064-minimum-path-sum.py

"""
最小路径和

给定一个包含非负整数的 m x n 网格，请找出一条从左上角到右下角的路径，使得路径上的数字总和为最小。

说明：每次只能向下或者向右移动一步。

示例:

输入:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
输出: 7
解释: 因为路径 1→3→1→1→1 的总和最小。
"""
from typing import List


def min_path_sum(grid: List[List[int]]) -> int:
    if not grid:
        return 0

    m, n = len(grid), len(grid[0])
    if m == 0 or n == 0:
        return 0

    dp = [[0 for _ in range(n)] for _ in range(m)]

    for i in range(m):
        for j in range(n):
            if i == 0 and j == 0:
                dp[i][j] = grid[i][j]
            elif i == 0:
                dp[i][j] = dp[i][j - 1] + grid[i][j]
            elif j == 0:
                dp[i][j] = dp[i - 1][j] + grid[i][j]
            else:
                dp[i][j] = min(dp[i - 1][j] + grid[i][j], dp[i][j - 1] + grid[i][j])

    return dp[m - 1][n - 1]


if __name__ == '__main__':
    print(min_path_sum([[], []]))
    print(min_path_sum([[8]]))
    print(min_path_sum([[1, 3, 1], [1, 5, 1], [4, 2, 1]]))