Leecode #64. 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。

解题思路

​ 典型的dp题

class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        cols = len(grid)
        rows = len(grid[0])

        arr = [[0]*rows for _ in range(cols)]
        arr[0][0] = grid[0][0]
        for i in range(1, rows):
            arr[0][i] = arr[0][i-1] + grid[0][i]
        for i in range(1, cols):
            arr[i][0] = arr[i-1][0] + grid[i][0]
            for j in range(1, rows):
                arr[i][j] = min(arr[i-1][j], arr[i][j-1]) + grid[i][j]
        return arr[-1][-1]

空间优化

    def minPathSum(self, grid: List[List[int]]) -> int:
        cols = len(grid)
        rows = len(grid[0])

        arr = [0]*rows
        arr[0] = grid[0][0]
        for i in range(1, rows):
            arr[i] = arr[i-1] + grid[0][i]
        for i in range(1, cols):
            arr[0] = arr[0] + grid[i][0]
            for j in range(1, rows):
                arr[j] = min(arr[j], arr[j-1]) + grid[i][j]
        return arr[-1]

在空间和时间上都是最优解了