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1. What does this program print, line by line? ``

python
from collections import Counter

values = [4, 2, 4, 4, 9, 2]
counts = Counter(values)
print(sorted(counts.items()))
print('most frequent:', counts.most_common(1)[0])
print(counts[7])

``

[(4, 3), (2, 2), (9, 1)], most frequent: (4, 3), then 0[(2, 2), (4, 3), (9, 1)], most frequent: (4, 3), then 0[(2, 2), (4, 3), (9, 1)], most frequent: (9, 1), then 0[(2, 2), (4, 3), (9, 1)], most frequent: (4, 3), then KeyError

2. What does this program print? ``

python
import heapq

def top_k(values, k):
    if k == 0:
        return []
    heap = []
    for v in values:
        if len(heap) < k:
            heapq.heappush(heap, v)
        elif v > heap[0]:
            heapq.heapreplace(heap, v)
    return sorted(heap)

print(top_k([8, 3, 6, 1, 10, 7], 2))

``

[10, 8][6, 8][8, 10][1, 3]

3. A top-k function reads n numbers and keeps a min-heap of size k. Which total cost does it take, in Big-O terms?

O(n log k)O(k log n)O(n), because each value is read only onceO(n * k)

4. A generator gives one million numbers, and you want the top 5. What is the most values the heap holds at any one time?

1,000,000About 20, which is log2 of 1,000,00015

5. The count_pairs function from the two-sum lesson counts pairs of positions whose values add up to the target. What does it return for 100,000 copies of the value 1 with a target of 2?

The total stops with an error once it passes about 2 billionThe total is 4999950000 and prints correctly, because a Python int has no fixed size limitThe total wraps around past 2 billion and prints a wrong number, with no errorThe total is always 0, because a dict cannot count equal values

Frequency and top-k with Counter and heapq