688

Author: Fect

t688. Knight Probability in Chessboard.cpp

@@ -0,0 +1,53 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+double query(vector<vector<double>>& dp,int N,int i,int j,int K){
+
+    if(i<0||i>=N||j<0||j>=N){
+        return 0;
+    }
+
+    if(dp[N*i+j][K]!=-1){
+        return dp[N*i+j][K];
+    }
+    double ans = 0;
+    ans+=query(dp,N,i+1,j+2,K-1)
+        +query(dp,N,i+1,j-2,K-1)
+        +query(dp,N,i-1,j+2,K-1)
+        +query(dp,N,i-1,j-2,K-1)
+        +query(dp,N,i+2,j+1,K-1)
+        +query(dp,N,i+2,j-1,K-1)
+        +query(dp,N,i-2,j+1,K-1)
+        +query(dp,N,i-2,j-1,K-1);
+    
+    ans/=8;
+    dp[i*N+j][K] = ans;
+    return ans;
+
+}
+
+double knightProbability(int N, int K, int r, int c) {
+
+    double ans = 0;
+
+    vector<vector<double>> dp(625,vector<double>(100));
+
+    for(int i=0;i<N*N;i++){
+        dp[i][0] = 0;
+        for(int j=1;j<=K;j++){
+            dp[i][j] = -1;
+        }
+    }
+
+    dp[r*N+c][0] = 1;
+    for(int i=0;i<N;i++){
+        for(int j=0;j<N;j++){
+            ans+=query(dp,N,i,j,K);
+        }
+    }
+
+
+    return ans;
+}
+
+