p>designated,a.指定的，特指的,,(da,si,nei,te,d) [‘dezɪɡneɪtɪd]</p>
<p>pertain,vi.附属，属于，关于,,(p,tin) [pərˈteɪn]</p>
<p>session,n.对话，通话,,(se,sheng) [ˈsɛʃən]</p>
<p>assembly,n.汇编，安装，装配,,(e,san,bo,li) [əˈsɛmbli]</p>
<p>retrieve,v.检索,,(e,chui,wu) [rɪˈtriv]</p>
<p>subtotal,n.&,v.小计，求部分和,,(sa,bo,tei,lou) [ˈsʌbtoʊtl]</p>
<p>partition,v.划分，分区，部分 [pɑrˈtɪʃn]</p>
<p>hexadecimal,a.十六进制的 [ˌhɛksəˈdɛsəməl]</p>
<p>nest,v.嵌套，后进先出 [nɛst]</p>
<p>modifier,n.修改量，变址数 [ˈmɑdɪfaɪə(r)]</p>
<p>interrupt,v.&,n.中断 [ˌɪntəˈrʌpt]</p>
<p>serial,a.串行的，串联的 [ˈsɪriəl]</p>
<p>corrupt,v.&,a.恶化；有毛病的 [kəˈrʌpt]</p>
<p>critical,a.&,n.临界的；临界值 [ˈkrɪtɪkəl]</p>
<table>
<thead>
<tr>
<th>单词</th>
<th>词性</th>
<th>释义</th>
<th>发音</th>
</tr>
</thead>
<tbody><tr>
<td>prompt</td>
<td>n.&,v.</td>
<td>提示</td>
<td>[prɑmpt]</td>
</tr>
<tr>
<td>execute</td>
<td>v.</td>
<td>实行，实施</td>
<td>[ˈɛksɪˌkjut]</td>
</tr>
<tr>
<td>argument</td>
<td>n.</td>
<td>变元，自变量</td>
<td>[ˈɑrgjumənt]</td>
</tr>
<tr>
<td>macro</td>
<td>n.</td>
<td>宏，宏功能，宏指令</td>
<td>[ˈmækroʊ]</td>
</tr>
<tr>
<td>restore</td>
<td>vt.</td>
<td>恢复，复原</td>
<td>[rɪˈstɔr, -ˈstor]</td>
</tr>
<tr>
<td>decimal</td>
<td>n.&,a.</td>
<td>十进制</td>
<td>[ˈdɛsəməl]</td>
</tr>
<tr>
<td>attribute</td>
<td>n.</td>
<td>属性，标志，表征</td>
<td>[əˈtrɪbjut]</td>
</tr>
<tr>
<td>scope</td>
<td>n.</td>
<td>范围，显示器</td>
<td>[skoʊp]</td>
</tr>
<tr>
<td>toggle</td>
<td>n.&,v.</td>
<td>触发器；系紧</td>
<td>[ˈtɑgl]</td>
</tr>
<tr>
<td>reflow</td>
<td>v.&,n.</td>
<td>回流，逆流</td>
<td>[ˈrifloʊ]</td>
</tr>
<tr>
<td>assign</td>
<td>vt.</td>
<td>赋值，指定，分派</td>
<td>[əˈsaɪn]</td>
</tr>
<tr>
<td>abbreviate</td>
<td>vt.</td>
<td>缩写，省略</td>
<td>[əˈbriːvɪeɪt]</td>
</tr>
<tr>
<td>delimiter</td>
<td>n.</td>
<td>定界符，分界符</td>
<td>[dɪ’lɪmɪtə]</td>
</tr>
<tr>
<td>omit</td>
<td>vt.</td>
<td>省略，删去，遗漏</td>
<td>[oˈmɪt]</td>
</tr>
<tr>
<td>coprocessor</td>
<td>n.</td>
<td>协同处理器</td>
<td>[‘koʊˌproʊsesə]</td>
</tr>
<tr>
<td>overlay</td>
<td>v.</td>
<td>覆盖，重叠</td>
<td>[ˌoʊvərˈleɪ]</td>
</tr>
<tr>
<td>recall</td>
<td>vt.</td>
<td>撤消，复活，检索</td>
<td>[rɪˈkɔl]</td>
</tr>
<tr>
<td>wildcard</td>
<td>n.</td>
<td>通配符</td>
<td>[‘waɪldkɑd]</td>
</tr>
<tr>
<td>spill</td>
<td>v.</td>
<td>漏出，溢出，漏失</td>
<td>[spɪl]</td>
</tr>
<tr>
<td>even</td>
<td>a.&,ad.</td>
<td>偶数的</td>
<td>[ˈivən]</td>
</tr>
<tr>
<td>syntax</td>
<td>n.</td>
<td>语法，文法，句法</td>
<td>[ˈsɪnˌtæks]</td>
</tr>
<tr>
<td>utility</td>
<td>n.&,a.</td>
<td>实用程序；实用性</td>
<td>[juˈtɪləti]</td>
</tr>
<tr>
<td>eject</td>
<td>n.</td>
<td>弹出</td>
<td>[ɪ’dʒekt]</td>
</tr>
<tr>
<td>term</td>
<td>n.</td>
<td>项，条款，术语</td>
<td>[tɜrm]</td>
</tr>
<tr>
<td>invoke</td>
<td>vt.</td>
<td>调用，请求</td>
<td>[ɪnˈvoʊk]</td>
</tr>
<tr>
<td>designated</td>
<td>a.</td>
<td>指定的，特指的</td>
<td>[‘dezɪɡneɪtɪd]</td>
</tr>
<tr>
<td>pertain</td>
<td>vi.</td>
<td>附属，属于，关于</td>
<td>[pərˈteɪn]</td>
</tr>
<tr>
<td>assembly</td>
<td>n.</td>
<td>汇编，安装，装配</td>
<td>[əˈsɛmbli]</td>
</tr>
<tr>
<td>retrieve</td>
<td>v.</td>
<td>检索</td>
<td>[rɪˈtriv]</td>
</tr>
<tr>
<td>subtotal</td>
<td>n.&v.</td>
<td>小计，求部分和</td>
<td>[ˈsʌbtoʊtl]</td>
</tr>
<tr>
<td>partition</td>
<td>v.</td>
<td>划分，分区，部分</td>
<td>[pɑrˈtɪʃn]</td>
</tr>
<tr>
<td>hexadecimal</td>
<td>a.</td>
<td>十六进制的</td>
<td>[ˌhɛksəˈdɛsəməl]</td>
</tr>
<tr>
<td>nest</td>
<td>v.</td>
<td>嵌套，后进先出</td>
<td>[nɛst]</td>
</tr>
<tr>
<td>modifier</td>
<td>n.</td>
<td>修改量，变址数</td>
<td>[ˈmɑdɪfaɪə(r)]</td>
</tr>
<tr>
<td>interrupt</td>
<td>v.&n.</td>
<td>中断</td>
<td>[ˌɪntəˈrʌpt]</td>
</tr>
<tr>
<td>serial</td>
<td>a.</td>
<td>串行的，串联的</td>
<td>[ˈsɪriəl]</td>
</tr>
<tr>
<td>corrupt</td>
<td>v.&a.</td>
<td>恶化；有毛病的</td>
<td>[kəˈrʌpt]</td>
</tr>
<tr>
<td>critical</td>
<td>a.&n.</td>
<td>临界的；临界值</td>
<td>[ˈkrɪtɪkəl]</td>
</tr>
</tbody></table>
]]></content>
<tags>
<tag>面试</tag>
</tags>
</entry>
<entry>
<title>机试第10章</title>
<url>/2023/03/08/%E6%9C%BA%E8%AF%95%E7%AC%AC10%E7%AB%A0/</url>
<content><![CDATA[<h2 id="前序遍历序列建二叉树"><a href="#前序遍历序列建二叉树" class="headerlink" title="前序遍历序列建二叉树"></a>前序遍历序列建二叉树</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line">string str;</span><br><span class="line"><span class="type">int</span> pos = <span class="number">0</span>;</span><br><span class="line"></span><br><span class="line"><span class="function">TreeNode *<span class="title">build</span><span class="params">(string str, <span class="type">int</span> &pos)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">char</span> c = str[pos++];</span><br><span class="line"> <span class="keyword">if</span> (c == <span class="string">'#'</span>)</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">nullptr</span>;</span><br><span class="line"> TreeNode *root = <span class="keyword">new</span> <span class="built_in">TreeNode</span>(c);</span><br><span class="line"> root->lchild = <span class="built_in">build</span>(str, pos);</span><br><span class="line"> root->rchild = <span class="built_in">build</span>(str, pos);</span><br><span class="line"> <span class="keyword">return</span> root;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="根据前序序列和中序序列确定二叉树"><a href="#根据前序序列和中序序列确定二叉树" class="headerlink" title="根据前序序列和中序序列确定二叉树"></a>根据前序序列和中序序列确定二叉树</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function">TreeNode *<span class="title">build</span><span class="params">(<span class="type">int</span> l1, <span class="type">int</span> r1, <span class="type">int</span> l2, <span class="type">int</span> r2, string &pre, string &in)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (l1 > r1)</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">nullptr</span>;</span><br><span class="line"> TreeNode *root = <span class="keyword">new</span> <span class="built_in">TreeNode</span>(pre[l1]);</span><br><span class="line"> <span class="type">int</span> pos = in.<span class="built_in">find</span>(pre[l1]);</span><br><span class="line"> root->lchild = <span class="built_in">build</span>(l1 + <span class="number">1</span>, l1 + pos + <span class="number">1</span>, l2, pos - <span class="number">1</span>, pre, in);</span><br><span class="line"> root->rchild = <span class="built_in">build</span>(l1 + pos + <span class="number">2</span>, r1, pos + <span class="number">1</span>, r2, pre, in);</span><br><span class="line"> <span class="keyword">return</span> root;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function">TreeNode *<span class="title">make</span><span class="params">(string &pre, string &in)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">return</span> <span class="built_in">build</span>(<span class="number">0</span>, pre.<span class="built_in">size</span>() - <span class="number">1</span>, <span class="number">0</span>, in.<span class="built_in">size</span>() - <span class="number">1</span>, pre, in);</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="二叉排序树建树"><a href="#二叉排序树建树" class="headerlink" title="二叉排序树建树"></a>二叉排序树建树</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function">TreeNode *<span class="title">insert</span><span class="params">(TreeNode *root, <span class="type">int</span> val, <span class="type">int</span> father)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (!root)</span><br><span class="line"> {</span><br><span class="line"> root = <span class="keyword">new</span> <span class="built_in">TreeNode</span>(val);</span><br><span class="line"> cout << father << <span class="string">" "</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (val < root->val)</span><br><span class="line"> root->lchild = <span class="built_in">insert</span>(root->lchild, val, root->val);</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> root->rchild = <span class="built_in">insert</span>(root->rchild, val, root->val);</span><br><span class="line"> <span class="keyword">return</span> root;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="判断两棵树是否相同"><a href="#判断两棵树是否相同" class="headerlink" title="判断两棵树是否相同"></a>判断两棵树是否相同</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">bool</span> <span class="title">isEqual</span><span class="params">(TreeNode *x, TreeNode *y)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (x == <span class="literal">nullptr</span> && y == <span class="literal">nullptr</span>)</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line"> <span class="keyword">if</span> ((x == <span class="literal">nullptr</span> && y != <span class="literal">nullptr</span>) || (x != <span class="literal">nullptr</span> && y == <span class="literal">nullptr</span>))</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line"> <span class="keyword">if</span> (x->val != y->val)</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line"> <span class="keyword">return</span> <span class="built_in">isEqual</span>(x->lchild, y->lchild) && <span class="built_in">isEqual</span>(x->rchild, y->rchild);</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="哈夫曼树最小带权路径长度和"><a href="#哈夫曼树最小带权路径长度和" class="headerlink" title="哈夫曼树最小带权路径长度和"></a>哈夫曼树最小带权路径长度和</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line">priority_queue<<span class="type">int</span>, vector<<span class="type">int</span>>, greater<<span class="type">int</span>>> q; <span class="comment">// 小根堆</span></span><br><span class="line"></span><br><span class="line"><span class="type">int</span> res = <span class="number">0</span>;</span><br><span class="line"><span class="keyword">while</span> (q.<span class="built_in">size</span>() > <span class="number">1</span>)</span><br><span class="line">{</span><br><span class="line"> <span class="type">int</span> a = q.<span class="built_in">top</span>();</span><br><span class="line"> q.<span class="built_in">pop</span>();</span><br><span class="line"> <span class="type">int</span> b = q.<span class="built_in">top</span>();</span><br><span class="line"> q.<span class="built_in">pop</span>();</span><br><span class="line"> res += a + b;</span><br><span class="line"> q.<span class="built_in">push</span>(a + b);</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="哈夫曼树建树及哈夫曼编码"><a href="#哈夫曼树建树及哈夫曼编码" class="headerlink" title="哈夫曼树建树及哈夫曼编码"></a>哈夫曼树建树及哈夫曼编码</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="keyword">struct</span> <span class="title class_">cmp</span></span><br><span class="line">{</span><br><span class="line"> <span class="function"><span class="type">bool</span> <span class="title">operator</span><span class="params">()</span><span class="params">(TreeNode *lhs, TreeNode *rhs)</span></span></span><br><span class="line"><span class="function"> </span>{</span><br><span class="line"> <span class="keyword">return</span> lhs->val > rhs->val;</span><br><span class="line"> }</span><br><span class="line">};</span><br><span class="line"></span><br><span class="line">string tmp;</span><br><span class="line">vector<string> res;</span><br><span class="line">unordered_map<TreeNode *, <span class="type">int</span>> mp; <span class="comment">// 给每个节点赋序号</span></span><br><span class="line">priority_queue<TreeNode *, vector<TreeNode *>, cmp> q;</span><br><span class="line">res.<span class="built_in">resize</span>(q.<span class="built_in">size</span>());</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">build</span><span class="params">()</span> <span class="comment">// 建树</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">while</span> (q.<span class="built_in">size</span>() > <span class="number">1</span>)</span><br><span class="line"> {</span><br><span class="line"> TreeNode *a = q.<span class="built_in">top</span>();</span><br><span class="line"> q.<span class="built_in">pop</span>();</span><br><span class="line"> TreeNode *b = q.<span class="built_in">top</span>();</span><br><span class="line"> q.<span class="built_in">pop</span>();</span><br><span class="line"> TreeNode *root = <span class="keyword">new</span> <span class="built_in">TreeNode</span>(a->val + b->val);</span><br><span class="line"> root->lchild = a, root->rchild = b;</span><br><span class="line"> q.<span class="built_in">push</span>(root);</span><br><span class="line"> }</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">solve</span><span class="params">(TreeNode *root)</span> <span class="comment">// 编码</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (!root)</span><br><span class="line"> <span class="keyword">return</span>;</span><br><span class="line"> <span class="keyword">if</span> (!root->lchild && !root->rchild)</span><br><span class="line"> {</span><br><span class="line"> res[mp[root]] = tmp;</span><br><span class="line"> <span class="keyword">return</span>;</span><br><span class="line"> }</span><br><span class="line"> tmp += <span class="string">"0"</span>;</span><br><span class="line"> <span class="built_in">solve</span>(root->lchild);</span><br><span class="line"> tmp.<span class="built_in">pop_back</span>();</span><br><span class="line"> tmp += <span class="string">"1"</span>;</span><br><span class="line"> <span class="built_in">solve</span>(root->rchild);</span><br><span class="line"> tmp.<span class="built_in">pop_back</span>();</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
]]></content>
<tags>
<tag>机试</tag>
<tag>数据结构</tag>
</tags>
</entry>
<entry>
<title>机试第12章</title>
<url>/2023/03/08/%E6%9C%BA%E8%AF%95%E7%AC%AC12%E7%AB%A0/</url>
<content><![CDATA[<h2 id="最大连续子序列和"><a href="#最大连续子序列和" class="headerlink" title="最大连续子序列和"></a>最大连续子序列和</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">10000</span>;</span><br><span class="line"><span class="type">long</span> <span class="type">long</span> a[MAXN], dp[MAXN];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">long</span> <span class="type">long</span> <span class="title">solve</span><span class="params">(<span class="type">int</span> n)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">long</span> <span class="type">long</span> res = <span class="number">0</span>;</span><br><span class="line"> dp[<span class="number">0</span>] = a[<span class="number">0</span>];</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i < n; ++i)</span><br><span class="line"> {</span><br><span class="line"> dp[i] = <span class="built_in">max</span>(a[i], dp[i - <span class="number">1</span>] + a[i]);</span><br><span class="line"> res = <span class="built_in">max</span>(res, dp[i]);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="最长递增子序列"><a href="#最长递增子序列" class="headerlink" title="最长递增子序列"></a>最长递增子序列</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">1000</span>;</span><br><span class="line"><span class="type">int</span> a[MAXN], dp[MAXN];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">solve</span><span class="params">(<span class="type">int</span> n)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> res = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < n; ++i)</span><br><span class="line"> {</span><br><span class="line"> dp[i] = <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = <span class="number">0</span>; j < i; ++j)</span><br><span class="line"> <span class="keyword">if</span> (a[i] > a[j])</span><br><span class="line"> dp[i] = <span class="built_in">max</span>(dp[i], dp[j] + <span class="number">1</span>);</span><br><span class="line"> res = <span class="built_in">max</span>(res, dp[i]);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="最大上升子序列和"><a href="#最大上升子序列和" class="headerlink" title="最大上升子序列和"></a>最大上升子序列和</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">1000</span>;</span><br><span class="line"><span class="type">int</span> a[MAXN], dp[MAXN];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">solve</span><span class="params">(<span class="type">int</span> n)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> res = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < n; ++i)</span><br><span class="line"> {</span><br><span class="line"> dp[i] = a[i];</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = <span class="number">0</span>; j < i; ++j)</span><br><span class="line"> <span class="keyword">if</span> (a[i] > a[j])</span><br><span class="line"> dp[i] = <span class="built_in">max</span>(dp[i], dp[j] + a[i]);</span><br><span class="line"> res = <span class="built_in">max</span>(res, dp[i]);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="最长公共子序列"><a href="#最长公共子序列" class="headerlink" title="最长公共子序列"></a>最长公共子序列</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">1000</span>;</span><br><span class="line"><span class="type">int</span> dp[MAXN][MAXN];</span><br><span class="line"><span class="type">char</span> s1[MAXN], s2[MAXN];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">solve</span><span class="params">(<span class="type">int</span> n, <span class="type">int</span> m)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i <= n; ++i)</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = <span class="number">0</span>; j <= m; ++j)</span><br><span class="line"> <span class="keyword">if</span> (i == <span class="number">0</span> || j == <span class="number">0</span>)</span><br><span class="line"> {</span><br><span class="line"> dp[i][j] = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">continue</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (s1[i] == s2[j])</span><br><span class="line"> dp[i][j] = dp[i - <span class="number">1</span>][j - <span class="number">1</span>] + <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> dp[i][j] = <span class="built_in">max</span>(dp[i - <span class="number">1</span>][j], dp[i][j - <span class="number">1</span>]);</span><br><span class="line"> <span class="keyword">return</span> dp[n][m];</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="编辑距离"><a href="#编辑距离" class="headerlink" title="编辑距离"></a>编辑距离</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">void</span> <span class="title">solve</span><span class="params">(string &s1, string &s2)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> n = s1.<span class="built_in">size</span>(), m = s2.<span class="built_in">size</span>();</span><br><span class="line"> vector<vector<<span class="type">int</span>>> <span class="built_in">f</span>(n + <span class="number">1</span>, <span class="built_in">vector</span><<span class="type">int</span>>(m + <span class="number">1</span>, <span class="number">0</span>));</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i <= n; ++i)</span><br><span class="line"> f[i][<span class="number">0</span>] = i;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i <= m; ++i)</span><br><span class="line"> f[<span class="number">0</span>][i] = i;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i <= n; ++i)</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = <span class="number">1</span>; j <= m; ++j)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (s1[i - <span class="number">1</span>] == s2[j - <span class="number">1</span>])</span><br><span class="line"> f[i][j] = <span class="built_in">min</span>(f[i - <span class="number">1</span>][j - <span class="number">1</span>], <span class="built_in">min</span>(f[i - <span class="number">1</span>][j] + <span class="number">1</span>, f[i][j - <span class="number">1</span>] + <span class="number">1</span>));</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> f[i][j] = <span class="number">1</span> + <span class="built_in">min</span>(f[i - <span class="number">1</span>][j - <span class="number">1</span>], <span class="built_in">min</span>(f[i - <span class="number">1</span>][j], f[i][j - <span class="number">1</span>]));</span><br><span class="line"> }</span><br><span class="line"> cout << f[n][m] << <span class="string">"\n"</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="背包问题"><a href="#背包问题" class="headerlink" title="背包问题"></a>背包问题</h2><h3 id="0-1背包"><a href="#0-1背包" class="headerlink" title="0-1背包"></a>0-1背包</h3><p><strong>每种物品至多只能选择1件。</strong><code>dp[i][j]</code>表示前 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="0.781ex" height="1.52ex" role="img" focusable="false" viewBox="0 -661 345 672"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D456" d="M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z"></path></g></g></g></svg></mjx-container> 个物品装进容量为 <mjx-container class="MathJax" jax="SVG"><svg style="vertical-align: -0.462ex;" xmlns="http://www.w3.org/2000/svg" width="0.932ex" height="1.957ex" role="img" focusable="false" viewBox="0 -661 412 865"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D457" d="M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z"></path></g></g></g></svg></mjx-container> 的背包能获得的最大价值。<code>dp[i][j]</code>的转移仅与<code>dp[i-1][j]</code>和<code>dp[i-1][j-w[i]]</code>有关，可简化为<code>dp[j]</code>。</p>
<div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">1000</span>;</span><br><span class="line"><span class="type">int</span> n, m; <span class="comment">// 物品个数，背包容量</span></span><br><span class="line"><span class="type">int</span> dp[MAXN];</span><br><span class="line"><span class="type">int</span> v[MAXN], w[MAXN]; <span class="comment">// 价值，重量</span></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">solve</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i <= m; ++i)</span><br><span class="line"> dp[i] = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < n; ++i)</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = m; j >= w[i]; --j)</span><br><span class="line"> dp[j] = <span class="built_in">max</span>(dp[j], dp[j - w[i]] + v[i]);</span><br><span class="line"> <span class="keyword">return</span> dp[m];</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h3 id="完全背包"><a href="#完全背包" class="headerlink" title="完全背包"></a>完全背包</h3><p><strong>每个物品可以选择多件。</strong> 与0-1背包相比，仅更新dp数组时遍历顺序发生改变。</p>
<div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">1000</span>;</span><br><span class="line"><span class="type">int</span> n, m; <span class="comment">// 物品个数，背包容量</span></span><br><span class="line"><span class="type">int</span> dp[MAXN];</span><br><span class="line"><span class="type">int</span> v[MAXN], w[MAXN]; <span class="comment">// 价值，重量</span></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">solve</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i <= m; ++i)</span><br><span class="line"> dp[i] = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < n; ++i)</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = w[i]; j <= m; ++j)</span><br><span class="line"> dp[j] = <span class="built_in">max</span>(dp[j], dp[j - w[i]] + v[i]);</span><br><span class="line"> <span class="keyword">return</span> dp[m];</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h3 id="多重背包"><a href="#多重背包" class="headerlink" title="多重背包"></a>多重背包</h3><p><strong>每种物品最多选k件。</strong> 转化为0-1背包问题求解。</p>
<div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">1000</span>;</span><br><span class="line"><span class="type">int</span> dp[MAXN];</span><br><span class="line"><span class="type">int</span> v[MAXN], w[MAXN], k[MAXN];</span><br><span class="line"><span class="type">int</span> value[MAXN], weight[MAXN]; <span class="comment">// 分解后的价值，质量</span></span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">solve</span><span class="params">(<span class="type">int</span> n, <span class="type">int</span> m)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> num = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < n; ++i)</span><br><span class="line"> {</span><br><span class="line"> cin >> v[i] >> w[i] >> k[i];</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = <span class="number">1</span>; j <= k[i]; j <<= <span class="number">1</span>)</span><br><span class="line"> {</span><br><span class="line"> value[num] = v[i] * j;</span><br><span class="line"> weight[num] = w[i] * j;</span><br><span class="line"> num++;</span><br><span class="line"> k[i] -= j;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> (k[i] > <span class="number">0</span>)</span><br><span class="line"> {</span><br><span class="line"> value[num] = v[i] * k[i];</span><br><span class="line"> weight[num] = w[i] * k[i];</span><br><span class="line"> num++;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"></span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i <= m; ++i)</span><br><span class="line"> dp[i] = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < num; ++i)</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = m; j >= weight[i]; --j)</span><br><span class="line"> dp[j] = <span class="built_in">max</span>(dp[j], dp[j - weight[i]] + value[i]);</span><br><span class="line"> <span class="keyword">return</span> dp[m];</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
]]></content>
<tags>
<tag>机试</tag>
<tag>动态规划</tag>
</tags>
</entry>
<entry>
<title>机试第2章</title>
<url>/2023/03/06/%E6%9C%BA%E8%AF%95%E7%AC%AC2%E7%AB%A0/</url>
<content><![CDATA[<h2 id="反序数"><a href="#反序数" class="headerlink" title="反序数"></a>反序数</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">int</span> <span class="title">reverse</span><span class="params">(<span class="type">int</span> x)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> res = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">while</span> (x)</span><br><span class="line"> {</span><br><span class="line"> res *= <span class="number">10</span>;</span><br><span class="line"> res += x % <span class="number">10</span>;</span><br><span class="line"> x /= <span class="number">10</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="闰年判断"><a href="#闰年判断" class="headerlink" title="闰年判断"></a>闰年判断</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">int</span> d1[<span class="number">13</span>] = {<span class="number">0</span>, <span class="number">31</span>, <span class="number">28</span>, <span class="number">31</span>, <span class="number">30</span>, <span class="number">31</span>, <span class="number">30</span>, <span class="number">31</span>, <span class="number">31</span>, <span class="number">30</span>, <span class="number">31</span>, <span class="number">30</span>, <span class="number">31</span>};</span><br><span class="line"><span class="type">int</span> d2[<span class="number">13</span>] = {<span class="number">0</span>, <span class="number">31</span>, <span class="number">29</span>, <span class="number">31</span>, <span class="number">30</span>, <span class="number">31</span>, <span class="number">30</span>, <span class="number">31</span>, <span class="number">31</span>, <span class="number">30</span>, <span class="number">31</span>, <span class="number">30</span>, <span class="number">31</span>};</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">bool</span> <span class="title">isLeapYear</span><span class="params">(<span class="type">int</span> n)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">return</span> (n % <span class="number">4</span> == <span class="number">0</span> && n % <span class="number">100</span> != <span class="number">0</span>) || (n % <span class="number">400</span> == <span class="number">0</span>);</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="日期格式化输出yyyy-mm-dd"><a href="#日期格式化输出yyyy-mm-dd" class="headerlink" title="日期格式化输出yyyy-mm-dd"></a>日期格式化输出yyyy-mm-dd</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="built_in">printf</span>(<span class="string">"%04d-%02d-%02d"</span>, y, m, d);</span><br></pre></td></tr></table></figure></div>
<h1 id=""><a href="#" class="headerlink" title=""></a></h1>]]></content>
<tags>
<tag>机试</tag>
<tag>暴力</tag>
</tags>
</entry>
<entry>
<title>机试第5章</title>
<url>/2023/03/07/%E6%9C%BA%E8%AF%95%E7%AC%AC5%E7%AB%A0/</url>
<content><![CDATA[<h2 id="约瑟夫问题变体（队列解法）"><a href="#约瑟夫问题变体（队列解法）" class="headerlink" title="约瑟夫问题变体（队列解法）"></a>约瑟夫问题变体（队列解法）</h2><p>用队列模拟循环队列</p>
<div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">int</span> n, p, m;</span><br><span class="line">cin >> n >> p >> m;</span><br><span class="line">queue<<span class="type">int</span>> q;</span><br><span class="line"><span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i <= n; ++i)</span><br><span class="line"> q.<span class="built_in">push</span>(i);</span><br><span class="line"><span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i < p; ++i) <span class="comment">// 让p号位于队首</span></span><br><span class="line">{</span><br><span class="line"> q.<span class="built_in">push</span>(q.<span class="built_in">front</span>());</span><br><span class="line"> q.<span class="built_in">pop</span>();</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="keyword">while</span> (!q.<span class="built_in">empty</span>())</span><br><span class="line">{</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i < m; ++i)</span><br><span class="line"> {</span><br><span class="line"> q.<span class="built_in">push</span>(q.<span class="built_in">front</span>());</span><br><span class="line"> q.<span class="built_in">pop</span>();</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> (q.<span class="built_in">size</span>() == <span class="number">1</span>)</span><br><span class="line"> cout << q.<span class="built_in">front</span>() << <span class="string">"\n"</span>;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> cout << q.<span class="built_in">front</span>() << <span class="string">" "</span>;</span><br><span class="line"> q.<span class="built_in">pop</span>();</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="括号匹配（栈）"><a href="#括号匹配（栈）" class="headerlink" title="括号匹配（栈）"></a>括号匹配（栈）</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">bool</span> <span class="title">judge</span><span class="params">(string str)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> stack<<span class="type">char</span>> stk;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < str.<span class="built_in">size</span>(); ++i)</span><br><span class="line"> <span class="keyword">if</span> (str[i] == <span class="string">'('</span>)</span><br><span class="line"> stk.<span class="built_in">push</span>(<span class="string">'('</span>);</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (str[i] == <span class="string">')'</span>)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (!stk.<span class="built_in">empty</span>())</span><br><span class="line"> stk.<span class="built_in">pop</span>();</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> stk.<span class="built_in">empty</span>();</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="简易计算器（栈）"><a href="#简易计算器（栈）" class="headerlink" title="简易计算器（栈）"></a>简易计算器（栈）</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line">unordered_map<<span class="type">char</span>, <span class="type">int</span>> pri;</span><br><span class="line">pri[<span class="string">'#'</span>] = <span class="number">0</span>;</span><br><span class="line">pri[<span class="string">'$'</span>] = <span class="number">1</span>;</span><br><span class="line">pri[<span class="string">'+'</span>] = pri[<span class="string">'-'</span>] = <span class="number">2</span>;</span><br><span class="line">pri[<span class="string">'*'</span>] = pri[<span class="string">'/'</span>] = <span class="number">3</span>;</span><br><span class="line"></span><br><span class="line">stack<<span class="type">char</span>> op;</span><br><span class="line">stack<<span class="type">int</span>> num;</span><br><span class="line">string str;</span><br><span class="line">str += <span class="string">'$'</span>;</span><br><span class="line">op.<span class="built_in">push</span>(<span class="string">'#'</span>);</span><br><span class="line"><span class="type">int</span> idx = <span class="number">0</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">while</span> (idx < str.<span class="built_in">size</span>())</span><br><span class="line">{</span><br><span class="line"> <span class="keyword">if</span> (str[idx] == <span class="string">' '</span>)</span><br><span class="line"> idx++;</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (<span class="built_in">isdigit</span>(str[idx]))</span><br><span class="line"> num.<span class="built_in">push</span>(<span class="built_in">getnum</span>(str, idx));</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (pri[op.<span class="built_in">top</span>()]) < pri[str[idx]])</span><br><span class="line"> {</span><br><span class="line"> op.<span class="built_in">push</span>(str[idx]);</span><br><span class="line"> idx++;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> {</span><br><span class="line"> <span class="type">double</span> y = num.<span class="built_in">top</span>();</span><br><span class="line"> num.<span class="built_in">pop</span>();</span><br><span class="line"> <span class="type">double</span> x = num.<span class="built_in">top</span>();</span><br><span class="line"> num.<span class="built_in">pop</span>();</span><br><span class="line"> num.<span class="built_in">push</span>(<span class="built_in">cal</span>(x, y, op.<span class="built_in">top</span>()));</span><br><span class="line"> op.<span class="built_in">pop</span>();</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
]]></content>
<tags>
<tag>机试</tag>
<tag>数据结构</tag>
</tags>
</entry>
<entry>
<title>机试第3章</title>
<url>/2023/03/07/%E6%9C%BA%E8%AF%95%E7%AC%AC3%E7%AB%A0/</url>
<content><![CDATA[<h2 id="快速排序-quicksort"><a href="#快速排序-quicksort" class="headerlink" title="快速排序(quicksort)"></a>快速排序(quicksort)</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">void</span> <span class="title">quicksort</span><span class="params">(<span class="type">int</span> *a, <span class="type">int</span> l, <span class="type">int</span> r)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> mid = a[(l + r) / <span class="number">2</span>];</span><br><span class="line"> <span class="type">int</span> i = l, j = r;</span><br><span class="line"> <span class="keyword">while</span> (i <= j)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">while</span> (a[i] < mid)</span><br><span class="line"> i++;</span><br><span class="line"> <span class="keyword">while</span> (a[j] > mid)</span><br><span class="line"> j--;</span><br><span class="line"> <span class="keyword">if</span> (i <= j)</span><br><span class="line"> {</span><br><span class="line"> <span class="built_in">swap</span>(a[i], a[j]);</span><br><span class="line"> i++, j--;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> (i < r)</span><br><span class="line"> <span class="built_in">quicksort</span>(a, i, r);</span><br><span class="line"> <span class="keyword">if</span> (l < j)</span><br><span class="line"> <span class="built_in">quicksort</span>(a, l, j);</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="结构体排序"><a href="#结构体排序" class="headerlink" title="结构体排序"></a>结构体排序</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="keyword">struct</span> <span class="title class_">student</span></span><br><span class="line">{</span><br><span class="line"> <span class="type">int</span> x, y;</span><br><span class="line">};</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">bool</span> <span class="title">cmp</span><span class="params">(<span class="type">const</span> student &a, <span class="type">const</span> student &b)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (a.x == b.x)</span><br><span class="line"> <span class="keyword">return</span> a.y < b.y;</span><br><span class="line"> <span class="keyword">return</span> a.x < b.x;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="二分查找"><a href="#二分查找" class="headerlink" title="二分查找"></a>二分查找</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">bool</span> <span class="title">search</span><span class="params">(<span class="type">int</span> *a, <span class="type">int</span> n, <span class="type">int</span> target)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> l = <span class="number">0</span>, r = n - <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">while</span> (l <= r)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> mid = l + (r - l) / <span class="number">2</span>;</span><br><span class="line"> <span class="keyword">if</span> (a[mid] < target)</span><br><span class="line"> l = mid + <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (a[mid] > target)</span><br><span class="line"> r = mid - <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="built_in">lower_bound</span>(begin, end, val); <span class="comment">// 返回大于等于val的地址</span></span><br><span class="line"><span class="built_in">upper_bound</span>(begin, end, val); <span class="comment">// 返回大于val的地址</span></span><br></pre></td></tr></table></figure></div>
]]></content>
<tags>
<tag>机试</tag>
<tag>排序和查找</tag>
</tags>
</entry>
<entry>
<title>机试第4章</title>
<url>/2023/03/07/%E6%9C%BA%E8%AF%95%E7%AC%AC4%E7%AB%A0/</url>
<content><![CDATA[<h2 id="string常用操作"><a href="#string常用操作" class="headerlink" title="string常用操作"></a>string常用操作</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line">s.<span class="built_in">insert</span>(idx, str);</span><br><span class="line">s.<span class="built_in">erase</span>(begin, end); <span class="comment">// 删除[begin, end)</span></span><br><span class="line">s.<span class="built_in">clear</span>();</span><br><span class="line">s.<span class="built_in">substr</span>(idx, len); <span class="comment">// 起始位置，长度</span></span><br><span class="line"></span><br><span class="line"><span class="keyword">if</span> (s.<span class="built_in">find</span>(str) != string::npos)</span><br></pre></td></tr></table></figure></div>
<h2 id="浮点数加法（类似大数加法）"><a href="#浮点数加法（类似大数加法）" class="headerlink" title="浮点数加法（类似大数加法）"></a>浮点数加法（类似大数加法）</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function">string <span class="title">add</span><span class="params">(string s1, string s2)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> string int1 = s1.<span class="built_in">substr</span>(<span class="number">0</span>, s1.<span class="built_in">find</span>(<span class="string">'.'</span>)), int2 = s2.<span class="built_in">substr</span>(<span class="number">0</span>, s2.<span class="built_in">find</span>(<span class="string">'.'</span>));</span><br><span class="line"> string frac1 = s1.<span class="built_in">substr</span>(s1.<span class="built_in">find</span>(<span class="string">'.'</span>) + <span class="number">1</span>), frac2 = s2.<span class="built_in">substr</span>(s2.<span class="built_in">find</span>(<span class="string">'.'</span>) + <span class="number">1</span>);</span><br><span class="line"></span><br><span class="line"> <span class="keyword">if</span> (int1.<span class="built_in">size</span>() < int2.<span class="built_in">size</span>())</span><br><span class="line"> int1 = <span class="built_in">string</span>(int2.<span class="built_in">size</span>() - int1.<span class="built_in">size</span>(), <span class="string">'0'</span>) + int1;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> int2 = <span class="built_in">string</span>(int1.<span class="built_in">size</span>() - int2.<span class="built_in">size</span>(), <span class="string">'0'</span>) + int2;</span><br><span class="line"> <span class="keyword">if</span> (frac1.<span class="built_in">size</span>() < frac2.<span class="built_in">size</span>())</span><br><span class="line"> frac1 = frac1 + <span class="built_in">string</span>(frac2.<span class="built_in">size</span>() - frac1.<span class="built_in">size</span>(), <span class="string">' '</span>);</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> frac2 = frac2 + <span class="built_in">string</span>(frac1.<span class="built_in">size</span>() - frac2.<span class="built_in">size</span>(), <span class="string">' '</span>);</span><br><span class="line"></span><br><span class="line"> <span class="type">int</span> carry = <span class="number">0</span>;</span><br><span class="line"> string fraction = <span class="built_in">string</span>(frac1.<span class="built_in">size</span>(), <span class="string">' '</span>);</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = fraction.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; --i)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> cur = frac1[i] - <span class="string">'0'</span> + frac2[i] - <span class="string">'0'</span> + carry;</span><br><span class="line"> carry = cur / <span class="number">10</span>;</span><br><span class="line"> fraction[i] = cur % <span class="number">10</span> + <span class="string">'0'</span>;</span><br><span class="line"> }</span><br><span class="line"> string integer = <span class="built_in">string</span>(int1.<span class="built_in">size</span>(), <span class="string">' '</span>);</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = integer.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; --i)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> cur = int1[i] - <span class="string">'0'</span> + int2[i] - <span class="string">'0'</span> + carry;</span><br><span class="line"> carry = cur / <span class="number">10</span>;</span><br><span class="line"> integer[i] = cur % <span class="number">10</span> + <span class="string">'0'</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> (carry == <span class="number">1</span>)</span><br><span class="line"> <span class="keyword">return</span> <span class="string">'1'</span> + integer + <span class="string">'.'</span> + fraction;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> <span class="keyword">return</span> integer + <span class="string">'.'</span> + fraction;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="kmp算法"><a href="#kmp算法" class="headerlink" title="kmp算法"></a>kmp算法</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">1e6</span> + <span class="number">5</span>;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> MAXM = <span class="number">1e3</span> + <span class="number">5</span>;</span><br><span class="line"><span class="type">char</span> s[MAXN], t[MAXM];</span><br><span class="line"><span class="type">int</span> nxt[MAXM];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">getnxt</span><span class="params">(<span class="type">int</span> m)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> nxt[<span class="number">0</span>] = <span class="number">-1</span>;</span><br><span class="line"> <span class="type">int</span> i = <span class="number">0</span>, j = <span class="number">-1</span>;</span><br><span class="line"> <span class="keyword">while</span> (i < m)</span><br><span class="line"> <span class="keyword">if</span> (j == <span class="number">-1</span> || t[i] == t[j])</span><br><span class="line"> nxt[++i] = ++j;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> j = nxt[j];</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">kmp</span><span class="params">(<span class="type">int</span> n, <span class="type">int</span> m)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="built_in">getnxt</span>(m);</span><br><span class="line"> <span class="type">int</span> i = <span class="number">0</span>, j = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">while</span> (i < n)</span><br><span class="line"> <span class="keyword">if</span> (j == <span class="number">-1</span> || s[i] == t[j])</span><br><span class="line"> {</span><br><span class="line"> i++, j++;</span><br><span class="line"> <span class="keyword">if</span> (j == m)</span><br><span class="line"> <span class="keyword">return</span> i - m + <span class="number">1</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> j = nxt[j];</span><br><span class="line"> <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
]]></content>
<tags>
<tag>机试</tag>
<tag>字符串</tag>
</tags>
</entry>
<entry>
<title>机试第6章</title>
<url>/2023/03/07/%E6%9C%BA%E8%AF%95%E7%AC%AC6%E7%AB%A0/</url>
<content><![CDATA[<h2 id="大整数加法"><a href="#大整数加法" class="headerlink" title="大整数加法"></a>大整数加法</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function">string <span class="title">add</span><span class="params">(string a, string b)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (a.<span class="built_in">size</span>() > b.<span class="built_in">size</span>())</span><br><span class="line"> a = <span class="built_in">string</span>(a.<span class="built_in">size</span>() - b.<span class="built_in">size</span>(), <span class="string">'0'</span>) + a;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> b = <span class="built_in">string</span>(b.<span class="built_in">size</span>() - a.<span class="built_in">size</span>(), <span class="string">'0'</span>) + b;</span><br><span class="line"> <span class="type">int</span> carry = <span class="number">0</span>;</span><br><span class="line"> <span class="function">string <span class="title">res</span><span class="params">(a.size(), <span class="string">' '</span>)</span></span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = res.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; --i)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> cur = a[i] - <span class="string">'0'</span> + b[i] - <span class="string">'0'</span> + carry;</span><br><span class="line"> res[i] = cur % <span class="number">10</span> + <span class="string">'0'</span>;</span><br><span class="line"> carry = cur / <span class="number">10</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> (carry)</span><br><span class="line"> <span class="keyword">return</span> <span class="string">'1'</span> + res;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="大整数乘法"><a href="#大整数乘法" class="headerlink" title="大整数乘法"></a>大整数乘法</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function">string <span class="title">mul</span><span class="params">(string str, <span class="type">int</span> x)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="function">string <span class="title">res</span><span class="params">(str.size(), <span class="string">' '</span>)</span></span>;</span><br><span class="line"> <span class="type">int</span> carry = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = res.<span class="built_in">size</span>() - <span class="number">1</span>; i >= <span class="number">0</span>; --i)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> cur = (str[i] - <span class="string">'0'</span>) * x + carry;</span><br><span class="line"> str[i] = cur / <span class="number">10</span> + <span class="string">'0'</span>;</span><br><span class="line"> carry = cur % <span class="number">10</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> (carry)</span><br><span class="line"> <span class="keyword">return</span> <span class="built_in">to_string</span>(carry) + res;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="function">string <span class="title">mul</span><span class="params">(string a, string b)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> string res = <span class="string">"0"</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < b.<span class="built_in">size</span>(); ++i)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> x = b[b.<span class="built_in">size</span>() - <span class="number">1</span> - i] - <span class="string">'0'</span>;</span><br><span class="line"> string cur = <span class="built_in">mul</span>(a, x);</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = <span class="number">0</span>; j < i; ++i)</span><br><span class="line"> cur = <span class="built_in">mul</span>(cur, <span class="number">10</span>);</span><br><span class="line"> res = <span class="built_in">add</span>(res, cur);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="大整数除法"><a href="#大整数除法" class="headerlink" title="大整数除法"></a>大整数除法</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function">string <span class="title">divide</span><span class="params">(string str, <span class="type">int</span> x)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> remainder = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < str.<span class="built_in">size</span>(); ++i)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> cur = remainder * <span class="number">10</span> + str[i] - <span class="string">'0'</span>;</span><br><span class="line"> str[i] = cur / x + <span class="string">'0'</span>;</span><br><span class="line"> remainder = cur % x;</span><br><span class="line"> }</span><br><span class="line"> <span class="type">int</span> pos = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">while</span> (str[pos] == <span class="string">'0'</span>)</span><br><span class="line"> pos++;</span><br><span class="line"> <span class="keyword">return</span> str.<span class="built_in">substr</span>(pos);</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="最大公约数"><a href="#最大公约数" class="headerlink" title="最大公约数"></a>最大公约数</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">int</span> <span class="title">gcd</span><span class="params">(<span class="type">int</span> a, <span class="type">int</span> b)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">return</span> b == <span class="number">0</span> ? a : <span class="built_in">gcd</span>(b, a % b);</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="最小公倍数"><a href="#最小公倍数" class="headerlink" title="最小公倍数"></a>最小公倍数</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">int</span> <span class="title">lcm</span><span class="params">(<span class="type">int</span> a, <span class="type">int</span> b)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">return</span> a * b / <span class="built_in">gcd</span>(a, b);</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="线性筛"><a href="#线性筛" class="headerlink" title="线性筛"></a>线性筛</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">1e4</span> + <span class="number">5</span>;</span><br><span class="line">vector<<span class="type">int</span>> pri;</span><br><span class="line"><span class="type">int</span> vis[MAXN];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">init</span><span class="params">(<span class="type">int</span> n)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">2</span>; i <= n; ++i)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (!vis[i])</span><br><span class="line"> pri.<span class="built_in">push_back</span>(i);</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = <span class="number">0</span>; j < pri.<span class="built_in">size</span>(); ++j)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (<span class="number">1ll</span> * i * pri[j] > n)</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> vis[i * pri[j]] = <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">if</span> (i % pri[j] == <span class="number">0</span>)</span><br><span class="line"> <span class="keyword">break</span>;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="分解质因数"><a href="#分解质因数" class="headerlink" title="分解质因数"></a>分解质因数</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line">vector<<span class="type">int</span>> factor;</span><br><span class="line"></span><br><span class="line"><span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < pri.<span class="built_in">size</span>() && pri[i] < n; ++i)</span><br><span class="line"> <span class="keyword">while</span> (n % pri[i] == <span class="number">0</span>)</span><br><span class="line"> factor.<span class="built_in">push_back</span>(pri[i]);</span><br><span class="line"><span class="keyword">if</span> (n > <span class="number">1</span>)</span><br><span class="line"> factor.<span class="built_in">push_back</span>(n);</span><br></pre></td></tr></table></figure></div>
<h2 id="快速幂"><a href="#快速幂" class="headerlink" title="快速幂"></a>快速幂</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MOD = <span class="number">114514</span>;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">fpow</span><span class="params">(<span class="type">int</span> a, <span class="type">int</span> b)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> res = <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">while</span> (b)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (b & <span class="number">1</span>)</span><br><span class="line"> res = res * a % MOD;</span><br><span class="line"> b >>= <span class="number">1</span>;</span><br><span class="line"> a = a * a % MOD;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">} </span><br></pre></td></tr></table></figure></div>
<h2 id="矩阵快速幂"><a href="#矩阵快速幂" class="headerlink" title="矩阵快速幂"></a>矩阵快速幂</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function">matrix <span class="title">fpow</span><span class="params">(matrix x, <span class="type">int</span> k)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="function">mat <span class="title">res</span><span class="params">(x.row, x.col)</span></span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < res.row; ++i)</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = <span class="number">0</span>; j < res.col; ++j)</span><br><span class="line"> <span class="keyword">if</span> (i == j)</span><br><span class="line"> res.mat[i][j] = <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> res.mat[i][j] = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">while</span> (k)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (k & <span class="number">1</span>)</span><br><span class="line"> res = <span class="built_in">mul</span>(res, k);</span><br><span class="line"> k >>= <span class="number">1</span>;</span><br><span class="line"> x = <span class="built_in">mul</span>(x, x);</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="判断大整数是否可被整除"><a href="#判断大整数是否可被整除" class="headerlink" title="判断大整数是否可被整除"></a>判断大整数是否可被整除</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">bool</span> <span class="title">isDividable</span><span class="params">(string str, <span class="type">int</span> k)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="type">int</span> total = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < str.<span class="built_in">size</span>(); ++i)</span><br><span class="line"> {</span><br><span class="line"> total *= <span class="number">10</span>;</span><br><span class="line"> total += str[i] - <span class="string">'0'</span>;</span><br><span class="line"> total %= k;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> total == <span class="number">0</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
]]></content>
<tags>
<tag>机试</tag>
<tag>数学</tag>
</tags>
</entry>
<entry>
<title>机试第8章</title>
<url>/2023/03/08/%E6%9C%BA%E8%AF%95%E7%AC%AC8%E7%AB%A0/</url>
<content><![CDATA[<h2 id="汉诺塔变种（递归）"><a href="#汉诺塔变种（递归）" class="headerlink" title="汉诺塔变种（递归）"></a>汉诺塔变种（递归）</h2><p>每次只允许将圆盘移到中间杆上或从中间杆上移出，不允许直接将圆盘从第一根杆上移到第二根杆上，或直接将圆盘从第三根杆上移到第一根杆上。</p>
<div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">long</span> <span class="type">long</span> <span class="title">solve</span><span class="params">(<span class="type">int</span> n)</span> <span class="comment">// f[1] = 2, f[i] = 3 * f[i - 1] + 2</span></span></span><br><span class="line"><span class="function"> <span class="title">if</span> <span class="params">(n == <span class="number">1</span>)</span></span></span><br><span class="line"><span class="function"> <span class="keyword">return</span> 2</span>;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> <span class="keyword">return</span> <span class="number">3</span> * <span class="built_in">solve</span>(n - <span class="number">1</span>) + <span class="number">2</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="杨辉三角（递归）"><a href="#杨辉三角（递归）" class="headerlink" title="杨辉三角（递归）"></a>杨辉三角（递归）</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">int</span> <span class="title">solve</span><span class="params">(<span class="type">int</span> r, <span class="type">int</span> c)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (r == <span class="number">1</span> || c == <span class="number">1</span> || r == c)</span><br><span class="line"> <span class="keyword">return</span> <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">return</span> <span class="built_in">solve</span>(r - <span class="number">1</span>, c - <span class="number">1</span>) + <span class="built_in">solve</span>(r - <span class="number">1</span>, c);</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="全排列"><a href="#全排列" class="headerlink" title="全排列"></a>全排列</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">10</span>;</span><br><span class="line"><span class="type">char</span> s[MAXN];</span><br><span class="line"><span class="type">int</span> vis[MAXN];</span><br><span class="line"><span class="type">char</span> res[MAXN];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">solve</span><span class="params">(<span class="type">char</span> *s, <span class="type">int</span> cnt)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (cnt == <span class="built_in">strlen</span>(s))</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < <span class="built_in">strlen</span>(res); ++i)</span><br><span class="line"> cout << res[i] << <span class="string">' '</span>;</span><br><span class="line"> cout << <span class="string">"\n"</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < <span class="built_in">strlen</span>(s); ++i)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (!vis[i])</span><br><span class="line"> {</span><br><span class="line"> vis[i] = <span class="number">1</span>;</span><br><span class="line"> res[cnt] = s[i];</span><br><span class="line"> <span class="built_in">solve</span>(s, cnt + <span class="number">1</span>);</span><br><span class="line"> vis[i] = <span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="计算二叉树子树节点个数"><a href="#计算二叉树子树节点个数" class="headerlink" title="计算二叉树子树节点个数"></a>计算二叉树子树节点个数</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">int</span> <span class="title">solve</span><span class="params">(<span class="type">int</span> n, <span class="type">int</span> m)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (m > n)</span><br><span class="line"> <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line"> <span class="type">int</span> res = <span class="number">1</span>;</span><br><span class="line"> res += <span class="built_in">solve</span>(n, <span class="number">2</span> * m);</span><br><span class="line"> res += <span class="built_in">solve</span>(n, <span class="number">2</span> * m + <span class="number">1</span>);</span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="分解2的幂次方"><a href="#分解2的幂次方" class="headerlink" title="分解2的幂次方"></a>分解2的幂次方</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function">string <span class="title">solve</span><span class="params">(<span class="type">int</span> n)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> stack<<span class="type">int</span>> p;</span><br><span class="line"> <span class="type">int</span> exp = <span class="number">0</span>;</span><br><span class="line"> <span class="keyword">while</span> (n)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (n % <span class="number">2</span>)</span><br><span class="line"> p.<span class="built_in">push</span>(exp);</span><br><span class="line"> exp++;</span><br><span class="line"> n /= <span class="number">2</span>;</span><br><span class="line"> }</span><br><span class="line"> string res = <span class="string">""</span>;</span><br><span class="line"> <span class="keyword">while</span> (!p.<span class="built_in">empty</span>())</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (p.<span class="built_in">top</span>() == <span class="number">0</span>)</span><br><span class="line"> res += <span class="string">"2(0)"</span>;</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (p.<span class="built_in">top</span>() == <span class="number">1</span>)</span><br><span class="line"> res += <span class="string">"2"</span>;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> res += <span class="string">"2("</span> + <span class="built_in">solve</span>(p.<span class="built_in">top</span>()) + <span class="string">")"</span>;</span><br><span class="line"> p.<span class="built_in">pop</span>();</span><br><span class="line"> <span class="keyword">if</span> (!p.<span class="built_in">empty</span>())</span><br><span class="line"> res += <span class="string">"+"</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> res;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
]]></content>
<tags>
<tag>机试</tag>
<tag>递归和分治</tag>
</tags>
</entry>
<entry>
<title>机试第7章</title>
<url>/2023/03/08/%E6%9C%BA%E8%AF%95%E7%AC%AC7%E7%AB%A0/</url>
<content><![CDATA[<h2 id="活动安排（区间贪心）"><a href="#活动安排（区间贪心）" class="headerlink" title="活动安排（区间贪心）"></a>活动安排（区间贪心）</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="function"><span class="type">bool</span> <span class="title">cmp</span><span class="params">(activity x, activity y)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">return</span> x.e < y.e; <span class="comment">// 按结束时间排序</span></span><br><span class="line">}</span><br><span class="line"></span><br><span class="line"><span class="built_in">sort</span>(arr, arr + n, cmp);</span><br><span class="line"><span class="type">int</span> cur = <span class="number">0</span>, res = <span class="number">0</span>;</span><br><span class="line"><span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < n; ++i)</span><br><span class="line"> <span class="keyword">if</span> (cur <= arr[i].s)</span><br><span class="line"> {</span><br><span class="line"> cur = arr[i].e;</span><br><span class="line"> res++;</span><br><span class="line"> }</span><br></pre></td></tr></table></figure></div>
]]></content>
<tags>
<tag>机试</tag>
<tag>贪心</tag>
</tags>
</entry>
<entry>
<title>机试第9章</title>
<url>/2023/03/08/%E6%9C%BA%E8%AF%95%E7%AC%AC9%E7%AB%A0/</url>
<content><![CDATA[<h2 id="Catch-That-Cow-BFS"><a href="#Catch-That-Cow-BFS" class="headerlink" title="Catch That Cow(BFS)"></a>Catch That Cow(BFS)</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">1e5</span>;</span><br><span class="line"><span class="type">int</span> step[MAXN], vis[MAXN];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">bfs</span><span class="params">(<span class="type">int</span> n, <span class="type">int</span> k)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> queue<<span class="type">int</span>> q;</span><br><span class="line"> q.<span class="built_in">push</span>(n);</span><br><span class="line"> step[n] = <span class="number">0</span>;</span><br><span class="line"> vis[n] = <span class="number">1</span>;</span><br><span class="line"> <span class="type">int</span> cur, nxt;</span><br><span class="line"> <span class="keyword">while</span> (!q.<span class="built_in">empty</span>())</span><br><span class="line"> {</span><br><span class="line"> cur = q.<span class="built_in">front</span>();</span><br><span class="line"> q.<span class="built_in">pop</span>();</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < <span class="number">3</span>; ++i)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">if</span> (i == <span class="number">0</span>)</span><br><span class="line"> nxt = cur + <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">else</span> <span class="keyword">if</span> (i == <span class="number">1</span>)</span><br><span class="line"> nxt = cur - <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">else</span></span><br><span class="line"> nxt = <span class="number">2</span> * cur;</span><br><span class="line"> <span class="keyword">if</span> (nxt < <span class="number">0</span> || nxt >= MAXN)</span><br><span class="line"> <span class="keyword">continue</span>;</span><br><span class="line"> <span class="keyword">if</span> (!vis[nxt])</span><br><span class="line"> {</span><br><span class="line"> q.<span class="built_in">push</span>(nxt);</span><br><span class="line"> vis[nxt] = <span class="number">1</span>;</span><br><span class="line"> step[nxt] = step[cur] + <span class="number">1</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">if</span> (nxt == k)</span><br><span class="line"> <span class="keyword">return</span> step[nxt];</span><br><span class="line"> }</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="number">-1</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="A-Knight’s-Journey-DFS"><a href="#A-Knight’s-Journey-DFS" class="headerlink" title="A Knight’s Journey(DFS)"></a>A Knight’s Journey(DFS)</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">const</span> <span class="type">int</span> MAXN = <span class="number">30</span>;</span><br><span class="line"><span class="type">int</span> p, q; <span class="comment">// 棋盘参数</span></span><br><span class="line"><span class="type">bool</span> vis[MAXN][MAXN];</span><br><span class="line"><span class="type">int</span> dir[<span class="number">8</span>][<span class="number">2</span>] = {{<span class="number">-1</span>, <span class="number">-2</span>}, {<span class="number">1</span>, <span class="number">-2</span>}, {<span class="number">-2</span>, <span class="number">-1</span>}, {<span class="number">2</span>, <span class="number">-1</span>}, {<span class="number">-2</span>, <span class="number">1</span>}, {<span class="number">2</span>, <span class="number">1</span>}, {<span class="number">-1</span>, <span class="number">2</span>}, {<span class="number">1</span>, <span class="number">2</span>}};</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">bool</span> <span class="title">dfs</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> y, <span class="type">int</span> step, string res)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (step == p * q)</span><br><span class="line"> {</span><br><span class="line"> cout << res << <span class="string">"\n"</span>;</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < <span class="number">8</span>; ++i)</span><br><span class="line"> {</span><br><span class="line"> <span class="type">int</span> nx = x + dir[i][<span class="number">0</span>], ny = y + dir[i][<span class="number">1</span>];</span><br><span class="line"> <span class="keyword">if</span> (nx < <span class="number">0</span> || nx >= p || ny < <span class="number">0</span> || ny >= q || vis[nx][ny])</span><br><span class="line"> <span class="keyword">continue</span>;</span><br><span class="line"> <span class="type">char</span> r = nx + <span class="string">'1'</span>, c = ny + <span class="string">'A'</span>;</span><br><span class="line"> vis[nx][ny] = <span class="number">1</span>;</span><br><span class="line"> <span class="keyword">if</span> (<span class="built_in">dfs</span>(nx, ny, step + <span class="number">1</span>, res + c + r))</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">true</span>;</span><br><span class="line"> vis[nx][ny] = <span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">return</span> <span class="literal">false</span>;</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
<h2 id="八皇后"><a href="#八皇后" class="headerlink" title="八皇后"></a>八皇后</h2><div class="highlight-container" data-rel="Cpp"><figure class="iseeu highlight cpp"><table><tr><td class="code"><pre><span class="line"><span class="type">int</span> res = <span class="number">0</span>, n;</span><br><span class="line">vector<<span class="type">int</span>> tmp;</span><br><span class="line"><span class="function">vector<<span class="type">int</span>> <span class="title">vis</span><span class="params">(n + <span class="number">1</span>)</span></span>;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">solve</span><span class="params">(<span class="type">int</span> cnt, vector<<span class="type">int</span>> &vis)</span></span></span><br><span class="line"><span class="function"></span>{</span><br><span class="line"> <span class="keyword">if</span> (cnt == n + <span class="number">1</span>)</span><br><span class="line"> {</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">0</span>; i < tmp.<span class="built_in">size</span>(); ++i)</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> j = <span class="number">0</span>; j < tmp.<span class="built_in">size</span>(); ++j)</span><br><span class="line"> <span class="keyword">if</span> (<span class="built_in">abs</span>(i - j) == <span class="built_in">abs</span>(tmp[i] - tmp[j]))</span><br><span class="line"> <span class="keyword">return</span>;</span><br><span class="line"> res++;</span><br><span class="line"> <span class="keyword">return</span>;</span><br><span class="line"> }</span><br><span class="line"> <span class="keyword">for</span> (<span class="type">int</span> i = <span class="number">1</span>; i <= n; ++i)</span><br><span class="line"> <span class="keyword">if</span> (!vis[i])</span><br><span class="line"> {</span><br><span class="line"> vis[i] = <span class="number">1</span>;</span><br><span class="line"> tmp.<span class="built_in">push_back</span>(i);</span><br><span class="line"> <span class="built_in">solve</span>(cnt + <span class="number">1</span>, vis);</span><br><span class="line"> tmp.<span class="built_in">pop_back</span>();</span><br><span class="line"> vis[i] = <span class="number">0</span>;</span><br><span class="line"> }</span><br><span class="line">}</span><br></pre></td></tr></table></figure></div>
]]></content>
<tags>
<tag>机试</tag>
<tag>搜索</tag>
</tags>
</entry>
<entry>
<title>面试常见问题</title>
<url>/2023/03/10/%E9%9D%A2%E8%AF%95%E5%B8%B8%E8%A7%81%E9%97%AE%E9%A2%98/</url>
<content><![CDATA[<h3 id="内存分配结构"><a href="#内存分配结构" class="headerlink" title="内存分配结构"></a>内存分配结构</h3><p><strong>代码区</strong>：存放代码的位置，只读</p>
<p><strong>常量区</strong>：存放常量（如变量名字，非零的初始化值，字符串，const常量等），只读</p>
<p><strong>静态区、全局区</strong>：存放全局变量和静态变量，具体分为两个段，<code>.bss</code>段和<code>.data</code>段</p>
<ul>
<li><p><code>.bss</code>段：存放<strong>未初始化的</strong>和<strong>初始化为0</strong>的全局变量或者静态变量</p>
</li>
<li><p><code>.data</code>段：<strong>初始化不为0</strong>的全局变量或者静态变量</p>
</li>
</ul>
<p><strong>堆</strong>：程序运行期间动态分配<code>malloc</code>所使用的区域</p>
<p><strong>栈</strong>：用于存放地址（用于函数的现场恢复）、临时变量（函数内部定义的变量，或是函数定义的参数）等</p>
<h3 id="快速排序平均复杂度"><a href="#快速排序平均复杂度" class="headerlink" title="快速排序平均复杂度"></a>快速排序平均复杂度</h3><p><mjx-container class="MathJax" jax="SVG" display="true"><svg style="vertical-align: -2.819ex;" xmlns="http://www.w3.org/2000/svg" width="66.83ex" height="6.712ex" role="img" focusable="false" viewBox="0 -1720.9 29538.8 2966.8"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><path data-c="1D436" d="M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 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<h3 id="各种排序和查找比较"><a href="#各种排序和查找比较" class="headerlink" title="各种排序和查找比较"></a>各种排序和查找比较</h3><p><a class="link" href="https://blog.csdn.net/qq_41958041/article/details/107318190">排序和查找时间复杂度总结 <i class="fa-regular fa-arrow-up-right-from-square fa-sm"></i></a></p>
<h3 id="union、struct和class"><a href="#union、struct和class" class="headerlink" title="union、struct和class"></a>union、struct和class</h3><ol>
<li><p>Union：Union是一种特殊的数据结构，它允许在相同的内存位置存储不同的数据类型。<strong>Union中所有的成员都共享同一块内存，只有最后一次赋值的成员有效。</strong>Union适用于需要在不同数据类型之间进行转换的情况。</p>
</li>
<li><p>Struct：Struct是一种用户自定义的数据类型，它允许将不同的数据类型组合在一起成为一个新的数据类型。Struct中的每个成员都有自己的内存地址，可以分别进行访问和赋值。Struct适用于需要表示具有多个属性的对象的情况。</p>
</li>
<li><p>Class：Class是一种用户自定义的数据类型，它可以包含数据成员和成员函数，并且可以实现面向对象的编程。<strong>Class中的数据成员和成员函数默认是私有的，</strong>可以通过public、protected和private关键字进行访问控制。Class适用于需要表示真实世界中的对象和实现面向对象的编程的情况。</p>
</li>
</ol>
<h3 id="连通分量和强连同分量"><a href="#连通分量和强连同分量" class="headerlink" title="连通分量和强连同分量"></a>连通分量和强连同分量</h3><ul>
<li><p>连通分量指的是<strong>无向图</strong>中的一个极大连通子图。具体来说，对于无向图G=(V,E)，若存在一个子集U⊆V，使得U中任意两个点在图G中都可以通过一条路径相互到达，且U是极大的，即U不能再加入任何其他的点，那么U就是图G的一个连通分量。</p>
</li>
<li><p>强连通分量则是<strong>有向图</strong>中的一个极大强连通子图。具体来说，对于有向图G=(V,E)，若存在一个子集U⊆V，使得U中任意两个点在图G中都可以通过一条有向路径相互到达，且U是极大的，即U不能再加入任何其他的点，那么U就是图G的一个强连通分量。</p>
</li>
</ul>
<p><strong>一个弱连通分量不一定是强连通分量，而一个强连通分量必然是一个弱连通分量。</strong></p>
<h4 id="tarjan算法"><a href="#tarjan算法" class="headerlink" title="tarjan算法"></a>tarjan算法</h4><h3 id="面向对象的特征"><a href="#面向对象的特征" class="headerlink" title="面向对象的特征"></a>面向对象的特征</h3><ol>
<li><p><strong>封装（Encapsulation）</strong>：封装是指将数据和方法进行包装，使其对外部隐藏，只保留必要的接口暴露给外部使用。封装可以有效地保护数据和方法，确保其不会被误用或滥用，从而提高程序的可靠性和安全性。</p>
</li>
<li><p><strong>继承（Inheritance）</strong>：继承是指通过定义子类来继承父类的属性和方法。子类可以继承父类的<strong>公共方法和属性</strong>，并且可以添加自己的方法和属性。继承可以有效地减少代码的重复，提高代码的复用性。</p>
</li>
<li><p><strong>多态（Polymorphism）</strong>：多态是指同一个方法名可以具有不同的实现方式。在面向对象编程中，多态可以通过<strong>重载、重写和接口</strong>实现。多态可以提高代码的灵活性和可扩展性，使代码更加简洁易懂。</p>
</li>
<li><p><strong>抽象（Abstraction）</strong>：抽象是指将复杂的实体抽象成类和对象，并仅保留必要的属性和方法。抽象可以让程序员更加专注于问题的本质，而不是实现的细节。同时，抽象也可以提高代码的复用性和可维护性，使代码更加健壮。</p>
</li>
</ol>
<h3 id="引用和指针"><a href="#引用和指针" class="headerlink" title="引用和指针"></a>引用和指针</h3><p>区别：</p>
<ol>
<li><p>定义方式：引用在定义时必须初始化，而指针可以先定义，后赋值。</p>
</li>
<li><p>操作方式：引用在使用时类似于变量名，直接操作被引用对象，不需要使用 * 取值运算符；指针需要通过 * 取值运算符来获取被指向对象的值。</p>
</li>
<li><p>空指针：指针可以指向空值，而引用不能引用空值。</p>
</li>
<li><p>引用的一些特性：引用一旦绑定对象就不能更改，指针可以随时改变指向的对象。</p>
</li>
</ol>
<p>联系：</p>
<ol>
<li><p>都可以用于访问内存中的数据。</p>
</li>
<li><p>都可以用于实现函数参数的传递，引用参数和指针参数都可以用于在函数内部改变外部数据。</p>
</li>
<li><p>引用和指针都可以作为返回值，引用作为返回值可以避免拷贝大对象的开销。</p>
</li>
</ol>
<h3 id="C-和C的关系"><a href="#C-和C的关系" class="headerlink" title="C++和C的关系"></a>C++和C的关系</h3><p>C++：面向对象，引入新语法和特性，包括类、继承、多态、模板。</p>
<h3 id="判断有向图是否有环"><a href="#判断有向图是否有环" class="headerlink" title="判断有向图是否有环"></a>判断有向图是否有环</h3><p>深搜、拓扑排序</p>
]]></content>
<tags>
<tag>面试</tag>
</tags>
</entry>
</search>