LeetCode 381. Insert Delete GetRandom O(1)

题目：

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

Note: Duplicate elements are allowed.

1. insert(val): Inserts an item val to the collection.
2. remove(val): Removes an item val from the collection if present.
3. getRandom: Returns a random element from current collection of elements. The probability of each element being returned is linearly related to the number of same value the collection contains.

Example:

// Init an empty collection.
RandomizedCollection collection = new RandomizedCollection();

// Inserts 1 to the collection. Returns true as the collection did not contain 1.
collection.insert(1);

// Inserts another 1 to the collection. Returns false as the collection contained 1. Collection now contains [1,1].
collection.insert(1);

// Inserts 2 to the collection, returns true. Collection now contains [1,1,2].
collection.insert(2);

// getRandom should return 1 with the probability 2/3, and returns 2 with the probability 1/3.
collection.getRandom();

// Removes 1 from the collection, returns true. Collection now contains [1,2].
collection.remove(1);

// getRandom should return 1 and 2 both equally likely.
collection.getRandom();

分析：

这道题是leetcode380的进阶版，也就是允许出现重复的元素。这里附上380的题解LeetCode 380. Insert Delete GetRandom O(1) 常数时间插入、删除和获取随机元素(C++/Java)。

同样使用HashMap来支持插入和移除操作，利用数组来支持对数据的随机访问。只不过hashmap中val对应的是一个存放该元素在数组中索引的数组，当删除操作时，可以快速定位到该元素在数组的位置。

而数组中不只存放val，而是将val和该val在hashmap中对应的数组的索引，用来支持

我们来配合例子看一下：

依次执行

insert(1);insert(1);insert(2);

此时存储的情况如图：

此时我们执行remove(1)的操作，我们首先通过map找到1这个元素对应的数组，取出数组中最后一个元素，表示的便是1这个元素在Array数组中的索引。

由于数组删除最后一个元素的时间复杂度为O(1)(不考虑扩容这种情况)，我们将要删除的位置和数组中最后一个元素置换，或者是覆盖都可以。

然后我们再根据当前位置的这个元素去修改Map中数据，Array中元素的第二个值表示这个val在map中val对应的数组中的索引，此时我们要修改这个索引的值，改为array中调整后的索引值。最后在将无用的数据删除掉即可。

说着确实有些繁琐，不过通过实例配合图片过一遍应该比较好理解！

程序：

C++

class RandomizedCollection {
public:
    /** Initialize your data structure here. */
    RandomizedCollection() {
        
    }
    
    /** Inserts a value to the collection. Returns true if the collection did not already contain the specified element. */
    bool insert(int val) {
        m[val].push_back(v.size());
        v.emplace_back(val, m[val].size() - 1);
        return true;
    }
    
    /** Removes a value from the collection. Returns true if the collection contained the specified element. */
    bool remove(int val) {
        if(!m.count(val))
            return false;
        int lIndex = m[val].back();
        auto entry = v.back();
        v[lIndex] = entry;
        m[entry.first][entry.second] = lIndex;
        v.pop_back();
        m[val].pop_back();
        if(m[val].empty())
            m.erase(val);
        return true;
    }
    
    /** Get a random element from the collection. */
    int getRandom() {
        int index = rand() % v.size();
        return v[index].first;
    }
private:
    unordered_map<int, vector<int>> m;
    vector<pair<int, int>> v;
};

Java

class RandomizedCollection {

    /** Initialize your data structure here. */
    public RandomizedCollection() {

    }

    /** Inserts a value to the collection. Returns true if the collection did not already contain the specified element. */
    public boolean insert(int val) {
        List<Integer> l = map.getOrDefault(val, new ArrayList<Integer>());
        l.add(list.size());
        map.put(val, l);
        list.add(new Pair<>(val, l.size()-1));
        return true;
    }

    /** Removes a value from the collection. Returns true if the collection contained the specified element. */
    public boolean remove(int val) {
        if(!map.containsKey(val))
            return false;
        List<Integer> l = map.get(val);
        int lastIndex = l.get(l.size()-1);
        Pair<Integer, Integer> p = list.get(list.size()-1);
        list.set(lastIndex, p);
        List<Integer> cl = map.get(p.getKey());
        cl.set(p.getValue(), lastIndex);
        map.put(p.getKey(), cl);
        list.remove(list.size()-1);
        l.remove(l.size()-1);
        if(l.size() == 0)
            map.remove(val);
        return true;
    }

    /** Get a random element from the collection. */
    public int getRandom() {
        Random r = new Random();
        int index = r.nextInt(list.size());
        return list.get(index).getKey();
    }
    private HashMap<Integer, List> map = new HashMap<>();
    private ArrayList<Pair<Integer, Integer>> list = new ArrayList<>();
}