题目描述：

LeetCode 380. Insert Delete GetRandom O(1)

Design a data structure that supports all following operations in O(1) time.

1. insert(val): Inserts an item val to the set if not already present.
2. remove(val): Removes an item val from the set if present.
3. getRandom: Returns a random element from current set of elements. Each element must have the same probability of being returned.

Example:

// Init an empty set.
RandomizedSet randomSet = new RandomizedSet();

// Inserts 1 to the set. Returns true as 1 was inserted successfully.
randomSet.insert(1);

// Returns false as 2 does not exist in the set.
randomSet.remove(2);

// Inserts 2 to the set, returns true. Set now contains [1,2].
randomSet.insert(2);

// getRandom should return either 1 or 2 randomly.
randomSet.getRandom();

// Removes 1 from the set, returns true. Set now contains [2].
randomSet.remove(1);

// 2 was already in the set, so return false.
randomSet.insert(2);

// Since 1 is the only number in the set, getRandom always return 1.
randomSet.getRandom();

题目大意：

设计一个数据结构支持在O(1)时间内完成如下操作：

insert(val): 如果集合中不包含val，则插入val

remove(val): 如果集合中包含val，则移除val

getRandom: 从现有集合中随机返回一个元素，每个元素被返回的概率应该相等

解题思路：

哈希表 + 数组 （HashMap + Array）

利用数组存储元素，利用哈希表维护元素在数组中的下标

由于哈希表的新增/删除操作是O(1)，而数组的随机访问操作开销也是O(1)，因此满足题设要求

记数组为dataList，哈希表为dataMap

insert(val): 将val添至dataList末尾，并在dataMap中保存val的下标idx

remove(val): 记val的下标为idx，dataList末尾元素为tail，弹出tail并将其替换至idx处，在dataMap中更新tail的下标为idx，最后从dataMap中移除val

getRandom: 从dataList中随机选取元素返回

Python代码：

import random
class RandomizedSet(object):

    def __init__(self):
        """
        Initialize your data structure here.
        """
        self.dataMap = {}
        self.dataList = []

    def insert(self, val):
        """
        Inserts a value to the set. Returns true if the set did not already contain the specified element.
        :type val: int
        :rtype: bool
        """
        if val in self.dataMap:
            return False
        self.dataMap[val] = len(self.dataList)
        self.dataList.append(val)
        return True

    def remove(self, val):
        """
        Removes a value from the set. Returns true if the set contained the specified element.
        :type val: int
        :rtype: bool
        """
        if val not in self.dataMap:
            return False
        idx = self.dataMap[val]
        tail = self.dataList.pop()
        if idx < len(self.dataList):
            self.dataList[idx] = tail
            self.dataMap[tail] = idx
        del self.dataMap[val]
        return True

    def getRandom(self):
        """
        Get a random element from the set.
        :rtype: int
        """
        return random.choice(self.dataList)


# Your RandomizedSet object will be instantiated and called as such:
# obj = RandomizedSet()
# param_1 = obj.insert(val)
# param_2 = obj.remove(val)
# param_3 = obj.getRandom()

 

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