# [Solved] 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.

## 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: 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

## 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]