Update santa-banta.cpp

Medium/Santa Banta/santa-banta.cpp

@@ -5,70 +5,93 @@ using namespace std;
 
 // } Driver Code Ends
 
+// Constant defining the maximum size of the array
+const int maxn=1000001;
+
+// Array for marking prime numbers
+int a[maxn+1];
+
+// Vector for storing prime numbers
+vector<int> pl={2};
+
 class Solution{
 public:
-    int prime[100001];
-
-    bool isPrime(int n)
-    {
-        if(n==1)return false;
-        if(n==2 or n==3)return true;
-        for(int i=2;i<=sqrt(n);i++){
-            if(n%i==0) return false;
+    // Function to precompute the prime numbers
+    void precompute(){
+        // Marking all numbers as prime initially
+        for(int i=1;i<=maxn;i++)
+            a[i]=1;
+
+        // Marking 0 and 1 as not prime
+        a[0]=a[1]=0;
+
+        // Sieve of Eratosthenes algorithm to mark non-prime numbers
+        for(int i=2;i*i<=maxn;i++){
+            if(a[i]==1){
+                for(int j=i*i;j<=maxn;j+=i){
+                    a[j]=0;
+                }
+            }
         }
 
-        return true;
+        // Storing all the prime numbers in the vector
+        for(int i=3;i<=maxn;i++)
+            if(a[i])
+                pl.push_back(i);
     }
 
-    int count= 0;
-    void precompute(){
-        for(int i=2;i<=1000000;i++)
-        {
-            if(isPrime(i))
-            {
-                count++;
-                prime[count]= i;
+    // Depth-first search function to find the number of reachable nodes in a graph
+    int dfs(int i, vector<int> g[], vector<int> &vis){
+        // Marking the current node as visited
+        vis[i]=1;
+
+        // Counter variable to keep track of the number of reachable nodes
+        int cnt=1;
+
+        // Recursively traversing all the adjacent nodes of the current node
+        for(auto x:g[i]){
+            if(!vis[x]){
+                cnt+=dfs(x, g, vis);
             }
         }
-        prime[1]=-1;
+
+        // Returning the total number of reachable nodes
+        return cnt;
     }
 
-    int dfs(int node,vector<bool> &vis,vector<vector<int>> &g)
+    // Function to help Santa navigate the given graph
+    int helpSanta(int n, int m, vector<vector<int>> &g)
     {
-        vis[node]=true;
+        // Initializing the visited array
+        vector<int> vis(n+1, 0);
 
-        int ans=0;
-        for(auto it: g[node])
-        {
-            if(vis[it]==false)
-            {
-                ans+= 1+ dfs(it,vis,g);
-            }
+        // Creating an adjacency list for the given graph
+        vector<int> adj[n + 1];
+        for(auto i : g){
+            adj[i[0]].push_back(i[1]);
+            adj[i[1]].push_back(i[0]);
         }
 
-        return ans;
-    }
-    int helpSanta(int n, int m, vector<vector<int>> &g){
-        vector<bool> vis(n+1, false);
+        // Variable to store the largest component size
+        int lc=0;
 
-        int maxi = -1;
-        for(int i=1;i<=n;i++)
-        {
-            if(vis[i]==false)
-            {
-                int val =1 + dfs(i,vis,g);
-                maxi= max(maxi,val);
+        // Traversing all the nodes from 0 to n and finding the largest component
+        for(int i = 0; i <= n; i++){
+            if(!vis[i]){
+                lc=max(lc,dfs(i, adj, vis));
             }
         }
 
-        if(maxi==-1)return -1;
-
-        return prime[maxi];
+        // Checking if there is only one component in the graph
+        // If yes, returning -1
+        if(lc==1)
+            return -1;
 
+        // Returning the prime number at the (largest component size - 1) index
+        return pl[lc-1];
     }
 };
 
-
 //{ Driver Code Starts.
 
 int main(){
@@ -93,4 +116,4 @@ int main(){
 
 
 
-// } Driver Code Ends
+// } Driver Code Ends