Minimum Path Sum — LeetCode 64 Python Solution

The problem

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

grid = [[1,3,1],[1,5,1],[4,2,1]]

Output

7

Explanation

Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.

Python solution

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

Complexity

Pattern: Matrix and Grid

Treat a 2-D grid as a graph whose neighbours are the four adjacent cells. LeetCode 64. Minimum Path Sum is filed here because LeetCode tags it Matrix, which is the vocabulary this hub collects.

The matrix and grid guide has the Python template for the pattern and the 216 LeetCode problems that use it.

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