Top-K with the heap pointing the wrong way

A dashboard shows the k highest scores out of n (n up to 10⁸ streamed from disk, k = 100). The current implementation is correct but runs out of memory and is slow. A junior engineer "fixed" the memory issue in top_k_v2, which is now wrong. Diagnose both versions.

1import heapq
2 
3def top_k_v1(scores, k):
4    # correct but heavy
5    heap = []
6    for s in scores:
7        heapq.heappush(heap, -s)
8    return [-heapq.heappop(heap) for _ in range(k)]
9 
10 
11def top_k_v2(scores, k):
12    # "memory fix" — keeps only k elements
13    heap = []
14    for s in scores:
15        heapq.heappush(heap, -s)
16        if len(heap) > k:
17            heapq.heappop(heap)
18    return sorted((-x for x in heap), reverse=True)
19 
20print(top_k_v2([5, 1, 9, 3, 7], 2))   # prints [3, 1], expected [9, 7]

1. Explain why top_k_v1 is correct and what its time and space costs are for n = 10⁸, k = 100.
2. Explain exactly why top_k_v2 returns the two *smallest* values.
3. Write the correct bounded-size version and state the invariant the heap maintains.
4. Compare with heapq.nlargest, sorting, and quickselect. When would you choose each?