Description

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();

Solution

HashMap & ArrayList, time O(1), space O(n)

蛮妙的一道题诶。其实一开始我就想到了需要两种数据结构配合使用才能解决，例如用HashSet和ArrayList结合，但就是想不通如何让remove达到常数时间。

后来发现，应该用HashMap结合ArrayList，ArrayList中存储所有插入进来的元素，HashMap存储元素对应ArrayList中的index。在remove的时候，只需要将该元素和ArrayList中最后一个元素交换即可！这样就能保证其他元素的index不受影响，从而达到常数时间。

另外，new Random().nextInt(int bound)这个API要记起来哦，可以等概率返回0到bound - 1之间的随机数。

class RandomizedSet {
    private Map<Integer, Integer> valToIndex;
    private List<Integer> valList;
    private java.util.Random random;
    /** Initialize your data structure here. */
    public RandomizedSet() {
        valToIndex = new HashMap<>();
        valList = new ArrayList<>();
        random = new Random();
    }
    
    /** Inserts a value to the set. Returns true if the set 
    did not already contain the specified element. */
    public boolean insert(int val) {
        if (valToIndex.containsKey(val)) {
            return false;
        }
        valToIndex.put(val, valList.size());
        valList.add(val);
        return true;
    }
    
    /** Removes a value from the set. Returns true if the set 
    contained the specified element. */
    public boolean remove(int val) {
        if (!valToIndex.containsKey(val)) {
            return false;
        }
        int index = valToIndex.get(val);
        int lastIndex = valList.size() - 1;
        if (index < lastIndex) {
            // swap val with the last element in valList
            valList.set(index, valList.get(lastIndex));
            // don't forget to update last index in map!
            valToIndex.put(valList.get(lastIndex), index);
        }
        valToIndex.remove(val);
        valList.remove(valList.size() - 1);
        return true;
    }
    
    /** Get a random element from the set. */
    public int getRandom() {
        return valList.get(random.nextInt(valList.size()));
    }
}

/**
 * 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();
 */