LeetCode 64: Minimum Path Sum

最新推荐文章于 2024-06-04 23:33:59 发布

claviclelau

最新推荐文章于 2024-06-04 23:33:59 发布

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分类专栏： LeetCode

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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。详细阐述了递归方法结合动态规划思想解决该问题的过程，并提供了一段C++实现代码。

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Difficulty: 3

Frequency: 3

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.

Solution:

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        vector<vector<int> >pathSumMatrix(grid);
        for (int i = 0; i<grid.size(); i++)
        {
            for (int j = 0; j<grid[i].size(); j++)
            {
                pathSumMatrix[i][j] = -1;
            }
        }
        pathSumMatrix[0][0] = grid[0][0];
        return minPathSumRecursive(grid, pathSumMatrix, grid.size() - 1, grid[0].size() - 1);
    }
    int minPathSumRecursive(vector<vector<int> > &grid, vector<vector<int> > &pathSumMatrix, int i_row, int i_col)
    {
        if (pathSumMatrix[i_row][i_col]!=-1)
            return pathSumMatrix[i_row][i_col];
        
        int i_up = i_row==0?0x7FFFFFFF:minPathSumRecursive(grid, pathSumMatrix, i_row - 1, i_col);
        int i_left = i_col==0?0x7FFFFFFF:minPathSumRecursive(grid, pathSumMatrix, i_row, i_col - 1);
        return pathSumMatrix[i_row][i_col] = (i_up<i_left?i_up:i_left) + grid[i_row][i_col];
    }
};

Notes:

No comment. Haha.