leetcode64. Minimum Path Sum

给一个非负数二维数组，从左上到右下，最短的路径

只能向右或者向下走

Example:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

动态规划

这里面存在一个问题，要想求出下一步的最短距离，必须求出上一步的最短距离

边界：mins[0][0] = grid[0][0]

状态转移公式3个：

1. grid[0]那一排，依赖于左侧
2. grid[x][0]那一列，依赖于上侧
3. 其他的依赖于左侧和上侧

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

        int[][] mins = new int[grid.length][grid[0].length];

        for (int i = 0; i < grid.length; i++) {
            int[] gridInner = grid[i];
            for (int j = 0; j < gridInner.length; j++) {
                if (i == 0) {
                    if (j == 0) {
                        mins[i][j] = grid[i][j];
                    } else {
                        mins[i][j] = mins[i][j - 1] + grid[i][j];
                    }
                } else {
                    if (j == 0) {
                        mins[i][j] = mins[i - 1][j] + grid[i][j];
                    } else {
                        mins[i][j] = Math.min(mins[i - 1][j], mins[i][j - 1]) + grid[i][j];
                    }
                }
            }
        }
        return mins[grid.length - 1][grid[0].length - 1];
    }
}