# LeetCode 703: Kth Largest Element In A Stream — Step-by-Step Visual Trace

**Easy** — Heap | Priority Queue | Data Stream | Design

## The Problem

Design a class that efficiently finds the kth largest element in a stream of integers, where new values are continuously added and we need to return the kth largest element after each addition.

## Approach

Use a min-heap of size k to maintain the k largest elements seen so far. The root of this min-heap will always be the kth largest element, allowing constant-time retrieval after each insertion.

**Time:** O(log k) per add operation, O(n log k) for initialization · **Space:** O(k)

## Code

```python
import heapq

class KthLargest:
    def __init__(self, k: int, nums: List[int]):
        self.min_heap = []
        self.k = k

        for num in nums:
            self.add(num)

    def add(self, val: int) -> int:
        heapq.heappush(self.min_heap, val)

        if len(self.min_heap) > self.k:
            heapq.heappop(self.min_heap)

        return self.min_heap[0]

# Your KthLargest object will be instantiated and called as such:
# obj = KthLargest(k, nums)
# param_1 = obj.add(val)
```

## Watch It Run

> **[Open interactive visualization](https://tracelit.dev/app?trace=0703_kth-largest-element-in-a-stream)**

> **Try it yourself:** Open [TraceLit](https://tracelit.dev/app?trace=0703_kth-largest-element-in-a-stream) and step through every line.

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