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* Retranslate the complete English edition from Simplified Chinese * Polish three English explanations after reader-focused review
55 lines
2.0 KiB
Python
55 lines
2.0 KiB
Python
"""
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File: binary_search_insertion.py
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Created Time: 2023-08-04
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Author: krahets (krahets@163.com)
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"""
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def binary_search_insertion_simple(nums: list[int], target: int) -> int:
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"""Find an insertion point using binary search (no duplicates)"""
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i, j = 0, len(nums) - 1 # Initialize the closed interval [0, n-1]
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while i <= j:
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m = (i + j) // 2 # Calculate the midpoint index m
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if nums[m] < target:
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i = m + 1 # Target must be in [m+1, j] if it exists
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elif nums[m] > target:
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j = m - 1 # Target must be in [i, m-1] if it exists
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else:
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return m # Target was found; return insertion point m
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# Target was not found; return insertion point i
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return i
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def binary_search_insertion(nums: list[int], target: int) -> int:
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"""Find an insertion point using binary search (with duplicates)"""
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i, j = 0, len(nums) - 1 # Initialize the closed interval [0, n-1]
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while i <= j:
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m = (i + j) // 2 # Calculate the midpoint index m
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if nums[m] < target:
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i = m + 1 # Target must be in [m+1, j] if it exists
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elif nums[m] > target:
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j = m - 1 # Target must be in [i, m-1] if it exists
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else:
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j = m - 1 # Continue in [i, m-1] to find the rightmost element smaller than target
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# Return insertion point i
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return i
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"""Driver code"""
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if __name__ == "__main__":
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# Array with no duplicate elements
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nums = [1, 3, 6, 8, 12, 15, 23, 26, 31, 35]
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print(f"\nArray nums = {nums}")
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# Find an insertion point using binary search
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for target in [6, 9]:
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index = binary_search_insertion_simple(nums, target)
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print(f"Insertion index for element {target}: {index}")
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# Array containing duplicate elements
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nums = [1, 3, 6, 6, 6, 6, 6, 10, 12, 15]
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print(f"\nArray nums = {nums}")
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# Find an insertion point using binary search
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for target in [2, 6, 20]:
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index = binary_search_insertion(nums, target)
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print(f"Insertion index for element {target}: {index}")
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