Greedy Algorithms - Minimum Cost to Connect Sticks
If the cost to connect two sticks is defined as the product of their lengths instead of the sum, which approach is most appropriate to find the minimum total cost to connect all sticks?
If the cost to connect two sticks is defined as the product of their lengths instead of the sum, which approach is most appropriate to find the minimum total cost to connect all sticks?
hard🔁 Follow-up Q10 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand cost function
Cost is product, not sum, so greedy merging smallest sticks first may not minimize total cost.Step 2: Complexity of product cost
Optimal merge order depends on future merges, requiring exploration of merge sequences.Step 3: Suitable approach
Dynamic programming can explore all merge orders and store intermediate results to find minimal total cost.Final Answer:
Option C -> Option CQuick Check:
Product cost breaks greedy assumptions [OK]
Quick Trick: Product cost requires DP, greedy fails [OK]
Common Mistakes:
MISTAKES- Applying greedy min-heap approach blindly
- Assuming sorting solves the problem
- Ignoring complexity of product cost merges
Trap Explanation:
PITFALL- Greedy looks simpler but doesn't guarantee minimal product cost.
Interviewer Note:
CONTEXT- Tests ability to adapt algorithmic approach when cost function changes.
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