64. Minimum Path Sum

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本文介绍了一个经典动态规划问题——给定一个填充了非负数的矩阵，寻找从左上角到右下角路径中数字之和最小的路径。文章通过示例代码详细解释了解决方案，采用动态规划的方法逐步计算出最优解。

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.
题目大意：继续动态规划

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {
        int F[200][200];
        int rows = grid.size(), cols = grid[0].size();
        F[0][0] = grid[0][0];
        for(int j = 1; j < cols; ++j)
            F[0][j] = F[0][j - 1] + grid[0][j];
        for(int i = 1; i < rows; ++i){
            F[i][0] = F[i - 1][0] + grid[i][0];
            for(int j = 1; j < cols; ++j)
                F[i][j] = min(F[i][j - 1], F[i - 1][j]) + grid[i][j];
        }
        return F[rows - 1][cols - 1];
    }
};