Question
A counter starts at 1. In one operation you either add 1 to it or double it. Count the distinct sequences of operations that turn 1 into exactly n (n >= 1). Two sequences are different if they differ anywhere, even when they pass through the same values — for example, reaching 2 by adding 1 and reaching 2 by doubling are two different sequences. Return the count; n = 1 gives 1 (the empty sequence).
count_counter_paths(n: int) → int[4]out4[6]out6State your approach and its time/space complexity out loud before you optimize. Handle the edge cases (empty input, duplicates, overflow), and say why you chose this over the brute force. Green tests are the floor, not the grade.
Vibe coding: describe the solution in plain language (or narrate it) and the coach grades your approach. Generating runnable code from your description is coming next.