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KnightProbabilityInChessBoard.java
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KnightProbabilityInChessBoard.java
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package Leetcode;
/**
* @author kalpak
*
* On an NxN chessboard, a knight starts at the r-th row and c-th column and attempts to make exactly K moves.
*
* The rows and columns are 0 indexed, so the top-left square is (0, 0), and the bottom-right square is (N-1, N-1).
*
* A chess knight has 8 possible moves it can make, as illustrated below.
* Each move is two squares in a cardinal direction, then one square in an orthogonal direction.
*
*
* Each time the knight is to move, it chooses one of eight possible moves uniformly at random
* (even if the piece would go off the chessboard) and moves there.
*
* The knight continues moving until it has made exactly K moves or has moved off the chessboard.
* Return the probability that the knight remains on the board after it has stopped moving.
*
*
* Example:
* Input: 3, 2, 0, 0
* Output: 0.0625
* Explanation: There are two moves (to (1,2), (2,1)) that will keep the knight on the board.
* From each of those positions, there are also two moves that will keep the knight on the board.
* The total probability the knight stays on the board is 0.0625.
*
*
* Note:
*
* N will be between 1 and 25.
* K will be between 0 and 100.
* The knight always initially starts on the board.
*
*/
public class KnightProbabilityInChessBoard {
private static final int[][]dir = new int[][]{{-2, -1}, {-1, -2}, {1, -2}, {2, -1}, {2, 1}, {1, 2}, {-1, 2}, {-2, 1}};
public static double knightProbability(int N, int K, int r, int c) {
double[][][] dp = new double[N][N][K + 1];
return find(dp, N, K, r, c);
}
private static double find(double[][][] dp, int N,int K,int r,int c) {
if (r < 0 || r > N - 1 || c < 0 || c > N - 1)
return 0;
if(K == 0)
return 1;
if(dp[r][c][K] != 0)
return dp[r][c][K];
double rate = 0;
for(int i = 0;i < dir.length;i++) {
rate += 0.125 * find(dp, N, K - 1, r + dir[i][0], c + dir[i][1]);
dp[r][c][K] = rate;
}
return dp[r][c][K];
}
public static void main(String[] args) {
System.out.println(knightProbability(3, 2, 0, 0));
}
}