Insert Delete GetRandom O(1) - Duplicates allowed

题目地址：
https://leetcode.com/problems/insert-delete-getrandom-o1-duplicates-allowed/description/

题目：

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();

解题思路：
这道题可以用一个list来存数据，用map来存index和value的key-value pair。我们有两种选择，但是这里要注意我们要实现remove，所以用value来作为key是相对合理的，可以在O(1)时间找到该数字对应的index的集合。这里比较tricky的是当要remove的元素不是list最后一个，我们最好先把它和最后元素交换一下。

代码：

private List<Integer> nums;
private Map<Integer, Set<Integer>> map;

/** Initialize your data structure here. */public RandomizedCollection() {
    nums = new ArrayList<>();
    map = new HashMap<>();
}

/** Inserts a value to the collection. Returns true if the collection did not already contain the specified element. */public boolean insert(int val) {
    boolean rst = map.containsKey(val);
    if(!rst){
        map.put(val, new LinkedHashSet<>());
    }
    nums.add(val);
    map.get(val).add(nums.size() - 1);
    return !rst;
}

/** 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;
    }
    // swap the last element with the element we are about to remove    if(!map.get(val).contains(nums.size() - 1)){
        int removeIndex = map.get(val).iterator().next();
        map.get(val).add(nums.size() - 1);
        map.get(val).remove(removeIndex);
        int lastVal = nums.get(nums.size() - 1);
        map.get(lastVal).remove(nums.size() - 1);
        map.get(lastVal).add(removeIndex);
        nums.set(removeIndex, lastVal);
    }
    map.get(val).remove(nums.size() - 1);
    nums.remove(nums.size() - 1);
    if(map.get(val).size() == 0){
        map.remove(val);
    }
    return true;
}

/** Get a random element from the collection. */public int getRandom() {
    Random random = new Random();
    int index = random.nextInt(nums.size());
    return nums.get(index);
}