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

一刷
题解：与380不同的是，这道题目允许重复的数字，从现有集合中随机返回一个元素时，每个元素被返回的概率应该与其在集合中的数量线性相关。

与380思路相同，有一个array, 一个map(value->position set)
如果取出的数字为数组中最后一个，直接移去，否则，与最后一个swap然后移去。

public class RandomizedCollection {
    ArrayList<Integer> nums;
    HashMap<Integer, Set<Integer>> locs;
    java.util.Random rand = new java.util.Random();
    /** Initialize your data structure here. */
    public RandomizedCollection() {
        nums = new ArrayList<Integer>();
        locs = new HashMap<Integer, Set<Integer>>();
    }
    
    /** Inserts a value to the collection. Returns true if the collection did not already contain the specified element. */
    public boolean insert(int val) {
        boolean contain = locs.containsKey(val);
        if ( ! contain ) locs.put( val, new LinkedHashSet<Integer>() ); 
        locs.get(val).add(nums.size());        
        nums.add(val);
        return ! contain ;
    }
    
    /** Removes a value from the collection. Returns true if the collection contained the specified element. */
    public boolean remove(int val) {
        boolean contain = locs.containsKey(val);
        if ( ! contain ) return false;
        int loc = locs.get(val).iterator().next();
        locs.get(val).remove(loc);
        if (loc < nums.size() - 1 ) {
           int lastone = nums.get( nums.size()-1 );
           nums.set( loc , lastone );
           locs.get(lastone).remove( nums.size()-1);
           locs.get(lastone).add(loc);
        }
        nums.remove(nums.size() - 1);
       
        if (locs.get(val).isEmpty()) locs.remove(val);
        return true;
    }
    
    /** Get a random element from the collection. */
    public int getRandom() {
        return nums.get( rand.nextInt(nums.size()) );
    }
}