Ugly numbers and comparators

Questions 1 to 5 of 8

1. 1. What does this print? ``python import heapq class NoOrder: def __init__(self, name): self.name = name heap = [] heapq.heappush(heap, NoOrder("A")) print("first push ok") try: heapq.heappush(heap, NoOrder("B")) except TypeError as e: print("TypeError:", e) ``

   first push ok, then second push okTypeError on the first push, so nothing is printedfirst push ok, then TypeError: '<' not supported between instances of 'NoOrder' and 'NoOrder'first push ok, then TypeError: NoOrder objects cannot be compared with ==
2. 2. Each job is pushed as a tuple (priority, arrival, name). What does this print? The names are joined by single spaces. ``python import heapq pq = [] for name, priority, arrival in [("X", 3, 7), ("Y", 1, 9), ("Z", 3, 2), ("W", 1, 4)]: heapq.heappush(pq, (priority, arrival, name)) out = [] while pq: out.append(heapq.heappop(pq)[2]) print(" ".join(out)) ``

   X Y Z WW Y Z XY W X ZW Z Y X
3. 3. A comparison function is meant to order jobs by priority. Two jobs both have priority 2. Which problem does it cause? ``python def bad(a, b): return -1 if a.priority <= b.priority else 1 ``

   It compares arrival numbers instead of priority, so the first key is ignoredIt returns -1 for every pair, which reverses the order of the jobsWhen priorities are equal it returns -1 in both directions, so each job says it comes first and the heap order becomes unreliableIt only works when cmp_to_key wraps it, so the code does not run on its own
4. 4. The function below should give the ugly numbers 1, 2, 3, 4, 5, 6, 8, 9, 10, 12. Its output for n = 10 has 6 twice. Which part is the cause? ``python def ugly_numbers(n): ugly = [0] * n ugly[0] = 1 i2 = i3 = i5 = 0 for k in range(1, n): next2 = ugly[i2] * 2 next3 = ugly[i3] * 3 next5 = ugly[i5] * 5 nxt = min(next2, next3, next5) ugly[k] = nxt if nxt == next2: i2 += 1 elif nxt == next3: i3 += 1 elif nxt == next5: i5 += 1 return ugly ``

   min should be max, so the largest candidate is storedThe ugly[k] = nxt line should store the candidate before the minimum is takenThe pointers should start at 1, not 0The elif chain moves only one pointer, so when 6 is both 2 times 3 and 3 times 2, the 3-times pointer stays behind
5. 5. What is the 11th ugly number?

   16151820