[LeetCode] 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:

Input: nums = 
[
  [9,9,4],
  [6,6,8],
  [2,1,1]
] 
Output: 4 
Explanation: The longest increasing path is [1, 2, 6, 9].

Example 2:

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

矩阵中的最长递增路径。题意是给一个二维矩阵，找出最长的递增路径。例子应该很好地解释了什么叫做最长的递增路径。

这道题也是偏flood fill那一类的题，同时因为是找最长路径，所以用DFS做更好。因为路径是连续的且只是往上下左右四个方向，所以需要再创建一个同样size的二维数组来记录遍历的结果，这样就不需要遍历整个input数组了，因为input数组中比如数字为9的坐标，实际是没什么扫描的意义的，因为数字非常大了，而他的邻居搞不好都比他本身小。具体做法还是应用DFS的模板，但是在设计dfs函数的时候记得加一个额外的二维数组记录结果，也加一个prev值，用来和当前坐标上的值作比较。其余的部分可参见代码。

时间O(mn)

空间O(mn) - 额外数组缓存结果

Java实现

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

    private int dfs(int[][] matrix, int row, int col, int[][] dp, int prev) {
        if (row > matrix.length - 1 || row < 0 || col > matrix[0].length - 1 || col < 0 || matrix[row][col] <= prev) {
            return 0;
        }
        if (dp[row][col] != 0) {
            return dp[row][col];
        }
        int left = dfs(matrix, row, col - 1, dp, matrix[row][col]);
        int right = dfs(matrix, row, col + 1, dp, matrix[row][col]);
        int up = dfs(matrix, row - 1, col, dp, matrix[row][col]);
        int down = dfs(matrix, row + 1, col, dp, matrix[row][col]);
        dp[row][col] = Math.max(left, Math.max(right, Math.max(up, down))) + 1;
        return dp[row][col];
    }
}

flood fill题型总结

LeetCode 题目总结