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// 688. Knight Probability in Chessboard
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.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.
*/
bool in_bound(int row, int col, int n) {
return 0 <= row && row < n && col >= 0 && col < n;
}
double knightProbability(int n, int k, int row, int col) {
double **a = (double **)malloc(sizeof(double *) * n);
double **b = (double **)malloc(sizeof(double *) * n);
for (int i = 0; i < n; i++) {
a[i] = (double *)malloc(sizeof(double) * n);
b[i] = (double *)malloc(sizeof(double) * n);
for (int j = 0; j < n; j++) {
a[i][j] = 0;
b[i][j] = 0;
}
}
static int dr[8] = {-1, -2, -2, -1, 1, 2, 2, 1};
static int dc[8] = {-2, -1, 1, 2, -2, -1, 1, 2};
a[row][col] = 1;
double **to = a;
double **from = NULL;
for (int step = 1; step <= k; step++) {
to = ((step % 2) != 0 ? b : a);
from = ((step % 2) != 0 ? a : b);
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
to[i][j] = 0;
for (int l = 0; l < 8; l++) {
to[i][j] += in_bound(i + dr[l], j + dc[l], n)
? from[i + dr[l]][j + dc[l]] / 8
: 0;
}
}
}
}
double ans = 0;
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
ans += to[i][j];
for (int i = 0; i < n; i++)
free(a[i]), free(b[i]);
free(a), free(b);
return ans;
}
int main() {
printf("%f\n", knightProbability(3, 2, 0, 0)); // expect: 0.06250
printf("%f\n", knightProbability(1, 0, 0, 0)); // expect: 1.00000
}
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