1. Runtime Distribution

2. Submission Details

3. Description

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).

4. Example

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

5. Code

private int[][] matrix;
    private int rowLength;
    private int colLength;
    private int[][] cache;

    public int longestIncreasingPath(int[][] matrix){
        if(matrix == null || matrix.length == 0 || matrix[0].length == 0){
            return 0;
        }
        this.matrix = matrix;
        rowLength = matrix.length;
        colLength = matrix[0].length;
        cache = new int[rowLength][colLength];
        int max = 0;
        for(int i = 0; i< rowLength; i++){
            for(int j = 0; j < colLength; j++){
                max = Math.max(max, dfs(i, j));
            }
        }
        return max;
    }

    private int dfs(int i, int j){
        if(cache[i][j] != 0){
            return cache[i][j];
        }
        int max = 0;
        if(i > 0 && matrix[i][j] < matrix[i-1][j]){
            max = Math.max(max, dfs(i - 1, j));
        }
        if(i + 1 < rowLength && matrix[i][j] < matrix[i+1][j]){
            max = Math.max(max, dfs(i+1, j));
        }
        if(j > 0 && matrix[i][j] < matrix[i][j-1]){
            max = Math.max(max, dfs(i, j - 1));
        }
        if(j + 1 < colLength && matrix[i][j] < matrix[i][j + 1]){
            max = Math.max(max, dfs(i, j + 1));
        }
        cache[i][j] = max + 1;
        return max + 1;
    }
}

6.Test

import org.junit.Test;

public class LeetCode0329 {

    private int[][] matrix;
    private int rowLength;
    private int colLength;
    private int[][] cache;

    public int longestIncreasingPath(int[][] matrix){
        if(matrix == null || matrix.length == 0 || matrix[0].length == 0){
            return 0;
        }
        this.matrix = matrix;
        rowLength = matrix.length;
        colLength = matrix[0].length;
        cache = new int[rowLength][colLength];
        int max = 0;
        for(int i = 0; i< rowLength; i++){
            for(int j = 0; j < colLength; j++){
                max = Math.max(max, dfs(i, j));
            }
        }
        return max;
    }

    private int dfs(int i, int j){
        if(cache[i][j] != 0){
            return cache[i][j];
        }
        int max = 0;
        if(i > 0 && matrix[i][j] < matrix[i-1][j]){
            max = Math.max(max, dfs(i - 1, j));
        }
        if(i + 1 < rowLength && matrix[i][j] < matrix[i+1][j]){
            max = Math.max(max, dfs(i+1, j));
        }
        if(j > 0 && matrix[i][j] < matrix[i][j-1]){
            max = Math.max(max, dfs(i, j - 1));
        }
        if(j + 1 < colLength && matrix[i][j] < matrix[i][j + 1]){
            max = Math.max(max, dfs(i, j + 1));
        }
        cache[i][j] = max + 1;
        return max + 1;
    }

    @Test
    public void test(){
        int[][] matrix = {
                {9,9,4},
                {6,6,8},
                {2,1,1}
        };
        System.out.println(longestIncreasingPath(matrix));
    }
}