LeetCode 329: Longest Increasing Path In A Matrix — Step-by-Step Visual Trace

Hard — Dynamic Programming | Depth-First Search | Matrix | Memoization The Problem Find the length of the longest increasing path in a matrix where you can move in four directions (up, down, left, right) to adjacent cells with strictly increasing values. Approach Uses depth-first search (DFS) with memoization to explore all possible increasing paths from each cell. The algorithm stores computed results in a DP table to avoid redundant calculations and returns the maximum path length found across all starting positions. Time: O(m*n) · Space: O(m*n) Code class Solution : def longestIncreasingPath ( self , matrix : List [ List [ int ]]) -> int : if not matrix : return 0 # Define directions for moving to neighboring cells: up, down, left, right. directions = [( - 1 , 0 ), ( 1 , 0 ), ( 0 , - 1 ), ( 0 , 1 )] # Function to perform DFS from a given cell (i, j). def dfs ( i , j ): # If the result for this cell is already calculated, return it. if dp [ i ][ j ] != - 1 : return dp [ i ][ j ] # In