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Consider the following Python code snippet that calculates the minimum cost to connect sticks: ```python import heapq def min_cost(sticks): heapq.heapify(sticks) total = 0 while len(sticks) > 1: a = heapq.heappop(sticks) b = heapq.heappop(sticks) cost = a + b total += cost heapq.heappush(sticks, cost) return total ``` What is the output of min_cost([1, 8, 3, 5])?

easy🧾 Trace Q3 of Q15
Greedy Algorithms - Minimum Cost to Connect Sticks
Consider the following Python code snippet that calculates the minimum cost to connect sticks: ```python import heapq def min_cost(sticks): heapq.heapify(sticks) total = 0 while len(sticks) > 1: a = heapq.heappop(sticks) b = heapq.heappop(sticks) cost = a + b total += cost heapq.heappush(sticks, cost) return total ``` What is the output of min_cost([1, 8, 3, 5])?
A29
B30
C27
D26
Step-by-Step Solution
Solution:
  1. Step 1: Initialize min-heap

    Heapify sticks: [1,3,5,8]
  2. Step 2: Merge smallest two sticks repeatedly

    Pop 1 and 3, cost=4, total=4, push 4 -> heap: [4,5,8]
    Pop 4 and 5, cost=9, total=13, push 9 -> heap: [8,9]
    Pop 8 and 9, cost=17, total=30, push 17 -> heap: [17]
  3. Final Answer:

    Option B -> Option B
  4. Quick Check:

    Sum of all merge costs is 30 [OK]
Quick Trick: Sum costs of merging smallest sticks repeatedly [OK]
Common Mistakes:
MISTAKES
  • Adding sticks incorrectly or missing a merge step
  • Confusing total cost with final stick length
  • Not using a min-heap leading to suboptimal merges
Trap Explanation:
PITFALL
  • Choosing 29 or 27 comes from incorrect merge order or calculation errors.
Interviewer Note:
CONTEXT
  • Tests ability to trace heap-based greedy algorithm step-by-step.
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