algorithm/hello-algo
1
0
Fork 0
mirror of https://github.com/krahets/hello-algo.git synced 2025-12-16 03:59:18 +08:00
Code Issues Packages Projects Releases Wiki Activity

Add the section of binary search insertion. (#671)

Browse Source 
Refactor the section of binary search edge.
Finetune the figures of binary search.
This commit is contained in:
Yudong Jin
2023-08-04 05:16:56 +08:00
committed by GitHub
parent 3d81b2d954
commit 71074d88f6
52 changed files with 546 additions and 621 deletions
Download Patch File Download Diff File Expand all files Collapse all files

61
codes/python/chapter_searching/binary_search_edge.py
View File

@@ -1,51 +1,48 @@
"""
File: binary_search_edge.py
Created Time: 2023-05-18
Created Time: 2023-08-04
Author: Krahets (krahets@163.com)
"""
import sys, os.path as osp
sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
from binary_search_insertion import binary_search_insertion
def binary_search_left_edge(nums: list[int], target: int) -> int:
"""二分查找最左一个元素"""
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
"""二分查找最左一个 target"""
# 等价于查找 target 的插入点
i = binary_search_insertion(nums, target)
# 未找到 target ，返回 -1
if i == len(nums) or nums[i] != target:
return -1 # 未找到目标元素，返回 -1
return -1
# 找到 target ，返回索引 i
return i
def binary_search_right_edge(nums: list[int], target: int) -> int:
"""二分查找最右一个元素"""
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:
i = m + 1 # 首个大于 target 的元素在区间 [m+1, j] 中
if j < 0 or nums[j] != target:
return -1 # 未找到目标元素，返回 -1
"""二分查找最右一个 target"""
# 转化为查找最左一个 target + 1
i = binary_search_insertion(nums, target + 1)
# j 指向最右一个 target ，i 指向首个大于 target 的元素
j = i - 1
# 未找到 target ，返回 -1
if j == -1 or nums[j] != target:
return -1
# 找到 target ，返回索引 j
return j
"""Driver Code"""
if __name__ == "__main__":
target = 6
# 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}")
# 二分查找最左一个元素
index_left = binary_search_left_edge(nums, target)
print("数组中最左一个元素 6 的索引 = ", index_left)
# 二分查找最右一个元素
index_right = binary_search_right_edge(nums, target)
print("数组中最右一个元素 6 的索引 = ", index_right)
# 二分查找左边界和右边界
for target in [6, 7]:
index = binary_search_left_edge(nums, target)
print(f"最左一个元素 {target} 的索引为 {index}")
index = binary_search_right_edge(nums, target)
print(f"最右一个元素 {target} 的索引为 {index}")

54
codes/python/chapter_searching/binary_search_insertion.py Normal file
View File

@@ -0,0 +1,54 @@
"""
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}")