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.

题目：从矩阵中找一条从左上角到右下角的路线，求最小路径和

思路：dp问题，dp[i][j]表示从左上节点走到[i,j]节点的最小路径和。注意在第一行时候只能从左往右走，第一列时候只能从上往下走。

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