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

  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 the same probability of being returned.

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();
[code lang="java"]
class RandomizedSet {

    /** Initialize your data structure here. */
    public RandomizedSet() {
        
    }
    
    /** Inserts a value to the set. Returns true if the set did not already contain the specified element. */
    public boolean insert(int val) {
        
    }
    
    /** Removes a value from the set. Returns true if the set contained the specified element. */
    public boolean remove(int val) {
        
    }
    
    /** Get a random element from the set. */
    public int getRandom() {
        
    }
}

/**
 * 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();
 */
[code]

Idea – 1

It is easy to make insert/remove O(1) using a hash-based data structure. From n elements, to drant at random, we choose a random id between [0..n-1] and get the corresponding element. Since given an id we need to find the element in O(1) time, we need hash map from id to element. Since we insert/remove elements (not ids), we need another hash map from element to its id. When we remove an element, we find its id and swap with the element with largest id (we need to update the element-to-id map for the element with largest id), then first remove the largest id from id-to-element map, and then remove the element from element-to-id map. 
[code lang="java"]
class RandomizedSet {
    
    private HashMap<Integer, Integer> elementToIdMap;
    private HashMap<Integer, Integer> idToElementMap;
    private static final Random rng = new Random(System.currentTimeMillis()%Integer.MAX_VALUE); 

    /** Initialize your data structure here. */
    public RandomizedSet() {
        elementToIdMap = new HashMap<>();
        idToElementMap = new HashMap<>();
    }
    
    /** Inserts a value to the set. Returns true if the set did not already contain the specified element. */
    public boolean insert(int val) {
        boolean exists = elementToIdMap.containsKey(val);
        
        if(!exists)
        {
            int id = elementToIdMap.size();
            elementToIdMap.put(val, id);
            idToElementMap.put(id, val);
        }
        
        return !exists;
    }
    
    /** Removes a value from the set. Returns true if the set contained the specified element. */
    public boolean remove(int val) {
        boolean exists = elementToIdMap.containsKey(val);
        
        if(exists)
        {
            int maxIdElement = idToElementMap.get(elementToIdMap.size()-1);
            int id = elementToIdMap.get(val);
            
            idToElementMap.put(id, maxIdElement);
            elementToIdMap.put(maxIdElement, id);
            
            idToElementMap.remove(elementToIdMap.size()-1);
            elementToIdMap.remove(val);
        }
        
        return exists;
    }
    
    /** Get a random element from the set. */
    public int getRandom() {
        int n = elementToIdMap.size();
        int draw = rng.nextInt(n);
        return idToElementMap.get(draw);
    }
}

/**
 * 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();
 */
[code]

Runtime: 57 ms, faster than 54.30% of Java online submissions for Insert Delete GetRandom O(1).Memory Usage: 46.5 MB, less than 80.37% of Java online submissions for Insert Delete GetRandom O(1).

Leave a comment