> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Kth Largest Element in a Stream

> Tested Python solution for LeetCode 703 with 13 pytest cases. Generate a practice environment with lcpy.

LeetCode 703, Easy. Topics: Tree, Design, Binary Search Tree, Heap (Priority Queue), Binary Tree, Data Stream. [View on LeetCode](https://leetcode.com/problems/kth-largest-element-in-a-stream/description/).

Generate this problem as a practice environment: tested reference solution, 13 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 703   # by problem number
lcpy gen -s kth_largest_element_in_a_stream   # by problem name
```

## Problem

You are part of a university admissions office and need to keep track of the `kth` highest test score from applicants in real-time. This helps to determine cut-off marks for interviews and admissions dynamically as new applicants submit their scores.

You are tasked to implement a class which, for a given integer `k`, maintains a stream of test scores and continuously returns the `k`th highest test score **after** a new score has been submitted. More specifically, we are looking for the `k`th highest score in the sorted list of all scores.

Implement the `KthLargest` class:

* `KthLargest(int k, int[] nums)` Initializes the object with the integer `k` and the stream of test scores `nums`.
* `int add(int val)` Adds a new test score `val` to the stream and returns the element representing the `k<sup>th</sup>` largest element in the pool of test scores so far.

### Examples

```
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
```

```
Input
["KthLargest", "add", "add", "add", "add"]
[[4, [7, 7, 7, 7, 8, 3]], [2], [10], [9], [9]]
Output
[null, 7, 7, 7, 8]

Explanation
KthLargest kthLargest = new KthLargest(4, [7, 7, 7, 7, 8, 3]);
kthLargest.add(2);   // return 7
kthLargest.add(10);  // return 7
kthLargest.add(9);   // return 7
kthLargest.add(9);   // return 8
```

### Constraints

* 0 \<= nums.length \<= 10\<sup>4\</sup>
* 1 \<= k \<= nums.length + 1
* -10\<sup>4\</sup> \<= nums\[i] \<= 10\<sup>4\</sup>
* -10\<sup>4\</sup> \<= val \<= 10\<sup>4\</sup>
* At most 10\<sup>4\</sup> calls will be made to `add`.

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/kth_largest_element_in_a_stream/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/kth_largest_element_in_a_stream/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
import heapq


class KthLargest:
    # Time: O(n log k) init, O(log k) per add
    # Space: O(k)
    def __init__(self, k: int, nums: list[int]) -> None:
        self.k = k
        self.min_heap: list[int] = []
        for num in nums:
            self.add(num)

    # Time: O(log k)
    # Space: O(k)
    def add(self, val: int) -> int:
        heapq.heappush(self.min_heap, val)
        if len(self.min_heap) > self.k:
            heapq.heappop(self.min_heap)
        # kth largest is the smallest among the k largest elements
        return self.min_heap[0]
```

## Complexity

| Time                              | Space |
| --------------------------------- | ----- |
| O(n log k) init, O(log k) per add | O(k)  |

## Tags

[NeetCode 150](/catalog/neetcode-150), [NeetCode 250](/catalog/neetcode-250), [NeetCode All](/catalog/neetcode).