[Solved] Suppose now you can reuse sticks after merging (i.e., merged sticks remain... Which modification to the algorithm correctly computes the minimum cost to connect all sticks under this new rule? | Greedy Algorithms

Greedy Algorithms - Minimum Cost to Connect Sticks

Suppose now you can reuse sticks after merging (i.e., merged sticks remain available for future merges without removal). Which modification to the algorithm correctly computes the minimum cost to connect all sticks under this new rule?

AUse a dynamic programming approach to consider all merge sequences

BSort sticks once and merge sticks in ascending order without a heap

CThe problem becomes ill-defined; no algorithm can guarantee minimum cost with reuse

DUse the same min-heap approach but do not remove merged sticks from the heap

Step-by-Step Solution

Solution:

Step 1: Understand reuse impact
If sticks can be reused infinitely, merges do not reduce the number of sticks, so the problem changes fundamentally.
Step 2: Analyze problem feasibility
Because sticks remain after merging, the process can continue indefinitely, making minimum total cost undefined or infinite.
Final Answer:
Option C -> Option C
Quick Check:
Reuse breaks the problem constraints -> no minimal cost solution [OK]

Quick Trick: Reusing sticks breaks problem constraints -> no minimal cost [OK]

Common Mistakes:

MISTAKES

Assuming min-heap still works without removing merged sticks
Trying to sort once ignoring dynamic merges
Attempting DP without problem redefinition

Trap Explanation:

PITFALL

Candidates may think reuse is a minor change, but it fundamentally breaks the problem's termination and minimality.

Interviewer Note:

CONTEXT

Tests candidate's ability to reason about problem constraints and algorithm applicability under variants.

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More Greedy Algorithms Quizzes

Which modification to the algorithm correctly computes the minimum cost to connect all sticks under this new rule?

Step 1: Understand reuse impact

Step 2: Analyze problem feasibility

Final Answer:

Quick Check:

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