Solution.ts

function knightProbability(
    n: number,
    k: number,
    row: number,
    column: number,
): number {
    const f = new Array(k + 1)
        .fill(0)
        .map(() => new Array(n).fill(0).map(() => new Array(n).fill(0)));
    for (let i = 0; i < n; ++i) {
        for (let j = 0; j < n; ++j) {
            f[0][i][j] = 1;
        }
    }
    const dirs = [-2, -1, 2, 1, -2, 1, 2, -1, -2];
    for (let h = 1; h <= k; ++h) {
        for (let i = 0; i < n; ++i) {
            for (let j = 0; j < n; ++j) {
                for (let p = 0; p < 8; ++p) {
                    const x = i + dirs[p];
                    const y = j + dirs[p + 1];
                    if (x >= 0 && x < n && y >= 0 && y < n) {
                        f[h][i][j] += f[h - 1][x][y] / 8;
                    }
                }
            }
        }
    }
    return f[k][row][column];
}