Minimum Path Sum

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.

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 Array Dynamic Programming

 

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        for(int i=1;i<grid.size();i++)
            grid[i][0]=grid[i-1][0]+grid[i][0];
        for(int j=1;j<grid[0].size();j++)
            grid[0][j]=grid[0][j-1]+grid[0][j];
        for(int i=1;i<grid.size();i++)
            for(int j=1;j<grid[0].size();j++)
                grid[i][j]=grid[i][j-1]<grid[i-1][j] ? grid[i][j-1]+grid[i][j] : grid[i-1][j]+grid[i][j];
        return grid[grid.size()-1][grid[0].size()-1];
    }
};