2022-12-23 00:44:40 +08:00
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"""
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2022-11-25 02:04:38 +08:00
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File: binary_search.py
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2022-12-03 22:52:58 +08:00
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Created Time: 2022-11-26
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Author: timi (xisunyy@163.com)
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2022-12-23 00:44:40 +08:00
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"""
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2022-11-25 02:04:38 +08:00
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2023-04-09 05:05:35 +08:00
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2023-03-23 18:51:56 +08:00
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def binary_search(nums: list[int], target: int) -> int:
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2023-04-09 05:05:35 +08:00
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"""二分查找(双闭区间)"""
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2022-12-03 22:52:58 +08:00
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# 初始化双闭区间 [0, n-1] ,即 i, j 分别指向数组首元素、尾元素
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i, j = 0, len(nums) - 1
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2023-05-21 04:51:32 +08:00
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# 循环,当搜索区间为空时跳出(当 i > j 时为空)
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2022-12-03 22:52:58 +08:00
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while i <= j:
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2023-08-20 14:51:39 +08:00
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# 理论上 Python 的数字可以无限大(取决于内存大小),无须考虑大数越界问题
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2023-04-09 05:05:35 +08:00
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m = (i + j) // 2 # 计算中点索引 m
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2023-05-21 04:51:32 +08:00
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if nums[m] < target:
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i = m + 1 # 此情况说明 target 在区间 [m+1, j] 中
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elif nums[m] > target:
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j = m - 1 # 此情况说明 target 在区间 [i, m-1] 中
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2022-12-03 22:52:58 +08:00
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else:
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2023-04-09 05:05:35 +08:00
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return m # 找到目标元素,返回其索引
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return -1 # 未找到目标元素,返回 -1
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2022-12-03 22:52:58 +08:00
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2023-05-18 20:27:58 +08:00
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def binary_search_lcro(nums: list[int], target: int) -> int:
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2023-12-02 06:21:34 +08:00
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"""二分查找(左闭右开区间)"""
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# 初始化左闭右开区间 [0, n) ,即 i, j 分别指向数组首元素、尾元素+1
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2022-12-03 22:52:58 +08:00
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i, j = 0, len(nums)
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# 循环,当搜索区间为空时跳出(当 i = j 时为空)
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while i < j:
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2023-04-09 05:05:35 +08:00
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m = (i + j) // 2 # 计算中点索引 m
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2023-05-21 04:51:32 +08:00
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if nums[m] < target:
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i = m + 1 # 此情况说明 target 在区间 [m+1, j) 中
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elif nums[m] > target:
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j = m # 此情况说明 target 在区间 [i, m) 中
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else:
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return m # 找到目标元素,返回其索引
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2023-04-09 05:05:35 +08:00
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return -1 # 未找到目标元素,返回 -1
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2022-12-03 22:52:58 +08:00
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2023-04-09 05:30:02 +08:00
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"""Driver Code"""
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2023-04-09 05:05:35 +08:00
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if __name__ == "__main__":
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2023-05-22 22:03:57 +08:00
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target = 6
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nums = [1, 3, 6, 8, 12, 15, 23, 26, 31, 35]
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2022-12-03 22:52:58 +08:00
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# 二分查找(双闭区间)
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2023-03-12 18:49:52 +08:00
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index: int = binary_search(nums, target)
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2022-12-03 22:52:58 +08:00
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print("目标元素 6 的索引 = ", index)
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2023-04-09 05:05:35 +08:00
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2023-12-02 06:21:34 +08:00
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# 二分查找(左闭右开区间)
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2023-05-18 20:27:58 +08:00
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index: int = binary_search_lcro(nums, target)
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2022-12-03 22:52:58 +08:00
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print("目标元素 6 的索引 = ", index)
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