64. Minimum Path Sum

Problem Link

Description

---

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] <= 200

Solution

---

Python3

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