Kth Largest Values in a Stream

Question

The question asks you to design an algorithm that efficiently finds the Kth largest element in a stream of integers.

Codemia · Accepted Answer

To solve the problem of finding the Kth largest element in a stream, we need an efficient way to manage incoming integers and keep track of the largest elements. A naive approach would involve sorting the entire stream each time, which is not feasible for large datasets. Instead, we can utilize a min-heap to maintain the top K largest elements.

1. **Use a Min-Heap**: We will maintain a min-heap of size K. The root of the heap will always contain the Kth largest element. 
2. **Stream Processing**: As new elements arrive in the stream, we will add them to the heap. If the size of the heap exceeds K, we will remove the smallest element (the root). This ensures that only the largest K elements are stored in the heap at any time.

Here is a Python implementation of the approach:

```python
import heapq

class KthLargest:
    def __init__(self, k: int, nums: List[int]):
        self.k = k
        self.min_heap = nums[:k]
        heapq.heapify(self.min_heap)
        for num in nums[k:]:
            self.add(num)

def add(self, val: int) -> int:
        if len(self.min_heap) < self.k:
            heapq.heappush(self.min_heap, val)
        elif val > self.min_heap[0]:
            heapq.heappop(self.min_heap)
            heapq.heappush(self.min_heap, val)
        return self.min_heap[0]
```
This implementation initializes the heap with the first K elements and processes each new element in constant time.

The time complexity of adding a new element is O(log K) due to the heap operations. The space complexity is O(K) since we are storing K elements in the heap. This makes our solution efficient for streaming data, as we do not need to sort the entire dataset.

It's important to handle edge cases, such as when the stream has fewer than K elements initially. In such cases, we should decide how to return the Kth largest value (e.g., return None or a specific value). Additionally, we should consider the behavior of the algorithm with duplicate values and ensure that it still correctly identifies the Kth largest element.

Kth Largest Values in a Stream

Amazon

What the Interviewer Expects

Key Topics to Cover

How to Approach This

Possible Follow-up Questions

Sharpen Your Skills on Codemia

Sample Answer

Framing

Approach

Submit Your Answer

Amazon Software Engineer Interview Guide

Related Questions

Binary Search on graph

Count kth largest element in array

Find connected components in string

Merge Three Sorted strings

Binary Search on string