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Solution: Longest Increasing Path in a Matrix

Explore how to determine the longest strictly increasing path in a matrix by applying depth-first search combined with dynamic programming memoization. Understand how to traverse matrix cells in four directions to build paths, optimize redundant calculations, and evaluate the time and space complexity of this approach. This lesson helps you implement a solution that effectively handles complex grid-based problems common in coding interviews.

Statement

You are given an m×nm × n matrix of integers. Your task is to determine the length of the longest strictly increasing path within the matrix.

A path is defined by consecutively moving from one cell to another adjacent cell. From any cell, movement is allowed only in four directions: up, down, left and right.

Diagonal movement is not allowed. You also cannot move outside the matrix boundaries (no wrap-around).

A path is considered increasing if each subsequent cell contains a strictly greater integer than the previous one.

Your goal is to return the maximum length among all possible increasing paths in the matrix.

Constraints:

  • m==m == matrix.length

  • n==n == ...