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Minimum Path Sum

Tags : array, matrix, dynamic-programming, leetcode, cpp, medium

Problem Statement - link #

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.

Examples #

Example 1: 

Input: grid = [[1,3,1],[1,5,1],[4,2,1]]
Output: 7
Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.

Example 2:

Input: grid = [[1,2,3],[4,5,6]]
Output: 12

Constraints #

Solutions #


class Solution {
public:
    int minPathSum(vector<vector<int>>& grid) {

        int m = grid.size();
        int n = grid[0].size();
        
        for(int i=0; i<m; i++){
            for(int j=0; j<n; j++){
                if(i==0 and j>0)
                    grid[i][j]+=grid[i][j-1];
                else if(j==0 and i>0)
                    grid[i][j]+=grid[i-1][j];
                else if(i>0 && j>0)
                    grid[i][j] += min(grid[i-1][j],grid[i][j-1]);
            }
        }
        return grid[m-1][n-1];
    }
};