Is Longest Increasing Path in a Matrix easy or hard?

Longest Increasing Path in a Matrix is classified as a Hard problem on LeetCode. The difficulty comes from recognizing overlapping subproblems and transforming naive DFS into an efficient O(m*n) dynamic programming solution using memoization or graph topological ordering.

Longest Increasing Path in a Matrix Python/Java solution

Python and Java implementations typically use DFS with a memo table. A recursive function explores four directions and stores the computed longest path for each cell. This reduces the complexity to O(m*n) while keeping the implementation concise.

How to solve Longest Increasing Path in a Matrix in O(n)?

Treat the grid as m*n nodes and compute the longest path in O(m*n) time using DFS with memoization. Store the best path length starting from each cell in a cache so overlapping searches are avoided. Another O(m*n) method uses topological sorting by treating the matrix as a DAG and processing nodes by levels.

What is the best approach for Longest Increasing Path in a Matrix?

DFS with memoization is the most widely used approach. Start a DFS from every cell and cache the longest path length for that cell so repeated subproblems are not recomputed. Each cell is evaluated once, giving O(m*n) time and O(m*n) space complexity.

Is Longest Increasing Path in a Matrix asked at Google/Amazon/Meta?

Longest Increasing Path in a Matrix frequently appears in interviews at companies like Google, Amazon, and Meta because it tests DFS, dynamic programming, and graph modeling. Candidates must recognize overlapping subproblems and optimize recursion with memoization.

What data structure is used in Longest Increasing Path in a Matrix?

The main structures are a 2D memoization array for dynamic programming and recursion or a queue for BFS. The matrix itself can be interpreted as a directed graph where edges go from smaller values to larger neighbors.

What is the time complexity of Longest Increasing Path in a Matrix?

The optimal solutions run in O(m*n) time where m and n are the matrix dimensions. With DFS and memoization, each cell's result is computed once and reused. Every DFS checks at most four neighbors, keeping the total work linear in the number of cells.

Description Solution Video 17:45

329. Longest Increasing Path in a Matrix

Hard57.0% acceptance16 companies

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

Asked at 16 companies

DoorDash WeRide Duolingo Tiktok Adobe Nutanix Meta PhonePe Epic Systems

Google Uber Salesforce

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Amazon Microsoft Bloomberg Apple

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329. Longest Increasing Path in a Matrix

Asked at 16 companies

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