動機
複習dp
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 1:
Input: grid = [[1,3,1],[1,5,1],[4,2,1]]Output: 7Explanation: 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] <= 100
Sol
class Solution:
def minPathSum(self, grid: List[List[int]]) -> int:
@cache
def dp(i,j):
if i == 0 and j == 0:
return grid[i][j]
elif i < 0 or i >= len(grid) or j < 0 or j >= len(grid[i]):
return float('inf')
else:
return min(dp(i-1,j),dp(i,j-1))+grid[i][j]
return dp(len(grid)-1,len(grid[0])-1)