Algorithmic Complexity & Code-Level Optimization Questions

import heapq
from typing import List, Iterable

class TopKStream:
    def __init__(self, k: int):
        assert k >= 1
        self.k = k
        self.heap: List[int] = []  # min-heap of current top-k

    def process(self, value: int) -> None:
        """
        Process a single integer from the stream.
        O(log k) time.
        """
        if len(self.heap) < self.k:
            heapq.heappush(self.heap, value)
        else:
            # only replace if value is larger than the smallest in top-k
            if value > self.heap[0]:
                heapq.heapreplace(self.heap, value)

    def process_batch(self, values: Iterable[int]) -> None:
        """
        Process a batch/iterable of integers efficiently.
        """
        for v in values:
            self.process(v)

    def get_topk_sorted(self, reverse: bool = True) -> List[int]:
        """
        Return top-k sorted descending by default (largest first).
        Does not mutate the internal heap (we operate on a copy).
        Complexity: O(k log k) for sorting the k elements.
        """
        return sorted(self.heap, reverse=reverse)