Question
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
User a map to track the position of the values in the list. Use a list to track the order of values.
Code
class RandomizedCollection {
Map<Integer, Set<Integer>> map = new HashMap<>();
List<Integer> list = new ArrayList<>();
Random rand = new Random();
/** Initialize your data structure here. */
public RandomizedCollection() {
}
public boolean insert(int val) {
if(!map.containsKey(val)) {
map.put(val, new HashSet<Integer>());
map.get(val).add(list.size());
list.add(val);
return true;
}
else {
map.get(val).add(list.size());
list.add(val);
return false;
}
}
/** 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;
Set<Integer> set = map.get(val);
int index = set.iterator().next();
set.remove(index);
if(set.isEmpty()) map.remove(val);
int lastIndex = list.size()-1;
if(index == lastIndex) {
list.remove(index);
}
else {
int lastVal = list.get(lastIndex);
list.set(index, lastVal);
Set<Integer> setLastVal = map.get(lastVal);
setLastVal.remove(lastIndex);
setLastVal.add(index);
list.remove(lastIndex);
}
return true;
}
/** Get a random element from the collection. */
public int getRandom() {
return list.get(rand.nextInt(list.size()));
}
}
/**
* 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();
*/
Performance
O(1)