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:

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

難度：medium

題目：給定m * n的格子，找出從左上角到右下角和最小的路徑。

思路：動態規劃，狀態轉移方程
grid[i][j] = grid[i][j] + min(grid[i - 1][j], grid[i][j - 1]

Runtime: 4 ms, faster than 97.83% of Java online submissions for Minimum Path Sum.
Memory Usage: 40.8 MB, less than 1.47% of Java online submissions for Minimum Path Sum.

class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length, n = grid[0].length;
        for (int i = 1; i < n; i++) {
            grid[0][i] += grid[0][i - 1];
        }
        for (int i = 1; i < m; i++) {
            grid[i][0] += grid[i - 1][0];
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                grid[i][j] += Math.min(grid[i - 1][j], grid[i][j - 1]);
            }
        }
        
        return grid[m - 1][n - 1];
    }
}