mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-26 15:36:29 +08:00
e720aa2d24
* Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
60 lines
1.8 KiB
Python
60 lines
1.8 KiB
Python
"""
|
|
File: coin_change.py
|
|
Created Time: 2023-07-10
|
|
Author: Krahets (krahets@163.com)
|
|
"""
|
|
|
|
|
|
def coin_change_dp(coins: list[int], amt: int) -> int:
|
|
"""零钱兑换：动态规划"""
|
|
n = len(coins)
|
|
MAX = amt + 1
|
|
# 初始化 dp 表
|
|
dp = [[0] * (amt + 1) for _ in range(n + 1)]
|
|
# 状态转移：首行首列
|
|
for a in range(1, amt + 1):
|
|
dp[0][a] = MAX
|
|
# 状态转移：其余行和列
|
|
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 这两种方案的较小值
|
|
dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)
|
|
return dp[n][amt] if dp[n][amt] != MAX else -1
|
|
|
|
|
|
def coin_change_dp_comp(coins: list[int], amt: int) -> int:
|
|
"""零钱兑换：空间优化后的动态规划"""
|
|
n = len(coins)
|
|
MAX = amt + 1
|
|
# 初始化 dp 表
|
|
dp = [MAX] * (amt + 1)
|
|
dp[0] = 0
|
|
# 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 这两种方案的较小值
|
|
dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)
|
|
return dp[amt] if dp[amt] != MAX else -1
|
|
|
|
|
|
"""Driver Code"""
|
|
if __name__ == "__main__":
|
|
coins = [1, 2, 5]
|
|
amt = 4
|
|
|
|
# 动态规划
|
|
res = coin_change_dp(coins, amt)
|
|
print(f"凑到目标金额所需的最少硬币数量为 {res}")
|
|
|
|
# 空间优化后的动态规划
|
|
res = coin_change_dp_comp(coins, amt)
|
|
print(f"凑到目标金额所需的最少硬币数量为 {res}")
|