最小路径和—动态规划

思路：定义一个网格大小的二维数组，先为第一行和第一列赋值。然后后面的值等于网格当前值加上二维数组上面和右面的最小的值。

int minPathSum(vector<vector<int>> &grid) {
        // write your code here
        int row = grid.size();
        int col = grid[0].size();
        int ** sum = new int*[row];
        for (int i = 0; i < row; i++) {
            sum[i] = new int[col];
        }
        sum[0][0] = grid[0][0];
        for (int i = 1; i < row; i++) {
            sum[i][0] = sum[i-1][0] + grid[i][0];
        }
        for (int i = 0; i < col; i++) {
            sum[0][i] = sum[0][i-1] + grid[0][i];
        }
        for (int i = 1; i < row; i++) {
            for (int j= 1; j < col; j++) {
                int min_sum = min(sum[i-1][j], sum[i][j-1]);
                sum[i][j] = min_sum + grid[i][j];
            }
        }
        return sum[row-1][col-1];
    }