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Top K Problem

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.

If you are preparing for a tech interview at FAANG or any other Tier-1 tech company, register for Interview Kickstart's FREE webinar to understand the best way to prepare.

Interview Kickstart offers interview preparation courses taught by FAANG+ tech leads and seasoned hiring managers. Our programs include a comprehensive curriculum, unmatched teaching methods, and career coaching to help you nail your next tech interview.

We offer 18 interview preparation courses, each tailored to a specific engineering domain or role, including the most in-demand and highest-paying domains and roles, such as:

‍To learn more, register for the FREE webinar.

Try yourself in the Editor

Note: Input and Output will already be taken care of.

Top K Problem

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.

If you are preparing for a tech interview at FAANG or any other Tier-1 tech company, register for Interview Kickstart's FREE webinar to understand the best way to prepare.

Interview Kickstart offers interview preparation courses taught by FAANG+ tech leads and seasoned hiring managers. Our programs include a comprehensive curriculum, unmatched teaching methods, and career coaching to help you nail your next tech interview.

We offer 18 interview preparation courses, each tailored to a specific engineering domain or role, including the most in-demand and highest-paying domains and roles, such as:

‍To learn more, register for the FREE webinar.

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