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