65 lines
1.7 KiB
Python
65 lines
1.7 KiB
Python
#!/usr/bin/python
|
|
# -*- coding: UTF-8 -*-
|
|
|
|
from typing import List
|
|
|
|
Layer_nums = List[int]
|
|
|
|
|
|
def yh_triangle(nums: List[Layer_nums]) -> int:
|
|
"""
|
|
从根节点开始向下走，过程中经过的节点，只需存储经过它时最小的路径和
|
|
:param nums:
|
|
:return:
|
|
"""
|
|
assert len(nums) > 0
|
|
n = len(nums) # 层数
|
|
memo = [[0]*n for i in range(n)]
|
|
memo[0][0] = nums[0][0]
|
|
|
|
for i in range(1, n):
|
|
for j in range(i+1):
|
|
# 每一层首尾两个数字，只有一条路径可以到达
|
|
if j == 0:
|
|
memo[i][j] = memo[i-1][j] + nums[i][j]
|
|
elif j == i:
|
|
memo[i][j] = memo[i-1][j-1] + nums[i][j]
|
|
else:
|
|
memo[i][j] = min(memo[i-1][j-1] + nums[i][j], memo[i-1][j] + nums[i][j])
|
|
return min(memo[n-1])
|
|
|
|
|
|
def yh_triangle_space_optimization(nums: List[Layer_nums]) -> int:
|
|
assert len(nums) > 0
|
|
n = len(nums)
|
|
memo = [0] * n
|
|
memo[0] = nums[0][0]
|
|
|
|
for i in range(1, n):
|
|
for j in range(i, -1, -1):
|
|
if j == i:
|
|
memo[j] = memo[j-1] + nums[i][j]
|
|
elif j == 0:
|
|
memo[j] = memo[j] + nums[i][j]
|
|
else:
|
|
memo[j] = min(memo[j-1] + nums[i][j], memo[j] + nums[i][j])
|
|
return min(memo)
|
|
|
|
|
|
def yh_triangle_bottom_up(nums: List[Layer_nums]) -> int:
|
|
assert len(nums) > 0
|
|
n = len(nums)
|
|
memo = nums[-1].copy()
|
|
|
|
for i in range(n-1, 0, -1):
|
|
for j in range(i):
|
|
memo[j] = min(memo[j] + nums[i-1][j], memo[j+1] + nums[i-1][j])
|
|
return memo[0]
|
|
|
|
|
|
if __name__ == '__main__':
|
|
nums = [[3], [2, 6], [5, 4, 2], [6, 0, 3, 2]]
|
|
print(yh_triangle(nums))
|
|
print(yh_triangle_space_optimization(nums))
|
|
print(yh_triangle_bottom_up(nums))
|