64 Minimum Path Sum

64. Minimum Path Sum

1. Question

Given amxngrid filled with non-negative numbers, find a path from top left to bottom right whichminimizesthe sum of all numbers along its path.

Note:You can only move either down or right at any point in time.

Example 1:

[[1,3,1],
 [1,5,1],
 [4,2,1]]

Given the above grid map, return7. Because the path 1→3→1→1→1 minimizes the sum.

2. Implementation

(1) DP

class Solution {
    public int minPathSum(int[][] grid) {
        if (grid == null || grid.length == 0) {
            return 0;
        }

        int m = grid.length, n = grid[0].length;
        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];

        for (int i = 1; i < m; i++) {
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }

        for (int j = 1; j < n; j++) {
            dp[0][j] = dp[0][j - 1] + grid[0][j];
        }

        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j] = grid[i][j] + Math.min(dp[i][j - 1], dp[i - 1][j]);
            }
        }
        return dp[m - 1][n - 1];
    }
}

3. Time & Space Complexity

时间复杂度O(mn), 空间复杂度O(mn)