[LeetCode] Minimum Path Sum

最小路径和：动态规划解决多维数组最短路径问题

最新推荐文章于 2019-05-17 20:06:05 发布

原创最新推荐文章于 2019-05-17 20:06:05 发布 · 276 阅读

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本文介绍了一种使用动态规划方法解决多维数组中从左上角到右下角最小路径和的问题。通过构建状态转移矩阵并利用递推公式，实现了高效求解路径和的过程。

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) {
        int m = grid.size() - 1,n = grid[0].size() - 1;
        vector<vector<int> > num(m + 1,vector<int>(n +1));
        if(m == -1) return 0;
        num[m][n] = grid[m][n];
        for(int i = n - 1;i >= 0;i --)
            num[m][i] = grid[m][i] + num[m][i + 1];
        for(int i = m - 1;i >= 0;i --)
            num[i][n] = grid[i][n] + num[i + 1][n];
        for(int i = m - 1;i >= 0;i --){
            for(int j = n - 1;j >= 0;j --){
                num[i][j] = min(num[i + 1][j],num[i][j + 1]) + grid[i][j];
            }
        }
        return num[0][0];
    }
};