Table of Contents

## Question

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:7Explanation: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`

## Python Solution

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