You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
41 lines
974 B
41 lines
974 B
"""
|
|
File: climbing_stairs_dp.py
|
|
Created Time: 2023-06-30
|
|
Author: krahets (krahets@163.com)
|
|
"""
|
|
|
|
|
|
def climbing_stairs_dp(n: int) -> int:
|
|
"""爬楼梯：动态规划"""
|
|
if n == 1 or n == 2:
|
|
return n
|
|
# 初始化 dp 表，用于存储子问题的解
|
|
dp = [0] * (n + 1)
|
|
# 初始状态：预设最小子问题的解
|
|
dp[1], dp[2] = 1, 2
|
|
# 状态转移：从较小子问题逐步求解较大子问题
|
|
for i in range(3, n + 1):
|
|
dp[i] = dp[i - 1] + dp[i - 2]
|
|
return dp[n]
|
|
|
|
|
|
def climbing_stairs_dp_comp(n: int) -> int:
|
|
"""爬楼梯：空间优化后的动态规划"""
|
|
if n == 1 or n == 2:
|
|
return n
|
|
a, b = 1, 2
|
|
for _ in range(3, n + 1):
|
|
a, b = b, a + b
|
|
return b
|
|
|
|
|
|
"""Driver Code"""
|
|
if __name__ == "__main__":
|
|
n = 9
|
|
|
|
res = climbing_stairs_dp(n)
|
|
print(f"爬 {n} 阶楼梯共有 {res} 种方案")
|
|
|
|
res = climbing_stairs_dp_comp(n)
|
|
print(f"爬 {n} 阶楼梯共有 {res} 种方案")
|