Add knapsack multi

dp/knapsack_multi.cc

@@ -0,0 +1,66 @@
+// https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1167&lang=jp
+// 複数選択できるナップサック問題
+
+#include <iostream>
+#include <vector>
+using namespace std;
+
+int main() {
+  const int N = 1000000;
+  vector<int> pollock, pollock_odd;
+  for (int n = 1;; n++) {
+    int a = n * (n + 1) * (n + 2) / 6;
+    if (a > N) {
+      break;
+    }
+    pollock.push_back(a);
+    if (a % 2) {
+      pollock_odd.push_back(a);
+    }
+  }
+  int M0 = (int)pollock.size();
+  vector<vector<int> > dp0(N + 1, vector<int>(2));
+  // m = 0
+  for (int n = 0; n <= N; n++) {
+    dp0[n][0] = n;
+  }
+  for (int m = 1; m < M0; m++) {
+    int M = pollock[m];
+    dp0[0][m % 2] = 0;
+    for (int n = 1; n <= N; n++) {
+      dp0[n][m % 2] = dp0[n][1 - m % 2];
+      if (n - M >= 0) {
+        dp0[n][m % 2] = min(dp0[n][m % 2], dp0[n - M][1 - m % 2] + 1);
+        dp0[n][m % 2] = min(dp0[n][m % 2], dp0[n - M][m % 2] + 1);
+      }
+    }
+  }
+
+  int M1 = (int)pollock_odd.size();
+  vector<vector<int> > dp1(N + 1, vector<int>(2));
+  // m = 0
+  for (int n = 0; n <= N; n++) {
+    dp1[n][0] = n;
+  }
+  for (int m = 1; m < M1; m++) {
+    int M = pollock_odd[m];
+    dp1[0][m % 2] = 0;
+    for (int n = 1; n <= N; n++) {
+      dp1[n][m % 2] = dp1[n][1 - m % 2];
+      if (n - M >= 0) {
+        dp1[n][m % 2] = min(dp1[n][m % 2], dp1[n - M][1 - m % 2] + 1);
+        dp1[n][m % 2] = min(dp1[n][m % 2], dp1[n - M][m % 2] + 1);
+      }
+    }
+  }
+
+  while (true) {
+    int n;
+    cin >> n;
+    if (n == 0) {
+      break;
+    }
+    cout << dp0[n][1 - M0 % 2] << " " << dp1[n][1 - M1 % 2] << endl;
+  }
+  return 0;
+}