算法图解 第4章第一节习题解答

最近看算法图解，对个别章节习题尝试作答，如果错误，欢迎指出

4.1 请编写前述sum函数的代码

def sum(a):
	if len(a) == 0:
		return 0
	elif len(a) == 1:
		return a[0]
	else:
		return a[0] + sum(a[1:])

val = sum([1,2,3,4,5,6,7,8,9,10])
print val

4.2 编写一个递归函数来计算列表包含的元素数

def count(list):
	if len(list) == 0:
		return 0
	elif len(list) == 1:
		return 1
	else:
		return 1 + count(list[1:])

val = count([1,2,3,4,5,6,7,8,9])
print val

4.3 找出列表中最大的数字

def bigger(v1, v2):
	if v1 >= v2:
		return v1
	else:
		return v2

def max(list):
	if len(list) == 1:
		return list[0]
	elif len(list) == 2:
		return bigger(list[0], list[1])
	else:
		return bigger(list[0], max(list[1:]))

val = max([1,2,103,4,5,16,7,8,9])
print val

4.4 还记得第1章介绍的二分查找吗？它也是一种分而治之算法。你能找出二分查找算法的基线条件和递归条件吗？

def binary_search_impl(list, item, low, high):
	if low > high:
		return None
	else:
		mid = (low + high) / 2
		guess = list[mid]
		if guess == item:
			return mid
		elif guess > item:
			high = mid - 1
			return binary_search_impl(list, item, low, high)
		else:
			low = mid + 1
			return binary_search_impl(list, item, low, high)

def binary_search(list, item):
	return binary_search_impl(list, item, 0, len(list)-1)

list = [1,3,5,7,9]
val = binary_search(list, 8)
print val