[leetcode]Memoization-329. Longest Increasing Path in a Matrix

Posted 2020-10-20 chenhan05

en 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.

Credits:
Special thanks to @dietpepsi for adding this problem and creating all test cases.

 

public int longestIncreasingPath(int[][] matrix) {  
        if(matrix.length<=0 || matrix[0].length <=0) return 0;  
        int max=0, n = matrix.length, m = matrix[0].length;  
        int [][] cache = new int[n][m];  
        for(int i=0;i<matrix.length;i++){  
            for(int j=0;j<matrix[0].length;j++) {  
                max = Math.max(max, maxLen(matrix, Integer.MIN_VALUE, i, j, cache));  
            }  
        }  
        return max;  
    }  
    public int maxLen(int[][] matrix, int min, int r, int c, int[][] cache) {  
        if(r<0 || c<0 || r>=matrix.length || c>= matrix[0].length) {  
            return 0;  
        }  
        if(matrix[r][c] <= min) {  
            return 0;  
        }  
        if(cache[r][c] != 0) {  
            return cache[r][c];  
        }  
        min = matrix[r][c];  
        int up = maxLen(matrix, min, r-1, c, cache) + 1;  
        int left = maxLen(matrix, min, r, c-1, cache) + 1;  
        int right = maxLen(matrix, min, r, c+1, cache) + 1;  
        int down = maxLen(matrix, min, r+1, c, cache) + 1;  
        cache[r][c] = Math.max(up, Math.max(left, Math.max(right,down)));  
        return cache[r][c];  
    }