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hello-algo/en/codes/python/chapter_searching/binary_search_insertion.py
Yudong Jin 2778a6f9c7 Translate all code to English (#1836)
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2025-12-31 07:44:52 +08:00

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Python

"""
File: binary_search_insertion.py
Created Time: 2023-08-04
Author: krahets (krahets@163.com)
"""
def binary_search_insertion_simple(nums: list[int], target: int) -> int:
"""Binary search for insertion point (no duplicate elements)"""
i, j = 0, len(nums) - 1 # Initialize closed interval [0, n-1]
while i <= j:
m = (i + j) // 2 # Calculate midpoint index m
if nums[m] < target:
i = m + 1 # target is in the interval [m+1, j]
elif nums[m] > target:
j = m - 1 # target is in the interval [i, m-1]
else:
return m # Found target, return insertion point m
# Target not found, return insertion point i
return i
def binary_search_insertion(nums: list[int], target: int) -> int:
"""Binary search for insertion point (with duplicate elements)"""
i, j = 0, len(nums) - 1 # Initialize closed interval [0, n-1]
while i <= j:
m = (i + j) // 2 # Calculate midpoint index m
if nums[m] < target:
i = m + 1 # target is in the interval [m+1, j]
elif nums[m] > target:
j = m - 1 # target is in the interval [i, m-1]
else:
j = m - 1 # The first element less than target is in the interval [i, m-1]
# Return insertion point i
return i
"""Driver Code"""
if __name__ == "__main__":
# Array without duplicate elements
nums = [1, 3, 6, 8, 12, 15, 23, 26, 31, 35]
print(f"\nArray nums = {nums}")
# Binary search for insertion point
for target in [6, 9]:
index = binary_search_insertion_simple(nums, target)
print(f"Index of insertion point for element {target} is {index}")
# Array with duplicate elements
nums = [1, 3, 6, 6, 6, 6, 6, 10, 12, 15]
print(f"\nArray nums = {nums}")
# Binary search for insertion point
for target in [2, 6, 20]:
index = binary_search_insertion(nums, target)
print(f"Index of insertion point for element {target} is {index}")