mirror of
https://github.com/krahets/hello-algo.git
synced 2026-06-28 08:34:28 +00:00
Yudong Jin
d7b2277d2b
* Retranslate Japanese docs with GPT-5.4 * Retranslate Japanese code with GPT-5.4
41 lines
1.1 KiB
Python
41 lines
1.1 KiB
Python
"""
|
|
File: climbing_stairs_dp.py
|
|
Created Time: 2023-06-30
|
|
Author: krahets (krahets@163.com)
|
|
"""
|
|
|
|
|
|
def climbing_stairs_dp(n: int) -> int:
|
|
"""階段登り：動的計画法"""
|
|
if n == 1 or n == 2:
|
|
return n
|
|
# 部分問題の解を保存するために dp テーブルを初期化
|
|
dp = [0] * (n + 1)
|
|
# 初期状態：最小部分問題の解をあらかじめ設定
|
|
dp[1], dp[2] = 1, 2
|
|
# 状態遷移：小さい部分問題から大きい部分問題へ順に解く
|
|
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:
|
|
"""階段登り：空間最適化した動的計画法"""
|
|
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"{n} 段の階段を上る方法は全部で {res} 通りです")
|
|
|
|
res = climbing_stairs_dp_comp(n)
|
|
print(f"{n} 段の階段を上る方法は全部で {res} 通りです")
|