二分查找及几种变体的Python实现

1. 在不重复的有序数组中，查找等于给定值的元素

循环法

def search(lst, target):
	n = len(lst)
	if n == 0:
		return -1

	low = 0
	high = n - 1
	while low <= high:
		mid = (high-low)//2 + low
		if lst[mid] == target:
			return mid
		elif lst[mid] < target:
			low = mid +1
		elif lst[mid] > target:
			high = mid -1
	return -1

递归法

def search2(lst, target, low, high):
	if low > high:
		return -1

	mid = (high-low)//2 + low
	if lst[mid] == target:
		return mid
	elif lst[mid] < target:
		return search2(lst, target, mid+1, high)
	elif lst[mid] > target:
		return search2(lst, target, low, mid-1)

2. 查找第一个值等于给定值的元素

def bsearch(lst, value):
	n = len(lst)
	if n == 0:
		return -1
	low = 0
	high = n - 1
	while low <= high:
		mid = (high-low) // 2 + low
		if lst[mid] < value:
			low = mid + 1
		elif lst[mid] > value:
			low = mid - 1
		elif lst[mid] == value:
			if mid == 0 or lst[mid-1] != value:
				return mid
			else:
				high = mid - 1
	return -1

3. 查找最后一个值等于给定值的元素

def bsearch(lst, value):
	n = len(lst)
	if n == 0:
		return -1
	low = 0
	high = n - 1
	while low <= high:
		mid = (high-low) // 2 + low
		if lst[mid] > value:
			high = mid - 1
		elif lst[mid] < value:
			low = mid + 1
		elif lst[mid] == value:
			if mid == n-1 or lst[mid+1] != value:
				return mid
			else:
				low = mid + 1
	return -1

4. 查找第一个大于等于给定值的元素

def bsearch(lst, value):
	n = len(lst)
	if n == 0:
		return -1
	low = 0
	high = n - 1
	while low <= high:
		mid = (high-low) // 2 + low
		if lst[mid] < value:
			low = mid + 1
		elif lst[mid] >=value:
			if mid == 0 or lst[mid-1] < value:
				return mid
			high = mid - 1

5. 查找最后一个小于等于给定值的元素

def bsearch(lst, value):
	n = len(lst)
	if n == 0:
		return -1
	low = 0
	high = n - 1
	while low <= high:
		mid = (high-low) // 2 + low
		if lst[mid] > value:
			high = mid - 1
		elif lst[mid] <= value:
			if mid == n-1 or lst[mid+1] > 0:
				return mid
			low = mid + 1
	return -1