mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-26 20:16:29 +08:00
54 lines
1.8 KiB
Python
54 lines
1.8 KiB
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:
|
|
"""二分查找插入点（无重复元素）"""
|
|
i, j = 0, len(nums) - 1 # 初始化双闭区间 [0, n-1]
|
|
while i <= j:
|
|
m = (i + j) // 2 # 计算中点索引 m
|
|
if nums[m] < target:
|
|
i = m + 1 # target 在区间 [m+1, j] 中
|
|
elif nums[m] > target:
|
|
j = m - 1 # target 在区间 [i, m-1] 中
|
|
else:
|
|
return m # 找到 target ，返回插入点 m
|
|
# 未找到 target ，返回插入点 i
|
|
return i
|
|
|
|
|
|
def binary_search_insertion(nums: list[int], target: int) -> int:
|
|
"""二分查找插入点（存在重复元素）"""
|
|
i, j = 0, len(nums) - 1 # 初始化双闭区间 [0, n-1]
|
|
while i <= j:
|
|
m = (i + j) // 2 # 计算中点索引 m
|
|
if nums[m] < target:
|
|
i = m + 1 # target 在区间 [m+1, j] 中
|
|
elif nums[m] > target:
|
|
j = m - 1 # target 在区间 [i, m-1] 中
|
|
else:
|
|
j = m - 1 # 首个小于 target 的元素在区间 [i, m-1] 中
|
|
# 返回插入点 i
|
|
return i
|
|
|
|
|
|
"""Driver Code"""
|
|
if __name__ == "__main__":
|
|
# 无重复元素的数组
|
|
nums = [1, 3, 6, 8, 12, 15, 23, 26, 31, 35]
|
|
print(f"\n数组 nums = {nums}")
|
|
# 二分查找插入点
|
|
for target in [6, 9]:
|
|
index = binary_search_insertion_simple(nums, target)
|
|
print(f"元素 {target} 的插入点的索引为 {index}")
|
|
|
|
# 包含重复元素的数组
|
|
nums = [1, 3, 6, 6, 6, 6, 6, 10, 12, 15]
|
|
print(f"\n数组 nums = {nums}")
|
|
# 二分查找插入点
|
|
for target in [2, 6, 20]:
|
|
index = binary_search_insertion(nums, target)
|
|
print(f"元素 {target} 的插入点的索引为 {index}")
|