### 题目

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

• insert(val): Inserts an item val to the set if not already present.
• remove(val): Removes an item val from the set if present.
• 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 2 is the only number in the set, getRandom always return 2.
randomSet.getRandom();


### 一个HashMap加上一个ArrayList

$O(1)$ 时间内完成元素的随机访问，首先考虑的是数组，但因为不定长，所以ArrayList是很好的替代方案。难点是：如何处理remove()方法留下的空槽？ 传统做法是将空槽后的所有元素向前挪一个位置。复杂度还是 $O(n)$。但向前平移的做法是为了保持原集合序列的元素排序。但因为getRandom()函数不关心元素的排序，所以一个聪明的解决方案是：

#### 代码

class RandomizedSet {

private static HashMap<Integer,Integer> map = new HashMap<>();    // 键值对：[val,index]
private static List<Integer> list = new ArrayList<>();            // 所有数字的列表
private static Random r = new Random();

/** Initialize your data structure here. */
public RandomizedSet() {
map.clear();
list.clear();
}

/** 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;
} else {
int index = map.size();
map.put(val,map.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)) {
return false;
} else {
int last = list.get(list.size()-1);
int index = map.get(val);
map.put(last,index);
map.remove(val);
list.set(index,last);
list.remove(list.size()-1);
return true;
}
}

/** Get a random element from the set. */
public int getRandom() {
if (list.isEmpty()) { return 0; }
return list.get(r.nextInt(list.size()));
}
}

/**
* Your RandomizedSet object will be instantiated and called as such:
* RandomizedSet obj = new RandomizedSet();
* boolean param_1 = obj.insert(val);
* boolean param_2 = obj.remove(val);
* int param_3 = obj.getRandom();
*/