mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-27 16:56:30 +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
58 lines
1.6 KiB
Python
58 lines
1.6 KiB
Python
"""
|
||
File: coin_change_ii.py
|
||
Created Time: 2023-07-10
|
||
Author: krahets (krahets@163.com)
|
||
"""
|
||
|
||
|
||
def coin_change_ii_dp(coins: list[int], amt: int) -> int:
|
||
"""零钱兑换 II：动态规划"""
|
||
n = len(coins)
|
||
# 初始化 dp 表
|
||
dp = [[0] * (amt + 1) for _ in range(n + 1)]
|
||
# 初始化首列
|
||
for i in range(n + 1):
|
||
dp[i][0] = 1
|
||
# 状态转移
|
||
for i in range(1, n + 1):
|
||
for a in range(1, amt + 1):
|
||
if coins[i - 1] > a:
|
||
# 若超过目标金额，则不选硬币 i
|
||
dp[i][a] = dp[i - 1][a]
|
||
else:
|
||
# 不选和选硬币 i 这两种方案之和
|
||
dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]
|
||
return dp[n][amt]
|
||
|
||
|
||
def coin_change_ii_dp_comp(coins: list[int], amt: int) -> int:
|
||
"""零钱兑换 II：空间优化后的动态规划"""
|
||
n = len(coins)
|
||
# 初始化 dp 表
|
||
dp = [0] * (amt + 1)
|
||
dp[0] = 1
|
||
# 状态转移
|
||
for i in range(1, n + 1):
|
||
# 正序遍历
|
||
for a in range(1, amt + 1):
|
||
if coins[i - 1] > a:
|
||
# 若超过目标金额，则不选硬币 i
|
||
dp[a] = dp[a]
|
||
else:
|
||
# 不选和选硬币 i 这两种方案之和
|
||
dp[a] = dp[a] + dp[a - coins[i - 1]]
|
||
return dp[amt]
|
||
|
||
|
||
"""Driver Code"""
|
||
if __name__ == "__main__":
|
||
coins = [1, 2, 5]
|
||
amt = 5
|
||
|
||
# 动态规划
|
||
res = coin_change_ii_dp(coins, amt)
|
||
print(f"凑出目标金额的硬币组合数量为 {res}")
|
||
|
||
# 空间优化后的动态规划
|
||
res = coin_change_ii_dp_comp(coins, amt)
|
||
print(f"凑出目标金额的硬币组合数量为 {res}")
|