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.

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

class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        
        // Initialize the first row and first column
        for (int i = 1; i < m; i++) {
            grid[i][0] += grid[i - 1][0];
        }
        
        for (int j = 1; j < n; j++) {
            grid[0][j] += grid[0][j - 1];
        }
        
        // Calculate the minimum path sum for each cell
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                grid[i][j] += Math.min(grid[i - 1][j], grid[i][j - 1]);
            }
        }
        
        return grid[m - 1][n - 1]; // The bottom-right cell contains the minimum path sum
    }
}