43 lines
1.1 KiB
Python
43 lines
1.1 KiB
Python
"""
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找零问题 — 贪心算法
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使用最少硬币凑出指定金额
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"""
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def min_coins_greedy(coins, amount):
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"""贪心找零（硬币面额需满足贪心选择性质）"""
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coins_sorted = sorted(coins, reverse=True)
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result = []
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remaining = amount
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for coin in coins_sorted:
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while remaining >= coin:
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result.append(coin)
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remaining -= coin
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return result
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def min_coins_dp(coins, amount):
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"""动态规划找零（通用解法）"""
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MAX = float('inf')
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dp = [MAX] * (amount + 1)
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dp[0] = 0
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for i in range(1, amount + 1):
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for coin in coins:
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if i >= coin:
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dp[i] = min(dp[i], dp[i - coin] + 1)
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return dp[amount] if dp[amount] != MAX else -1
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if __name__ == "__main__":
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coins = [1, 5, 10, 25]
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amount = 63
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greedy_result = min_coins_greedy(coins, amount)
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dp_result = min_coins_dp(coins, amount)
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print(f"硬币面额: {coins}")
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print(f"需要凑出: {amount}")
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print(f"贪心结果: {greedy_result} (共 {len(greedy_result)} 枚)")
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print(f"DP最少数量: {dp_result} 枚")
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