_329_LongestIncreasingPathinaMatrix.java

package leetcode_1To300;

/**
 * 本代码来自 Cspiration，由 @Cspiration 提供
 * 题目来源：http://leetcode.com
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 * - 版权所有，转发请注明出处
 */
public class _329_LongestIncreasingPathinaMatrix {
    /**
     * 329. 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.

     time : O(m * n)
     space : O(m * n)

     */

    public int longestIncreasingPath(int[][] matrix) {
        if (matrix == null || matrix.length == 0) return 0;
        int res = 0;
        int m = matrix.length, n = matrix[0].length;
        int[][] cache = new int[m][n];
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                int max = dfs(matrix, Integer.MIN_VALUE, i, j, m, n, cache);
                res = Math.max(res, max);
            }
        }
        return res;
    }

    private int dfs(int[][] matrix, int min, int i, int j, int m, int n, int[][] cache) {
        if (i < 0 || j < 0 || i >= m || j >= n || matrix[i][j] <= min) {
            return 0;
        }
        if (cache[i][j] != 0) {
            return cache[i][j];
        }
        min = matrix[i][j];
        int a = dfs(matrix, min, i - 1, j, n, m, cache) + 1;
        int b = dfs(matrix, min, i + 1, j, n, m, cache) + 1;
        int c = dfs(matrix, min, i, j - 1, n, m, cache) + 1;
        int d = dfs(matrix, min, i, j + 1, n, m, cache) + 1;
        int max = Math.max(a, Math.max(b, Math.max(c, d)));
        cache[i][j] = max;
        return max;
    }
}