64. Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the 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, return 7. Because the path 1→3→1→1→1 minimizes the sum.

Solution：

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.
Note: You can only move either down or right at any point in time.

思路： DP
Time Complexity: O(mn) Space Complexity: O(mn)

如果需要path就是Dijisktra?

Solution Code：

class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;// row
        int n = grid[0].length; // column
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (i == 0 && j != 0) {
                    grid[i][j] = grid[i][j] + grid[i][j - 1];
                } else if (i != 0 && j == 0) {
                    grid[i][j] = grid[i][j] + grid[i - 1][j];
                } else if (i == 0 && j == 0) {
                    grid[i][j] = grid[i][j];
                } else {
                    grid[i][j] = Math.min(grid[i][j - 1], grid[i - 1][j])
                            + grid[i][j];
                }
            }
        }

        return grid[m - 1][n - 1];
    }
}