MD ARIFUL HAQUE

Posted on Aug 12

703. Kth Largest Element in a Stream

#php #leetcode #algorithms #programming

Difficulty: Easy

Topics: Tree, Design, Binary Search Tree, Heap (Priority Queue), Binary Tree, Data Stream

Design a class to find the k^th largest element in a stream. Note that it is the k^th largest element in the sorted order, not the k^th distinct element.

Implement KthLargest class:

KthLargest(int k, int[] nums) Initializes the object with the integer k and the stream of integers nums.
int add(int val) Appends the integer val to the stream and returns the element representing the k^th largest element in the stream.

Example 1:

*Input:

  ["KthLargest", "add", "add", "add", "add", "add"]
  [[3, [4, 5, 8, 2]], [3], [5], [10], [9], [4]]

Output: [null, 4, 5, 5, 8, 8]
Explanation:

  KthLargest kthLargest = new KthLargest(3, [4, 5, 8, 2]);
  kthLargest.add(3);   // return 4
  kthLargest.add(5);   // return 5
  kthLargest.add(10);  // return 5
  kthLargest.add(9);   // return 8
  kthLargest.add(4);   // return 8

Example 2:

Input:

  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Output:

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Constraints:

1 <= k <= 10⁴
0 <= nums.length <= 10⁴
-10⁴ <= nums[i] <= 10⁴
-10⁴ <= val <= 10⁴
At most 10⁴ calls will be made to add.
It is guaranteed that there will be at least k elements in the array when you search for the k^th element.

Solution:

We can use a min-heap data structure. Here’s a step-by-step guide to implementing the KthLargest class using PHP:

Min-Heap Data Structure: We will maintain a min-heap (priority queue) of size k. The root of this heap will always give us the k-th largest element.
Initialization: During initialization, we will add the first k elements of the stream to the min-heap. For any additional elements, we will compare each new element with the smallest element in the heap (the root). If the new element is larger, we replace the smallest element with this new element and adjust the heap to maintain the k size.
Adding Elements: Each time an element is added to the stream, we use the same process of comparing and possibly replacing elements in the heap.

Here’s the PHP code to implement the KthLargest class: 703. Kth Largest Element in a Stream

Explanation:

Class Constructor:
- Initializes a min-heap to keep track of the top k elements.
- Inserts each element from the initial nums array into the heap using the add method.
add Method:
- If the heap contains fewer than k elements, the new value is simply inserted.
- If the heap already contains k elements, compare the new value with the smallest value (root) in the heap:
  - If the new value is greater, remove the smallest value and insert the new value.
- Finally, return the smallest value in the heap, which is the k-th largest element.

This approach ensures that we efficiently keep track of the k-th largest element with each insertion into the stream, maintaining an O(log k) complexity for insertion operations due to heap operations.

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703. Kth Largest Element in a Stream

Explanation:

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