[LeetCode 381] Insert Delete GetRandom O(1) - Duplicates allowed (Hard)

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

Note: Duplicate elements are allowed.

• insert(val): Inserts an item val to the collection.
• remove(val): Removes an item val from the collection if present.
• 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();

Solution:

参考http://zxi.mytechroad.com/blog/hashtable/leetcode-381-insert-delete-getrandom-o1-duplicates-allowed/

1. 思路与#380类似，但不同在于有重复的数字。所以需要用HashMap>和List两个数据结构。

   • HashMap： 用于存储每个数字，和其在List中的Index
   • Node：An object, val ~ number, indexInMap ~ 当前数字在Map的List中对应的Index
   • List： 数字node的list
     
     image.png

2. Insert：需要向List中加入node，同时更新Map

3. remove: 难点！！ 同样也是与尾部的number交换，然后移除到尾部的数字。难点在于update index in map for last element

4. getRandom: 与#380相同。

//3. update index in map for the last element
        numberVsIndexes.get(lastEntry.val).set (lastEntry.indexInMap, removeIndex);

class RandomizedCollection {
    class Node {
        public int val;
        public int indexInMap;
        
        public Node (int val, int index) {
            this.val = val;
            this.indexInMap = index;
        }
    }
    
    Map> numberVsIndexes;
    List nodeList;

    /** Initialize your data structure here. */
    public RandomizedCollection() {
        numberVsIndexes = new HashMap> ();
        nodeList = new ArrayList ();
    }
    
    /** Inserts a value to the collection. Returns true if the collection did not already contain the specified element. */
    public boolean insert(int val) {
        boolean result = false;
        if (!numberVsIndexes.containsKey (val)) {
            result = true;
        }
        
        int indexInNodeList = nodeList.size ();
        List indexes = numberVsIndexes.getOrDefault (val, new ArrayList ());
        indexes.add (indexInNodeList);
        numberVsIndexes.put (val, indexes);
        
        int indexInMap = indexes.size () - 1;
        Node node = new Node (val, indexInMap);
        nodeList.add (node);
        
        return result;
    }
    
    /** Removes a value from the collection. Returns true if the collection contained the specified element. */
    public boolean remove(int val) {
        if (!numberVsIndexes.containsKey (val)) {
            return false;
        }
        
        //1. get the last entry of the remove number
        List removeCandidates = numberVsIndexes.get (val);
        int removeIndex = removeCandidates.get (removeCandidates.size () - 1);
        
        //2. get the last entry of the nodeList
        Node lastEntry = nodeList.get (nodeList.size () - 1);
        
        //3. update index in map for the last element
        numberVsIndexes.get(lastEntry.val).set (lastEntry.indexInMap, removeIndex);
        
        //3. swap 
        nodeList.set (removeIndex, lastEntry);
        
        //4. clean up the map
        nodeList.remove (nodeList.size () - 1);
        removeCandidates.remove (removeCandidates.size () - 1);
        
        if (removeCandidates.size () == 0) {
            numberVsIndexes.remove (val);
        }
        
        return true;
    }
    
    /** Get a random element from the collection. */
    public int getRandom() {
        Random rand = new Random ();
        return nodeList.get (rand.nextInt (nodeList.size ())).val;
    }
}

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