二分插入、bisect

在一个有序序列（从小到大）中查找一个元素
每次将元素与序列中间位置的元素进行比较
如果大于中点，则在后半段。如果小于中点，则在前半段。以此类推
时间复杂度为O(logn)

有一个无序序列[37, 99, 73, 48, 47, 40, 40, 25, 99, 51]，对其先排序输出新列表。
分别插入20、40、41、100到这个新序列中合适的位置，保证其有序。

origin = [37, 99, 73, 48, 47, 40, 40, 25, 99, 51]

origin = sorted(origin)
# print(origin)
# [25, 37, 40, 40, 47, 48, 51, 73, 99, 99]

# 有重复时从左边插入
def insert_sort(origin:list, num):
	low = 0
	high = len(origin)
	while low < high:
		mid = (low + high)//2
		# 如果大于中点，则在后半部分
		if num > origin[mid]:
			low = mid + 1
		# 否则在前半部分
		else:
			high = mid
	origin.insert(low, num)

for num in (20, 40, 41, 100):
	insert_sort(origin, num)

print(origin)
# [20, 25, 37, 40, 40, 40, 41, 47, 48, 51, 73, 99, 99, 100]

origin = [37, 99, 73, 48, 47, 40, 40, 25, 99, 51]

origin = sorted(origin)

# 有重复时从右边插入
def insert_sort(origin:list, num):
	low = 0
	high = len(origin)
	while low < high:
		mid = (low + high)//2
		if num < origin[mid]:
			high = mid
		else:
			low = mid + 1
	origin.insert(low, num)

for num in (20, 40, 41, 100):
	insert_sort(origin, num)

print(origin)
# [20, 25, 37, 40, 40, 40, 41, 47, 48, 51, 73, 99, 99, 100]

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bisect模块

bisect包含两个主要函数 bisect和insort，都是基于二分法实现

• bisect: bisect_right的别名，返回插入点位置，有重复时返回右边插入点
• bisect_left: 返回插入点位置，有重复时返回左边插入点
• insort: insort_right的别名，默认有重复时从右边插入
• insort_left: 有重复时从左边插入

import bisect

origin = [37, 99, 73, 48, 47, 40, 40, 25, 99, 51]
origin = sorted(origin)

for num in (20, 40, 41, 100):
	bisect.insort_left(origin, num)

print(origin)
# [20, 25, 37, 40, 40, 40, 41, 47, 48, 51, 73, 99, 99, 100]

判断学生成绩，成绩等级A-E，其中，90分以上为A，80-89为B，70-79为C，60-69为D，50-59为E

breakpoints = [60, 70, 80, 90]
grades = 'EDCBA'

index = bisect.bisect(breakpoints, 55)
print(grades[index])
# E

参考：
https://zh.wikipedia.org/wiki/二分搜索算法
https://docs.python.org/3/library/bisect.html