Problem Statement

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.

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:

• m == grid.length
• n == grid[i].length
• 1 <= m, n <= 200
• 0 <= grid[i][j] <= 100

Problem Link

Minimum Path Sum - LeetCode

Code

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