【LeeCode 困难 python3】329. 矩阵中的最长递增路径

想要看更加舒服的排版、更加准时的推送
关注公众号“不太灵光的程序员”
每日八点有干货推送，微信随时解答你的疑问

329. 矩阵中的最长递增路径 python3

困难 深度优先搜索 拓扑排序 记忆化
给定一个整数矩阵，找出最长递增路径的长度。

对于每个单元格，你可以往上，下，左，右四个方向移动。 你不能在对角线方向上移动或移动到边界外（即不允许环绕）。

示例 1:

输入: nums =
[
[9,9,4],
[6,6,8],
[2,1,1]
]
输出: 4
解释: 最长递增路径为 [1, 2, 6, 9]。

示例 2:

输入: nums =
[
[3,4,5],
[3,2,6],
[2,2,1]
]
输出: 4
解释: 最长递增路径是 [3, 4, 5, 6]。注意不允许在对角线方向上移动。

解析

从左到右 从上到小遍历
dic 记录已经计算过的点，减少计算次数

from typing import List


# 执行用时：544 ms, 在所有 Python3 提交中击败了64.30%的用户
# 内存消耗：17.4 MB, 在所有 Python3 提交中击败了50.00%的用户
class Solution:
    def longestIncreasingPath(self, matrix: List[List[int]]) -> int:
        if not matrix: return 0
        m = len(matrix)
        n = len(matrix[0])
        dic = {}

        def get_next_node(i, j):
            len1 = len2 = len3 = len4 = 1
            # 上
            if i - 1 >= 0 and matrix[i][j] < matrix[i - 1][j]:
                if (i - 1, j) in dic:
                    len1 = dic[(i - 1, j)]
                else:
                    len1 += get_next_node(i - 1, j)
                    dic[(i - 1, j)] = len1
            # 下
            if i + 1 < m and matrix[i][j] < matrix[i + 1][j]:
                if (i + 1, j) in dic:
                    len2 = dic[(i + 1, j)]
                else:
                    len2 += get_next_node(i + 1, j)
                    dic[(i + 1, j)] = len2

            # 左
            if j - 1 >= 0 and matrix[i][j] < matrix[i][j - 1]:
                if (i, j - 1) in dic:
                    len3 = dic[(i, j - 1)]
                else:
                    len3 += get_next_node(i, j - 1)
                    dic[(i, j - 1)] = len3
            # 右
            if j + 1 < n and matrix[i][j] < matrix[i][j + 1]:
                if (i, j + 1) in dic:
                    len4 = dic[(i, j + 1)]
                else:
                    len4 += get_next_node(i, j + 1)
                    dic[(i, j + 1)] = len4

            return max(len1, len2, len3, len4)

        max_len = 0
        for i in range(m):
            for j in range(n):
                lens = get_next_node(i, j)
                if lens > max_len:
                    max_len = lens

        return max_len


s = Solution()
nums = [
    [3, 4, 5],
    [3, 2, 6],
    [2, 2, 1]
]
ret = s.longestIncreasingPath(nums)
print(ret, ret == 4)

nums = [[9, 9, 4],
        [6, 6, 8],
        [2, 1, 1]]
ret = s.longestIncreasingPath(nums)
print(ret, ret == 4)

nums = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
        [19, 18, 17, 16, 15, 14, 13, 12, 11, 10],
        [20, 21, 22, 23, 24, 25, 26, 27, 28, 29],
        [39, 38, 37, 36, 35, 34, 33, 32, 31, 30],
        [40, 41, 42, 43, 44, 45, 46, 47, 48, 49],
        [59, 58, 57, 56, 55, 54, 53, 52, 51, 50],
        [60, 61, 62, 63, 64, 65, 66, 67, 68, 69],
        [79, 78, 77, 76, 75, 74, 73, 72, 71, 70],
        [80, 81, 82, 83, 84, 85, 86, 87, 88, 89],
        [99, 98, 97, 96, 95, 94, 93, 92, 91, 90],
        [100, 101, 102, 103, 104, 105, 106, 107, 108, 109],
        [119, 118, 117, 116, 115, 114, 113, 112, 111, 110],
        [120, 121, 122, 123, 124, 125, 126, 127, 128, 129],
        [139, 138, 137, 136, 135, 134, 133, 132, 131, 130],
        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]
ret = s.longestIncreasingPath(nums)
print(ret, ret == 4)