[LeetCode] Minimum Path Sum

zjjee

于 2014-11-17 16:29:23 发布

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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。

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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];
    }
};