329. Longest Increasing Path in a Matrix

九章算法班里講過的一道題，用記憶化搜索。

class Solution(object):
    def longestIncreasingPath(self, matrix):
        """
        :type matrix: List[List[int]]
        :rtype: int
        """
        if not matrix:
            return 0
        # write your code here
        A = matrix
        max_length = 0
        dp = [[0 for _ in range(len(A[0]))] for _ in range(len(A))]
        visited = [[False for _ in range(len(A[0]))] for _ in range(len(A))]
        for i in range(len(A)):
            for j in range(len(A[0])):
                max_length = max(max_length, self.dfs(dp, visited, A, i, j))
        
        return max_length
                
    def dfs(self, dp, visited, A, i, j):
        if visited[i][j]:
            return dp[i][j] # starting from i,j the longest subsequence
        
        length = 1
        for x, y in [[i-1, j], [i+1, j], [i, j-1], [i, j+1]]:
            if 0 <= x < len(A) and 0 <= y < len(A[0]) and A[x][y] < A[i][j]:
                length = max(length, self.dfs(dp, visited, A, x, y) + 1)
        
        dp[i][j] = length
        visited[i][j] = True
        return length