minimum-path-sum

原创于 2019-06-26 09:02:58 发布 · 89 阅读

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#动态规划 #数组

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本文深入探讨了在非负数网格中寻找从左上角到右下角的最小路径和问题，采用动态规划方法，通过优化辅助数组实现高效求解。适用于算法竞赛及面试准备。

【题目描述】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.

【解题思路】动态规划，仍用一个辅助数组

【考查内容】动态规划，数组

class Solution {
public:
    int min(int a,int b){
        return a < b? a : b;
    }
    
    int minPathSum(vector<vector<int>>& grid) {
        int row = grid.size();
        int col = grid[0].size();
        if(row == 1 && col == 1)
        return grid[0][0];
        vector<int>vec(row,0);
        vec[0] = grid[0][0];
        for(int k = 1; k < row; k++)
            vec[k] = grid[k][0]+vec[k-1];
        for(int j = 1; j < col; j++)
        for(int i = 0; i < row; i++){
            if(i == 0)
                vec[i] += grid[i][j];
            else
                vec[i] = min(vec[i],vec[i-1])+grid[i][j];
        }
        return vec[row-1];
    }
};