LeetCode 380 Insert Delete GetRandom O(1)

Table of contents

Description

Question Links: LeetCode 380

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.

Example 1:

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.

Constraints:

• $-2^{31} \leq val \leq 2^{31} - 1$
• At most $2 \times 10^5$ calls will be made to insert, remove, and getRandom.
• There will be at least one element in the data structure when getRandom is called.

Solution

Idea

The key insight is that we need O(1) for three different operations:

1. insert — checking membership and adding: use a hash map.
2. remove — finding and removing: hash map gives O(1) lookup, but we also need O(1) removal from the collection used by getRandom.
3. getRandom — uniform random access by index: use a dynamic array (ArrayList/Vec).

The trick for O(1) removal from the array is to swap the element to remove with the last element, then pop the last. The hash map stores val -> index so we can locate any element in the array instantly.

Before remove(val=3):

  Array:   [5, 3, 8, 7]     Map: {5:0, 3:1, 8:2, 7:3}
                ^
  Step 1: swap with last
  Array:   [5, 7, 8, 7]     Map: {5:0, 7:1, 8:2, ...}
  Step 2: pop last, remove from map
  Array:   [5, 7, 8]        Map: {5:0, 7:1, 8:2}

Complexity: Time $O(1)$ average for all operations, Space $O(n)$.

Java

class RandomizedSet {
    ArrayList<Integer> nums;
    HashMap<Integer, Integer> valIndex; // val -> index in nums
    Random rand;

    public RandomizedSet() {
        nums = new ArrayList<>();
        valIndex = new HashMap<>();
        rand = new Random();
    }

    public boolean insert(int val) {
        if (valIndex.containsKey(val)) return false; // O(1) lookup
        valIndex.put(val, nums.size());
        nums.add(val); // O(1) amortized append
        return true;
    }

    public boolean remove(int val) {
        if (!valIndex.containsKey(val)) return false; // O(1) lookup
        int i = valIndex.get(val);
        if (i < nums.size() - 1) { // swap with last, O(1)
            int last = nums.get(nums.size() - 1);
            nums.set(i, last);
            valIndex.put(last, i);
        }
        valIndex.remove(val);
        nums.remove(nums.size() - 1); // O(1) pop from end
        return true;
    }

    public int getRandom() {
        return nums.get(rand.nextInt(nums.size())); // O(1) random index
    }
}

Python

class RandomizedSet:

    def __init__(self):
        self.vals = []
        self.val_index = {}

    def insert(self, val: int) -> bool:
        if val in self.val_index:  # O(1) hash lookup
            return False
        self.val_index[val] = len(self.vals)
        self.vals.append(val)  # O(1) amortized append
        return True

    def remove(self, val: int) -> bool:
        if val not in self.val_index:  # O(1) hash lookup
            return False
        i = self.val_index[val]
        last = self.vals[-1]
        self.vals[i] = last  # O(1) swap last into removed slot
        self.val_index[last] = i
        self.vals.pop()  # O(1) pop from end
        del self.val_index[val]
        return True

    def getRandom(self) -> int:
        return random.choice(self.vals)  # O(1) random index access

C++

class RandomizedSet {
    vector<int> nums;
    unordered_map<int, int> valToIdx; // val -> index in nums

public:
    RandomizedSet() {}

    bool insert(int val) {
        if (valToIdx.count(val)) return false; // O(1) lookup
        valToIdx[val] = nums.size();
        nums.push_back(val); // O(1) amortized
        return true;
    }

    bool remove(int val) {
        if (!valToIdx.count(val)) return false; // O(1) lookup
        int idx = valToIdx[val];
        int last = nums.back();
        nums[idx] = last;         // O(1) swap with last
        valToIdx[last] = idx;
        nums.pop_back();          // O(1) pop
        valToIdx.erase(val);
        return true;
    }

    int getRandom() {
        return nums[rand() % nums.size()]; // O(1)
    }
};

Rust

use rand::Rng;
use std::collections::HashMap;

struct RandomizedSet {
    vals: Vec<i32>,
    val_index: HashMap<i32, usize>,
}

impl RandomizedSet {
    fn new() -> Self {
        Self { vals: Vec::new(), val_index: HashMap::new() }
    }

    fn insert(&mut self, val: i32) -> bool {
        if self.val_index.contains_key(&val) { // O(1) lookup
            return false;
        }
        self.val_index.insert(val, self.vals.len());
        self.vals.push(val); // O(1) amortized
        true
    }

    fn remove(&mut self, val: i32) -> bool {
        if let Some(&idx) = self.val_index.get(&val) { // O(1) lookup
            let last = *self.vals.last().unwrap();
            self.vals[idx] = last;       // O(1) swap with last
            self.val_index.insert(last, idx);
            self.vals.pop();             // O(1) pop
            self.val_index.remove(&val);
            true
        } else {
            false
        }
    }

    fn get_random(&self) -> i32 {
        let mut rng = rand::thread_rng();
        let idx = rng.gen_range(0..self.vals.len()); // O(1)
        self.vals[idx]
    }
}