Longest Increasing Path in a Matrix

Source

• leetcode: Longest Increasing Path in a Matrix

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:

nums = [
  [9,9,4],
  [6,6,8],
  [2,1,1]
]
Return 4
The longest increasing path is [1, 2, 6, 9].

Example 2:

nums = [
  [3,4,5],
  [3,2,6],
  [2,2,1]
]
Return 4
The longest increasing path is [3, 4, 5, 6]. Moving diagonally is not allowed.

Java

public class Solution {
    public static final int[][] dirs = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};

    public int longestIncreasingPath(int[][] matrix) {
        if(matrix.length == 0) return 0;
        int m = matrix.length, n = matrix[0].length;
        int[][] cache = new int[m][n];
        int globalMax = 1;
        for(int i = 0; i < m; i++) {
            for(int j = 0; j < n; j++) {
                int localMax = dfs(matrix, i, j, cache);
                globalMax = Math.max(globalMax, localMax);
            }
        }   
        return globalMax;
    }

    public int dfs(int[][] matrix, int i, int j, int[][] cache) {
        if(cache[i][j] != 0) return cache[i][j];
        int localMax = 1;
        for(int[] dir: dirs) {
            int x = i + dir[0], y = j + dir[1];
            if(x < 0 || x >= matrix.length || y < 0 || y >= matrix[0].length || matrix[x][y] <= matrix[i][j]) continue;
            int len = 1 + dfs(matrix, x, y, cache);
            localMax = Math.max(localMax, len);
        }
        cache[i][j] = localMax;
        return localMax;
    }
}