knight probablity on chaessboard if can not come back on chessboard

Author: rvguradiya

problems/general/knight_probability_on_chessboard.md

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+This problem was asked by **Two Sigma**.
+
+A knight is placed on a given square on an 8 x 8 chessboard. It is then moved randomly several times, where each move is a standard [knight move](<https://en.wikipedia.org/wiki/Knight_(chess)#Movement>). If the knight jumps off the board at any point, however, it is not allowed to jump back on.
+
+After k moves, what is the probability that the knight remains on the board?

solutions/general/knight_probability_on_chessboard/Approach.java

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+public class Approach{
+    
+    static  int  possibleMoves[][] = {
+        {2, -1},
+        {2, 1},
+        {-2, -1},
+        {-2, 1},
+        {1, 2},
+        {1, -2},
+        {-1, 2},
+        {-1, -2},
+    };
+
+    static  int [][]visited;
+
+    // for testing purpose 
+    static void print(){
+        for (int [] row:visited){
+            String s = " ";
+            for(int col: row){
+                s += col;
+            }
+            System.err.println(s);
+        }
+    }
+
+    static double   knightProbability(int K,int N,int row,int col){
+        if (visited[row][col] == 1) {
+            return 0;
+        } else if (K == 0) {
+            return 1;
+        }
+      
+        visited[row][col] = 1;
+        double probability = 0;
+        int countMove = 0;
+        for (int [] knightMove : possibleMoves) {
+            int xMove = knightMove[0] + row;
+            int yMove = knightMove[1] + col;
+            if (0 <= xMove && xMove < N && 0 <= yMove && yMove < N) {
+              countMove++;
+            //   System.err.println(""+K+""+probability+""+xMove+""+yMove);
+            //   print();
+              probability += knightProbability(K-1, N, xMove, yMove);
+            }
+          }
+          visited[row][col] = 0;
+          return countMove>0 ? probability / countMove : probability;
+        }
+    
+    public static void main(String args[]){
+        int N = 3;
+        int K = 7;
+
+        if (visited == null){
+            visited = new int[N][N];
+        }
+
+        System.out.println(knightProbability(K, N, 0, 0));
+    }
+}

solutions/general/knight_probability_on_chessboard/approach.js

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+function knightProbability(K, N, row, col) {
+  let possibleMoves = [
+    [2, -1],
+    [2, 1],
+    [-2, -1],
+    [-2, 1],
+    [1, 2],
+    [1, -2],
+    [-1, 2],
+    [-1, -2],
+  ];
+
+  let visited = [];
+  for (let i = 0; i < N; i++) {
+    visited.push(Array(N).fill(0));
+  }
+
+  function moveProbability(k, n, i, j) {
+    if (visited[i][j] == 1) {
+      return 0;
+    } else if (k == 0) {
+      return 1;
+    }
+
+    visited[i][j] = 1;
+    let probability = 0;
+    let countMove = 0;
+    for (let knightMove of possibleMoves) {
+      let xMove = knightMove[0] + i;
+      let yMove = knightMove[1] + j;
+      if (0 <= xMove && xMove < N && 0 <= yMove && yMove < N) {
+        countMove++;
+        // console.log(k, probability, xMove, yMove, visited);
+        probability += moveProbability(k - 1, n, xMove, yMove);
+      }
+    }
+    visited[i][j] = 0;
+    return countMove ? probability / countMove : probability;
+  }
+  return moveProbability(K, N, row, col);
+}
+
+console.log(knightProbability(7, 3, 0, 0));