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53 lines
1.9 KiB
53 lines
1.9 KiB
8 months ago
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"""
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File: binary_search.py
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Created Time: 2022-11-26
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Author: timi (xisunyy@163.com)
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"""
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def binary_search(nums: list[int], target: int) -> int:
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"""二分搜尋（雙閉區間）"""
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# 初始化雙閉區間 [0, n-1] ，即 i, j 分別指向陣列首元素、尾元素
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i, j = 0, len(nums) - 1
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# 迴圈，當搜尋區間為空時跳出（當 i > j 時為空）
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while i <= j:
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# 理論上 Python 的數字可以無限大（取決於記憶體大小），無須考慮大數越界問題
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m = (i + j) // 2 # 計算中點索引 m
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if nums[m] < target:
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i = m + 1 # 此情況說明 target 在區間 [m+1, j] 中
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elif nums[m] > target:
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j = m - 1 # 此情況說明 target 在區間 [i, m-1] 中
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else:
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return m # 找到目標元素，返回其索引
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return -1 # 未找到目標元素，返回 -1
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def binary_search_lcro(nums: list[int], target: int) -> int:
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"""二分搜尋（左閉右開區間）"""
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# 初始化左閉右開區間 [0, n) ，即 i, j 分別指向陣列首元素、尾元素+1
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i, j = 0, len(nums)
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# 迴圈，當搜尋區間為空時跳出（當 i = j 時為空）
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while i < j:
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m = (i + j) // 2 # 計算中點索引 m
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if nums[m] < target:
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i = m + 1 # 此情況說明 target 在區間 [m+1, j) 中
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elif nums[m] > target:
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j = m # 此情況說明 target 在區間 [i, m) 中
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else:
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return m # 找到目標元素，返回其索引
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return -1 # 未找到目標元素，返回 -1
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"""Driver Code"""
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if __name__ == "__main__":
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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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# 二分搜尋（雙閉區間）
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index = binary_search(nums, target)
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print("目標元素 6 的索引 = ", index)
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# 二分搜尋（左閉右開區間）
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index = binary_search_lcro(nums, target)
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print("目標元素 6 的索引 = ", index)
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