问题

1. 在一组相同类型的数据中（对象、数组、字符串、整形等任意类型的数据结构）请用时间空间最优的方式查找缺失的一项。例如有一组数据["A","B","C","D","E","F","G"]，现在给到["B","D","A","F"."G"]，需要找到缺失数据"C"？数据的个数不定。
2. 扩展上面的问题，用最优的方式查找缺失的多项。

解决

2层循环逐个比对查找

最简单的办法当然是逐项比对，几乎所有语言都提供对象实例、字符串、数字的比对方法。

但是这样做有2个问题：

1. 少量数据可行，但是海量数据肯定会非常慢，因为时间复杂度是O(n^2)。而且第一层循环是全遍历，第二层循要遍历n/2。
2. 在比对过程中如果是字符串比对，效率会非常差。

编码2叉树查找

可以对所有的事物进行有序编码，然后通过编码索引到对应的元素。编码也没有什么特别的要求，只要每增加一项将编码加一即可。例如上面的例子["A","B","C","D","E","F","G"]，对其编码建立索引：

{1:"A",2:"B",3:"C",4:"D",5:"E",6:"F",7:"G"}

这是一个标准的dict结构（Java中的map结构）。任何时候增加新的项目只要编码加一即可：

{1:"A",2:"B",3:"C",4:"D",5:"E",6:"F",7:"G",8:"ADD ITEM"}

使用编码还有一个好处是还可以查找一组不同类型的数据。

建立编码之后实际上就转换为一个数字查询问题。

如果仅仅是查找一个缺失项，实际上有一个非常简便的算法——求和计算差值：

    # origin_numbers是所有编码的列表，例如[1,2,3,4,5,6,7,8,9,10]。# random_numbers是缺失了一项的编码无序表，例如[6,2,5,4,7,8,9,10,1]。for _num in origin_numbers:total_sum = total_sum + _numfor _num in random_numbers:without_sum = without_sum + _num

差值正好是缺失的项目索引值。

但是如果是查找多个缺失项，只能用2叉树：

import copy
import random as rand
import datetime
import time# 2叉树结构
class Link:def __init__(self, value):self.value = valueself.left = Noneself.right = Nonedef insert(self, value):if value < self.value:self.__addLeftLeaf__(value)else:self.__addRightLeaf__(value)def __addLeftLeaf__(self, value):if self.left is not None:self.left.insert(value)else:self.left = Link(value)def __addRightLeaf__(self, value):if self.right is not None:self.right.insert(value)else:self.right = Link(value)def traversal(self, _list, _without):if self.left is not None:self.left.traversal(_list, _without)length = len(_list)if 0 < length:tail = _list[length - 1]diff = self.value - (tail + 1)if 0 < diff:for _d in range(1, diff + 1):_without.append(self.value - _d)_list.append(self.value)if self.right is not None:self.right.traversal(_list, _without)# 从队列中移除项目
def remove_number(without_size, numbers):for count in range(without_size):del numbers[rand.randrange(len(numbers))]return numbers# 使用有序数组生成随机数组
def generation_random(without_size, origin_numbers):origin_numbers_options = copy.copy(origin_numbers)length = len(origin_numbers)random_numbers = []# 随机while 0 < length:rand_number = rand.randrange(length)random_numbers.append(origin_numbers_options[rand_number])del origin_numbers_options[rand_number]length = len(origin_numbers_options)return remove_number(without_size, random_numbers)#
def generation_origin_numbers(without_size=1, total=10000):origin_numbers = list(range(total))return origin_numbers, generation_random(without_size, origin_numbers)def tree_2_leaf(numbers):root = Link(numbers[0])for pos in range(1, len(numbers)):root.insert(numbers[pos])# 使用二叉树_list = []_without = []root.traversal(_list=_list, _without=_without)return _withoutdef without_one_number(origin_numbers, random_numbers):print("=============== without_one_number start ==================")sum_search_start = time.time()total_sum = 0without_sum = 0print("Sum Search Begin.({})".format(datetime.datetime.now().strftime('%H:%M:%S')))for _num in origin_numbers:total_sum = total_sum + _numfor _num in random_numbers:without_sum = without_sum + _numtree_search_start = sum_search_end = time.time()print("Sum Search Complete.({})".format(datetime.datetime.now().strftime('%H:%M:%S')))print("Timer:{} S".format(sum_search_end - sum_search_start))print("Total Sum:{}".format(total_sum))print("Without One Number Sum:{}".format(without_sum))print("Without Number:{}".format(total_sum - without_sum))print("---")print("2 Tree Search Begin.({})".format(datetime.datetime.now().strftime('%H:%M:%S')))without_number = tree_2_leaf(random_numbers)print("2 Tree Complete.({})".format(datetime.datetime.now().strftime('%H:%M:%S')))print("Timer:{} S".format(time.time() - tree_search_start))print("Without Element:{}".format(without_number))print("=============== without_one_number end ==================")def without_multi_number(random_numbers):print("=============== without_multi_number start ==================")start = time.time()print("Search Begin.({})".format(datetime.datetime.now().strftime('%H:%M:%S')))without_number = tree_2_leaf(random_numbers)print("Search End.({})".format(datetime.datetime.now().strftime('%H:%M:%S')))print("Timer:{} S".format(time.time() - start))print("Without Element:{}".format(without_number))print("=============== without_multi_number end ==================")if __name__ == '__main__':print("Generation Numbers Begin.({})".format(datetime.datetime.now().strftime('%H:%M:%S')))generation_number_start = time.time()origin, random = generation_origin_numbers()print("Generation Numbers Complete.({})".format(datetime.datetime.now().strftime('%H:%M:%S')))generation_number_end = time.time()print("Timer:{} S".format(generation_number_end - generation_number_start))without_one_number(origin, random)without_multi_number(remove_number(4, random))