Insert Delete Search and GetRandom in Constant Time 2 - Duplicates allowed | K5kC

Problem

RandomizedCollection is a data structure that contains a collection of numbers, possibly duplicates (i.e., a multiset). It should support inserting and removing specific elements and also removing a random element.

Implement the RandomizedCollection class:

RandomizedCollection() Initializes the empty RandomizedCollection object.
bool insert(int val) Inserts an item val into the multiset, even if the item is already present. Returns true if the item is not present, false otherwise.
bool remove(int val) Removes an item val from the multiset if present. Returns true if the item is present, false otherwise. Note that if val has multiple occurrences in the multiset, we only remove one of them.
int getRandom() Returns a random element from the current multiset of elements. The probability of each element being returned is linearly related to the number of same values the multiset contains.

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

Note: The test cases are generated such that getRandom will only be called if there is at least one item in the RandomizedCollection.

Examples

Example 1:

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

**Explanation**
RandomizedCollection randomizedCollection = new RandomizedCollection();
randomizedCollection.insert(1);   // return true since the collection does not contain 1.
                                  // Inserts 1 into the collection.
randomizedCollection.insert(1);   // return false since the collection contains 1.
                                  // Inserts another 1 into the collection. Collection now contains [1,1].
randomizedCollection.insert(2);   // return true since the collection does not contain 2.
                                  // Inserts 2 into the collection. Collection now contains [1,1,2].
randomizedCollection.getRandom(); // getRandom should:
                                  // - return 1 with probability 2/3, or
                                  // - return 2 with probability 1/3.
randomizedCollection.remove(1);   // return true since the collection contains 1.
                                  // Removes 1 from the collection. Collection now contains [1,2].
randomizedCollection.getRandom(); // getRandom should return 1 or 2, both equally likely.

This question is follow up of - Insert Delete Search and GetRandom in Constant Time 1 - Dupes not allowed

Solution

Method 1 – HashMap of Sets and List

Intuition

We had already discussed why we need arraylist and map in method 1 - Insert Delete Search and GetRandom in Constant Time 1 - Dupes not allowed. But now we have duplicates. So, some cases to handle:

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For example, after insert(1), insert(1), insert(2), getRandom() should have 2/3 chance return 1 and 1/3 chance return 2.

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remove(1), 1 and 2 should have an equal chance of being selected by getRandom().

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So, instead of saving Map of <Value and Location in List>, we need to add a set of locations to hashmap to remember all the locations of a duplicated number.

To support duplicates and achieve average O(1) time for insert, remove, and getRandom, we use a list to store all elements and a hash map to track the indices of each value in the list. For duplicates, the hash map stores a set of indices for each value. This allows us to quickly find and update positions when inserting or removing elements.

Approach

Use a list to store all elements, including duplicates.
Use a hash map where each value maps to a set of indices in the list.
On insert, add the value to the list and record its index in the hash map.
On remove, pick any index for the value, swap the last element into that index, update the hash map, and remove the last element from the list.
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 collection.

Code

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using namespace std;
class RandomizedCollection {
    vector<int> arr;
    unordered_map<int, unordered_set<int>> idx;
    mt19937 rng{random_device{}()};
public:
    bool insert(int val) {
        arr.push_back(val);
        idx[val].insert(arr.size() - 1);
        return idx[val].size() == 1;
    }
    bool remove(int val) {
        if (!idx[val].size()) return false;
        int removeIdx = *idx[val].begin();
        int lastVal = arr.back();
        arr[removeIdx] = lastVal;
        idx[lastVal].insert(removeIdx);
        idx[lastVal].erase(arr.size() - 1);
        idx[val].erase(removeIdx);
        arr.pop_back();
        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 RandomizedCollection {
    private final List<Integer> arr = new ArrayList<>();
    private final Map<Integer, Set<Integer>> idx = new HashMap<>();
    private final Random rand = new Random();
    public boolean insert(int val) {
        arr.add(val);
        idx.computeIfAbsent(val, k -> new HashSet<>()).add(arr.size() - 1);
        return idx.get(val).size() == 1;
    }
    public boolean remove(int val) {
        Set<Integer> set = idx.get(val);
        if (set == null || set.isEmpty()) return false;
        int removeIdx = set.iterator().next();
        int lastVal = arr.get(arr.size() - 1);
        arr.set(removeIdx, lastVal);
        idx.get(lastVal).add(removeIdx);
        idx.get(lastVal).remove(arr.size() - 1);
        set.remove(removeIdx);
        arr.remove(arr.size() - 1);
        return true;
    }
    public int getRandom() {
        return arr.get(rand.nextInt(arr.size()));
    }
}

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import random
class RandomizedCollection:
    def __init__(self) -> None:
        self.arr: list[int] = []
        self.idx: dict[int, set[int]] = {}
    def insert(self, val: int) -> bool:
        self.arr.append(val)
        if val not in self.idx:
            self.idx[val] = set()
        self.idx[val].add(len(self.arr) - 1)
        return len(self.idx[val]) == 1
    def remove(self, val: int) -> bool:
        if val not in self.idx or not self.idx[val]:
            return False
        removeIdx = next(iter(self.idx[val]))
        lastVal = self.arr[-1]
        self.arr[removeIdx] = lastVal
        self.idx[lastVal].add(removeIdx)
        self.idx[lastVal].discard(len(self.arr) - 1)
        self.idx[val].remove(removeIdx)
        self.arr.pop()
        return True
    def getRandom(self) -> int:
        return random.choice(self.arr)

Problem#

Examples#

Solution#

Method 1 – HashMap of Sets and List#

Intuition#

Approach#

Complexity#

Code#