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矩阵中的最长递增路径

Longest Increasing Path in a Matrix

专题
Algorithmic Programming / 算法编程
难度
L4
来源
Citadel

题目详情

问题：矩阵中的最长递增路径

考察：数组、动态规划、图、递归

来源：Citadel

链接：https://www.jointaro.com/interviews/questions/longest-increasing-path-in-a-matrix/

Given an m x n integers matrix, return the length of the longest increasing path in matrix.

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

 

Example 1:

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

Example 2:

Input: matrix = [[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.

Example 3:

Input: matrix = [[1]]
Output: 1

 

Constraints:

  • m == matrix.length
  • n == matrix[i].length
  • 1 <= m, n <= 200
  • 0 <= matrix[i][j] <= 231 - 1
解析

思路：把每个格子看成有向图节点，只能走向值更大的相邻格。用 DFS + 记忆化计算从每个格子出发的最长路径，避免重复搜索。

复杂度：时间 O(mn)，空间 O(mn)。