Here, We see Minimum Path Sum LeetCode Solution. This Leetcode problem is done in many programming languages like C++, Java, JavaScript, Python, etc. with different approaches.

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Minimum Path Sum LeetCode Solution

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

Minimum Path Sum Leetcode Solution C++

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

Minimum Path Sum Leetcode Solution Java

class Solution {
    public int minPathSum(int[][] grid) {
        if(grid.length == 0)  return 0;
        
        int r = grid.length;
        int c = grid[0].length;
        
        for(int i=0;i<r; i++) {
            for(int j=0; j<c; j++) {
                int leftSum = (j>0) ? grid[i][j-1] : Integer.MAX_VALUE;
                int topSum = (i>0) ? grid[i-1][j] : Integer.MAX_VALUE;
                if(i==0 && j==0) continue;
                
                grid[i][j] += Math.min(leftSum, topSum);
            }
        }
        return grid[r-1][c-1];        
    }
}Code language: JavaScript (javascript)

Minimum Path Sum Leetcode Solution JavaScript

var minPathSum = function(grid) {
    const n = grid.length;
    const m = grid[0].length;
    for(let i=1; i<n; i++) {
        grid[i][0] += grid[i-1][0];
    }
    for(let j=1; j<m; j++) {
        grid[0][j] += grid[0][j-1];
    }
    for(let i=1; i<n; i++) {
        for(let j=1; j<m; j++) {
            grid[i][j] += Math.min(grid[i-1][j], grid[i][j-1]);
        }
    }
    return grid[n-1][m-1];    
};Code language: JavaScript (javascript)

Minimum Path Sum Leetcode Solution Python

class Solution(object):
    def minPathSum(self, grid):
        m = len(grid)
        n = len(grid[0])
        for i in range(1, n):
            grid[0][i] += grid[0][i-1]
        for i in range(1, m):
            grid[i][0] += grid[i-1][0]
        for i in range(1, m):
            for j in range(1, n):
                grid[i][j] += min(grid[i-1][j], grid[i][j-1])
        return grid[-1][-1]