380. Insert Delete GetRandom O(1)

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

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 thesame probability

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();

思路：
要求插入、删除、随机读取的时间复杂度平均为O(1)，注意这里的平均，即题目中的average，并非exactly。这样就能使用HashMap了。看了这道题的Discuss，Discuss里的争论焦点在于能否使用HashMap，要知道，当插入数据遇到冲突时，HashMap的时间复杂度可能降至O(n)。目前主流的观点是，一般情况下HashMap的插入和删除的时间复杂度为O(1)，只有当我们遇到散列冲突时，才需要详细分析HashMap时间复杂度。只要能用HashMap，在插入和删除时，我们就可以在O(1)的复杂度下，迅速判断出HashMap内是否包含某个key的键值对。

随机读取元素需要用到类似数组的存储结构，Java中类似的容器是ArrayList。有一个问题需要注意，ArrayList在删除元素时，需要把删除位置后面的元素，依次向前覆盖，最差情况下，时间复杂度降至O(n)。只有在删除最后一个元素时，因为不用移动元素，复杂度为O(1)。因此在删除ArrayList中的某个元素时，可以用最后一个元素替换当前元素，然后删除最后一个元素即可。（当然，此时ArrayList中元素的顺序也发生了变化，最后一个元素被前移了，不过对于本题来讲无所谓，见下图）

import java.util.HashMap;
import java.util.ArrayList;
import java.util.Random;

public class RandomizedSet

    ArrayList<Integer> arr;
    HashMap<Integer, Integer> map;
    Random rand;

    /** Initialize your data structure here. */
    public RandomizedSet() {
        arr = new ArrayList<Integer>();
        map = new HashMap<Integer, Integer>();
        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) {
        boolean contain = map.containsKey(val);
        if(!contain) {
            map.put(val, arr.size());
            arr.add(val);
        }
        return !contain;
    }

    /** Removes a value from the set. Returns true if the set contained the specified element. */
    public boolean remove(int val) {
        boolean contain = map.containsKey(val);
        if(contain) {
            int index = map.get(val);
            int lastIndex = arr.size() - 1;
            Integer lastEle = arr.get(lastIndex);
            arr.set(index, lastEle);
            map.put(lastEle, index);
            arr.remove(lastIndex);
            map.remove(val);
        }
        return contain;
    }

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

/**
 * 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();
 */