LeetCode Minimum Path Sum

最小路径和问题解析

最新推荐文章于 2022-11-04 10:58:54 发布

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本文介绍了一个经典的算法问题——寻找二维网格中从左上角到右下角的最小路径和。通过动态规划的方法解决了该问题，并给出了详细的实现过程。

题目：

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:
	//DP 
    int minPathSum(vector<vector<int> > &grid) {
    	int m = grid.size();
    	int n = grid[0].size();
    	if(m == 0 || n == 0)
    		return 0;
    	//初始化 
    	for(int j = 1; j < n; j++)
    		grid[0][j] += grid[0][j-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] += min(grid[i][j-1], grid[i-1][j]);
		return grid[m-1][n-1];   
    }
private:
	int min(int &a, int &b) {
		return a < b? a : b;
	}
};