62 lines
1.5 KiB
Python
62 lines
1.5 KiB
Python
"""
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递归三定律：
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1 递 归 算 法 必 须 具 有 基 本 情 况
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2 递 归 算 法 必 须 向 基 本 情 况 靠 近
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3 递 归 算 法 必 须 以 递 归 方 式 调 用 自 身
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"""
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def recursive_sum(nums: list):
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if 1 == len(nums):
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return nums[0]
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return nums[0] + recursive_sum(nums[1:])
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# 使用递归的方式实现进制转换
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def recursive_num_conversion(num: int) -> str:
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if num == 0:
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return ''
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return recursive_num_conversion(num // 2) + str(num % 2)
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# 找零问题：类似贪婪，经量找出最少纸币搭配
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def rec_mc1(changes: list[int], cash: int):
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# 全用1元纸币时最少找零数
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min_amount = cash
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try:
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if changes.index(cash):
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return 1
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except Exception as e:
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for c in changes:
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# cash - c，表示使用了一张面额为c的来找零，所以需要+1
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num = 1 + rec_mc1(changes, cash-c)
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if num < min_amount:
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min_amount = num
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return min_amount
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def rec_mc2(changes: list[int], cash: int, min_changes: int,):
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min_amount = cash
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try:
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if changes.index(cash):
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min_changes[cash] = 1
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return 1
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except Exception as e:
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if min_changes[cash] > 0:
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return min_changes[cash]
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else:
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for c in changes:
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num = 1 + rec_mc2(changes, cash - c, min_changes)
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if num < min_amount:
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min_amount = num
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min_changes[cash] = min_amount
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return min_amount
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