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// 688. Knight Probability in Chessboard
#include "leetcode.h"
/*
* on an 'n x n' chessboard, a knight starts at the cell '(row, column)' and
* attempts to make exactly 'k' moves. the rows and columns are 0-indexed, so
* the top-left cell is '(0, 0)', and the bottom-right cell is '(n - 1, n - 1)'.
* a chess knight has eight possible moves it can make, as illustrated below
* [see image]. each move is two cells in a cardinal direction, then one cell in
* an orthogonal direction.
*/
class Solution {
public:
double knightProbability(int n, int k, int row, int col) {
unordered_map<int, unordered_map<int, unordered_map<int, double>>> dp;
if (dp.count(row) && dp[row].count(col) && dp[row][row].count(k))
return dp[row][col][k];
if (row < 0 || row >= n || col < 0 || col >= n)
return 0;
if (!k)
return 1;
double total = knightProbability(n, k - 1, row - 1, col - 2) +
knightProbability(n, k - 1, row - 2, col - 1) +
knightProbability(n, k - 1, row - 1, col + 2) +
knightProbability(n, k - 1, row - 2, col + 1) +
knightProbability(n, k - 1, row + 1, col + 2) +
knightProbability(n, k - 1, row + 2, col + 1) +
knightProbability(n, k - 1, row + 1, col - 2) +
knightProbability(n, k - 1, row + 2, col - 1);
double ans = total / 8;
dp[row][col][k] = ans;
return ans;
}
};
int main() {
Solution obj;
printf("%f\n", obj.knightProbability(3, 2, 0, 0)); // expect: 0.06250
printf("%f\n", obj.knightProbability(1, 0, 0, 0)); // expect: 1.00000
}
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