Leetcode 688 Solution

This article provides solution to leetcode question 688 (knight-probability-in-chessboard)
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https://leetcode.com/problems/knight-probability-in-chessboard

Solution

class Solution:
    def knightProbability(self, N: int, K: int, r: int, c: int) -> float:
        cache = {}



        def dfs(N, K, r, c, prop):
            if K == 0 and (0 <= r < N and 0 <= c < N):
                return prop



            if not (0 <= r < N and 0 <= c < N):
                return 0



            key = (r, c, prop)
            if key in cache:
                return cache[key]



            ans = 0
            for r_delta, c_delta in [(1, 2), (2, 1), (-1, 2), (2, -1), (1, -2), (-2, 1), (-1, -2), (-2, -1)]:
                ans += dfs(N, K - 1, r + r_delta, c + c_delta, prop * 0.125)
            cache[key] = ans
            return ans



        return dfs(N, K, r, c, 1)