Design a data structure that supports all following operations in average 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();

设计一个数据结构在O(1)时间内完成：insert(val)，remove(val)，getRandom()

由于是O(1)时间，要用哈希表 + 数组(HashMap + Array)，数组用来保存数字，哈希表用来建立每个数字和其在数组中的位置之间的映射。

插入操作：先判断是否在HashMap里，如果存在则不需要插入，直接返回false。不存在的话，把此数插入到数组的末尾，然后在HashMap中建立数字和其位置的映射。

删除操作：先判断是否在HashMap里，如果没有，直接返回false。由于HashMap的删除是O(1)时间，而数组并不是。为了保证了O(1)时间内的删除，把要删除的数字和数组的最后一个数调换个位置，然后修改对应的HashMap中的值，删除数组的最后一个元素即可。

返回随机数：随机生成一个数组位置，返回该位置上的数字。

Java:

public class RandomizedSet {
Map<Integer, Integer> map;//<val, index in arrlist>
List<Integer> list;//keep a record of value for get random
int size;//map and list are the same size
Random rand;
/** Initialize your data structure here. */
public RandomizedSet() {
this.map = new HashMap<>();
this.list = new ArrayList<>();
this.size = 0;
this.rand = new Random();
}

/** Inserts a value to the set. Returns true if the set did not already contain the specified element. */
public boolean insert(int val) {
if(map.containsKey(val)) return false;
map.put(val, size);
list.add(val);
size++;
return true;
}

/** Removes a value from the set. Returns true if the set contained the specified element. */
public boolean remove(int val) {
if(map.containsKey(val)){
int last = list.get(size - 1);
list.set(map.get(val), last);//use last added ele to fill the element to be removed
map.put(last, map.get(val));//update last added ele's index in list
map.remove(val);
list.remove(size - 1);//remove at end is constant
size--;
return true;
}
return false;
}

/** Get a random element from the set. */
public int getRandom() {
return list.get(rand.nextInt(size));
}
}

Python:

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)　　

C++:

class RandomizedSet {
public:
/** Initialize your data structure here. */
RandomizedSet() {}

/** Inserts a value to the set. Returns true if the set did not already contain the specified element. */
bool insert(int val) {
if (m.count(val)) return false;
nums.push_back(val);
m[val] = nums.size() - 1;
return true;
}

/** Removes a value from the set. Returns true if the set contained the specified element. */
bool remove(int val) {
if (!m.count(val)) return false;
int last = nums.back();
m[last] = m[val];
nums[m[val]] = last;
nums.pop_back();
m.erase(val);
return true;
}

/** Get a random element from the set. */
int getRandom() {
return nums[rand() % nums.size()];
}
private:
vector<int> nums;
unordered_map<int, int> m;
};

类似题目：

[LeetCode] 381. Insert Delete GetRandom O(1) - Duplicates allowed 插入删除和获得随机数O(1)时间 - 允许重复　　

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