Problem

Implement the RandomizedSet class:

  • RandomizedSet() Initializes the RandomizedSet object.
  • bool insert(int val) Inserts an item val into the set if not present. Returns true if the item was not present, false otherwise.
  • bool remove(int val) Removes an item val from the set if present. Returns true if the item was present, false otherwise.
  • int getRandom() Returns a random element from the current set of elements (it’s guaranteed that at least one element exists when this method is called). Each element must have the same probability of being returned.

You must implement the functions of the class such that each function works in average O(1) time complexity.

Examples

Example 1:

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**Input**
["RandomizedSet", "insert", "remove", "insert", "getRandom", "remove", "insert", "getRandom"]
[[], [1], [2], [2], [], [1], [2], []]
**Output**
[null, true, false, true, 2, true, false, 2]

**Explanation**
RandomizedSet randomizedSet = new RandomizedSet();
randomizedSet.insert(1); // Inserts 1 to the set. Returns true as 1 was inserted successfully.
randomizedSet.remove(2); // Returns false as 2 does not exist in the set.
randomizedSet.insert(2); // Inserts 2 to the set, returns true. Set now contains [1,2].
randomizedSet.getRandom(); // getRandom() should return either 1 or 2 randomly.
randomizedSet.remove(1); // Removes 1 from the set, returns true. Set now contains [2].
randomizedSet.insert(2); // 2 was already in the set, so return false.
randomizedSet.getRandom(); // Since 2 is the only number in the set, getRandom() will always return 2.

Follow up: Insert Delete Search and GetRandom in Constant Time 2 - Duplicates allowed

Solution

Method 1 – HashMap and List

Intuition

Hash maps are efficient for O(1) insert and get operations.

Get Random

However, to get a random element, we need a list or array. For example, if we insert 3 values into an array, we can pick any value randomly using arr[(int)(arr.length * Math.random())], which is O(1). Arrays provide O(1) access by index, but O(n) time for searching by value.

Combining a map and an array solves this: the map stores the mapping between each value and its index in the array. This allows us to check for existence and get the index in O(1) time.

Remove a Value

The key trick for removal is that ArrayList’s remove method is O(n) if you remove from a random location. To avoid this, we swap the value to be removed with the last element, then remove the last element. After swapping, we update the index of the swapped value (which was previously at the end) in the map.

list.set(index, element) sets the value element at the specified index.

Approach

  1. Use a list to store all elements.
  2. Use a hash map to map each value to its index in the list.
  3. On insert, add the value to the list and record its index in the hash map.
  4. On remove, swap the value to be removed with the last element, update the hash map, and remove the last element.
  5. On getRandom, pick a random index from the list and return the value at that index.

Complexity

  • ⏰ Time complexity: O(1) average for insert, remove, and getRandom, due to direct access and updates in the list and hash map.
  • 🧺 Space complexity: O(n), where n is the number of elements in the set.

Code

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#include <vector>
#include <unordered_map>
#include <random>
using namespace std;
class RandomizedSet {
    vector<int> arr;
    unordered_map<int, int> idx;
    mt19937 rng{random_device{}()};
public:
    RandomizedSet() {}
    bool insert(int val) {
        if (idx.count(val)) return false;
        arr.push_back(val);
        idx[val] = arr.size() - 1;
        return true;
    }
    bool remove(int val) {
        if (!idx.count(val)) return false;
        int removeIdx = idx[val];
        int lastVal = arr.back();
        arr[removeIdx] = lastVal;
        idx[lastVal] = removeIdx;
        arr.pop_back();
        idx.erase(val);
        return true;
    }
    int getRandom() {
        uniform_int_distribution<int> dist(0, arr.size() - 1);
        return arr[dist(rng)];
    }
};
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import java.util.*;
class RandomizedSet {
    private final Map<Integer, Integer> map = new HashMap<>();
    private final List<Integer> list = new ArrayList<>();
    private final Random random = new Random();
    public RandomizedSet() {}
    public boolean insert(int val) {
        if (map.containsKey(val)) return false;
        list.add(val);
        map.put(val, list.size() - 1);
        return true;
    }
    public boolean remove(int val) {
        if (!map.containsKey(val)) return false;
        int idxToRemove = map.get(val);
        int lastVal = list.get(list.size() - 1);
        list.set(idxToRemove, lastVal);
        map.put(lastVal, idxToRemove);
        list.remove(list.size() - 1);
        map.remove(val);
        return true;
    }
    public int getRandom() {
        return list.get(random.nextInt(list.size()));
    }
}
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import random
class RandomizedSet:
    def __init__(self) -> None:
        self.arr: list[int] = []
        self.idx: dict[int, int] = {}
    def insert(self, val: int) -> bool:
        if val in self.idx:
            return False
        self.arr.append(val)
        self.idx[val] = len(self.arr) - 1
        return True
    def remove(self, val: int) -> bool:
        if val not in self.idx:
            return False
        removeIdx = self.idx[val]
        lastVal = self.arr[-1]
        self.arr[removeIdx] = lastVal
        self.idx[lastVal] = removeIdx
        self.arr.pop()
        del self.idx[val]
        return True
    def getRandom(self) -> int:
        return random.choice(self.arr)