LeetCode: Minimum Path Sum

最新推荐文章于 2018-09-23 20:06:35 发布

Tingmei

最新推荐文章于 2018-09-23 20:06:35 发布

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分类专栏：算法 C++ 文章标签： path numbers function

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本文探讨了如何使用动态规划算法解决最小路径和问题，在给定的m×n网格中找到从左上角到右下角的路径，使得路径上的数字之和最小。通过迭代更新每个节点的最小路径和，最终得到终点的最优路径。

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Problem:

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 minPathSum(vector<vector<int> > &grid) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int y = grid.size();
        if (y == 0) return 0;
        int x = grid[0].size();
        
        for (int i = 1; i < x; ++i)
            grid[0][i] += grid[0][i-1];
        for (int i = 1; i < y; ++i)
            grid[i][0] += grid[i-1][0];
            
        int a, b;
        for(int j = 1; j < y; ++j)
        {
            for (int i = 1; i < x; ++i)
            {
                a = grid[j][i] + grid[j-1][i];
                b = grid[j][i] + grid[j][i-1];
                grid[j][i] = a > b ? b : a;
            }
        }
        return grid[y-1][x-1];
    }
};