Top K Problem Statement

You are given an array of integers, arr, of size n, which is analogous to a continuous stream of integers input. Your task is to find k largest elements from a given stream of numbers.

By definition, we don’t know the size of the input stream. Hence, produce k largest elements seen so far, at any given time. For repeated numbers, return them only once.

If there are less than k distinct elements in arr, return all of them.

• Don’t rely on size of input array arr.
• Feel free to use built-in functions if you need a specific data-structure.

Example One

{
"arr": [1, 5, 4, 4, 2],
"k": 2
}

Output:

[4, 5]

Example Two

{
"arr": [1, 5, 1, 5, 1],
"k": 3
}

Output:

[5, 1]

Notes

• Return an integer array, containing k largest elements.
• Order of elements in the output does not matter.

Constraints:

• 1 <= n <= 10⁵
• 1 <= k <= 10⁵
• arr may contain duplicate numbers
• arr may or may not be sorted

We have provided one solution for this problem.

Top K Solution: Optimal

We need to preserve the order of elements in a sorted manner. If we can do that, we can obtain top k elements. Also, if an element is smaller than the last element in top k, then that element can be dropped as we are not deleting elements.

We can maintain a balanced BST or a sorted set collection. Keep adding new elements to the sorted set and if the size of the tree increases more than k, remove the smallest element.

Time Complexity

O(n * log(k)).

Auxiliary Space Used

O(k).

Space Complexity

O(n + k).

Code For Top K Solution: Optimal

    /*
    * Asymptotic complexity in terms of size of `arr` `n` and `k`:
    * Time: O(n * log(k)).
    * Auxiliary space: O(k).
    * Total space: O(n + k).
    */
    static ArrayList<Integer> top_k(ArrayList<Integer> arr, int k) {
        // TreeSet will maintain set of elements in a sorted fashion
        TreeSet<Integer> tree = new TreeSet<Integer>();
        /*
        We will add all elements to the sorted set and when size of the set increases over
        required size k, we will remove the smallest element.
        */
        for (int x : arr) {
            tree.add(x);
            if (tree.size() > k) {
                tree.pollFirst();
            }
        }
        ArrayList<Integer> ans= new ArrayList<Integer>();
        for (int x : tree) {
            ans.add(x);
        }
        return ans;
    }

We hope that these solutions to top Kth problem have helped you level up your coding skills. You can expect problems like these at top tech companies like Amazon and Google.

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