Minimum Path Sum

最小路径和算法解析

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本文介绍了一个算法问题：在一个非负数构成的矩阵中寻找从左上角到右下角的路径，使得路径上的数字之和最小。文章详细解释了递归动态规划的方法，并提供了完整的C++代码实现。

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.

class Solution {
public:
	int rows,cols;
    int minPathSum(vector<vector<int> > &grid) {
        if(!grid.size() || !grid[0].size())return 0;
		rows = grid.size();
		cols = grid[0].size();

		vector<vector<int> >dp;
		vector<int> v;
		for(int i = 0; i < rows; i++)
		{
			v.clear();//vector二维初始化，不要像数组那样直接dp[i][j] = xx,越界，习惯！
			for(int j = 0; j < cols; j++)
				v.push_back(-1);
			dp.push_back(v);
		}
			

		return minSum(0, 0, dp, grid);
		
    }

	int minSum(int r, int c, vector<vector<int> > &dp,vector<vector<int> > &grid)
	{
		if(r == rows - 1 && c == cols - 1)
		{
			dp[r][c] = grid[r][c];
			return dp[r][c];
		}

		if(dp[r][c] != -1)return dp[r][c];
		int rst = INT_MAX;

		if(c < cols - 1)rst = grid[r][c] + minSum(r, c + 1, dp, grid);
		if(r < rows - 1)rst = min(rst, grid[r][c] + minSum(r + 1, c, dp, grid));

		dp[r][c] = rst;
		return rst;
	}
};