minimum-path-sum.py

'''
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:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.
'''


class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:

        # Approach one
        n , m = len(grid), len(grid[0])
        for i in range(1,m): grid[0][i] += grid[0][i-1]
        for i in range(1,n): grid[i][0] += grid[i-1][0]
        for i in range(1,n):
            for j in range(1,m):
                grid[i][j] += min(grid[i-1][j],grid[i][j-1])
        return grid[n-1][m-1]