[Leetcode 59] 64 Minimum Path Sum

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.

Analysis:

Simple DP problem, always choose the minimum path preceed the current position.

Code:

class Solution {
public:
    int minPathSum(vector<vector<int> > &grid) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int m = grid.size();
        int n = grid[0].size();
        int tab[m][n];
        
        tab[0][0] = grid[0][0];
        for (int i=1; i<n; i++)
            tab[0][i] = tab[0][i-1] + grid[0][i];
        
        for (int i=1; i<m; i++)
            tab[i][0] = tab[i-1][0] + grid[i][0];
            
        for (int i=1; i<m; i++)
            for (int j=1; j<n; j++) {
                tab[i][j] = min(tab[i][j-1], tab[i-1][j]) + grid[i][j];
            }
        
        return tab[m-1][n-1];
    }
    
    int min(int &a, int &b) {
        return (a<b)?a:b;
    }
};