[Solved] If the Combination Sum II problem is modified to return only the top K unique combinations with the largest sums less than or equal to the target, which approach best adapts the backtracking... | Subsets & Combinations

Subsets & Combinations - Combination Sum II (No Reuse, Duplicates)

If the Combination Sum II problem is modified to return only the top K unique combinations with the largest sums less than or equal to the target, which approach best adapts the backtracking algorithm?

AUse backtracking without pruning and store all combinations before filtering.

BUse dynamic programming to find all combinations and then sort to pick top K.

CUse greedy approach selecting largest candidates first without backtracking.

DUse backtracking with pruning and maintain a max-heap of size K to track top sums.

Step-by-Step Solution

Solution:

Step 1: Understand problem change
We want top K unique combinations with largest sums ≤ target, not all combinations.
Step 2: Backtracking with pruning
Backtracking can generate combinations efficiently; pruning avoids unnecessary paths.
Step 3: Maintain max-heap
Use a max-heap (or min-heap depending on implementation) of size K to keep track of top sums dynamically.
Step 4: Avoid storing all combinations
Storing all combinations (Use backtracking without pruning and store all combinations before filtering.) is inefficient; greedy (Use greedy approach selecting largest candidates first without backtracking.) may miss valid combos; DP (Use dynamic programming to find all combinations and then sort to pick top K.) is costly.
Final Answer:
Option D -> Option D
Quick Check:
Heap keeps top K efficiently during backtracking [OK]

Quick Trick: Use pruning plus heap to track top K combos [OK]

Common Mistakes:

MISTAKES

Trying greedy approach which misses combinations
Storing all combinations causing memory issues
Ignoring pruning leading to inefficiency

Trap Explanation:

PITFALL

Option B looks plausible but DP is inefficient for large inputs; greedy misses combos.

Interviewer Note:

CONTEXT

Tests ability to adapt backtracking for optimization and top-K selection.

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More Subsets & Combinations Quizzes

If the Combination Sum II problem is modified to return only the top K unique combinations with the largest sums less than or equal to the target, which approach best adapts the backtracking algorithm?

Step 1: Understand problem change

Step 2: Backtracking with pruning

Step 3: Maintain max-heap

Step 4: Avoid storing all combinations

Final Answer:

Quick Check:

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