mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-26 00:16:28 +08:00
a005c6ebd3
* Update avatar's link in the landing page * Bug fixes * Move assets folder from overrides to docs * Reduce figures' corner radius * Update copyright * Update header image * Krahets -> krahets * Update the landing page
29 lines
809 B
Python
29 lines
809 B
Python
"""
|
|
File: climbing_stairs_constraint_dp.py
|
|
Created Time: 2023-06-30
|
|
Author: krahets (krahets@163.com)
|
|
"""
|
|
|
|
|
|
def climbing_stairs_constraint_dp(n: int) -> int:
|
|
"""带约束爬楼梯：动态规划"""
|
|
if n == 1 or n == 2:
|
|
return 1
|
|
# 初始化 dp 表，用于存储子问题的解
|
|
dp = [[0] * 3 for _ in range(n + 1)]
|
|
# 初始状态：预设最小子问题的解
|
|
dp[1][1], dp[1][2] = 1, 0
|
|
dp[2][1], dp[2][2] = 0, 1
|
|
# 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][1] = dp[i - 1][2]
|
|
dp[i][2] = dp[i - 2][1] + dp[i - 2][2]
|
|
return dp[n][1] + dp[n][2]
|
|
|
|
|
|
"""Driver Code"""
|
|
if __name__ == "__main__":
|
|
n = 9
|
|
|
|
res = climbing_stairs_constraint_dp(n)
|
|
print(f"爬 {n} 阶楼梯共有 {res} 种方案")
|