53 lines
1.7 KiB
Python
53 lines
1.7 KiB
Python
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"""
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动态规划的核心：
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将大问题分解为多个小问题，通过解决一个个小问题，
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并保存解决每个小问题时的状态最终解决大问题
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动态规划实现找零：
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1. 先看找零1元需要多少：1
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2. 找零2元需要多少：两张1元
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3. 找零3元需要多少：找零2元的结果+找零1元的结果
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"""
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# 动态规划找零
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def dp_rec_mc1(changes: list[int], cash: int):
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min_changes = [0 for _ in range(cash + 1)]
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for i in range(1, cash + 1):
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min_amount = i
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for c in filter(lambda x: x <= i, changes):
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temp_min_amount = 1 + min_changes[i - c]
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if temp_min_amount < min_amount:
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min_amount = temp_min_amount
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min_changes[i] = min_amount
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return min_changes[cash]
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# 动态规划找零，并保存每一种找零所需的纸币情况
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def dp_rec_mc2(changes: list[int], cash: int):
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change_used: dict[int, dict[int, int]] = {}
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min_amounts = [0 for _ in range(cash + 1)]
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for i in range(1, cash + 1):
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min_amount = i
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changes_less_then_i = filter(lambda x: x <= i, changes)
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for c in changes_less_then_i:
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temp_min_amount = 1 + min_amounts[i - c]
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if temp_min_amount < min_amount:
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min_amount = temp_min_amount
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if i - c > 0:
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change_used[i] = change_used[i - c].copy()
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if change_used[i].get(c):
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change_used[i][c] += 1
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else:
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change_used[i][c] = 1
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else:
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change_used[i] = {c: 1}
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min_amounts[i] = min_amount
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if min_amount == i:
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change_used[i] = {1: i}
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return change_used[cash]
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