# 329. Longest Increasing Path in a Matrix 矩阵中的最长递增路径

## # 题目描述：

Given an integer matrix, find the length of the longest increasing path.

From each cell, you can either move to four directions: left, right, up or down. You may NOT move diagonally or move outside of the boundary (i.e. wrap-around is not allowed).

Example 1:

``````Input: nums =
[
[9,9,4],
[6,6,8],
[2,1,1]
]
Output: 4
Explanation: The longest increasing path is [1, 2, 6, 9].
``````

Example 2:

``````Input: nums =
[
[3,4,5],
[3,2,6],
[2,2,1]
]
Output: 4
Explanation: The longest increasing path is [3, 4, 5, 6]. Moving diagonally is not allowed.
``````

## # 解题方法

417. Pacific Atlantic Water Flowopen in new window非常类似，直接DFS求解。一般来说DFS需要有固定的起点，但是对于这个题，二维矩阵中的每个位置都算作起点。

``````class Solution(object):
def longestIncreasingPath(self, matrix):
"""
:type matrix: List[List[int]]
:rtype: int
"""
if not matrix or not matrix[0]:
return 0
m, n = len(matrix), len(matrix[0])
res = 0
cache = [[-1] * n for _ in range(m)]
for i in range(m):
for j in range(n):
path = self.dfs(matrix, cache, m, n, i, j)
res = max(res, path)
return res

def dfs(self, matrix, cache, m, n, i, j):
if cache[i][j] != -1:
return cache[i][j]
directions = [(-1, 0), (1, 0), (0, 1), (0, -1)]
res = 1
for dire in directions:
x, y = i + dire[0], j + dire[1]
if x < 0 or x >= m or y < 0 or y >= n or matrix[x][y] <= matrix[i][j]:
continue
path = 1 + self.dfs(matrix, cache, m, n, x, y)
res = max(path, res)
cache[i][j] = res
return cache[i][j]
``````

https://leetcode.com/problems/pacific-atlantic-water-flow/discuss/90739/Python-DFS-bests-85.-Tips-for-all-DFS-in-matrix-question./181815

## # 日期

2018 年 10 月 1 日 —— 欢度国庆！