Which change to the backtracking algorithm correctly handles this variant?
hard🎤 Interviewer Follow-up Q15 of Q15
Subsets & Combinations - Combination Sum III (K Numbers to N)
Suppose the problem is modified so that numbers 1 to 9 can be reused any number of times in combinations summing to n with size k. Which change to the backtracking algorithm correctly handles this variant?
AAdd a visited set to prevent reusing numbers and keep backtrack(i + 1, comb, total + i)
BKeep the recursive call as backtrack(i + 1, comb, total + i) but allow duplicates in the result
CChange the recursive call to backtrack(i, comb, total + i) to allow reuse of the same number i
DUse a dynamic programming approach instead of backtracking to handle reuse efficiently
Step-by-Step Solution
Step 1: Understand reuse requirement
Allowing reuse means the same number can be chosen multiple times, so next recursion should start at current number i, not i+1.
Step 2: Modify recursive call
Change backtrack(i + 1, ...) to backtrack(i, ...) to allow repeated picks of i.
Step 3: Confirm correctness
This change correctly explores combinations with repeated numbers without duplicates.
Final Answer:
Option C -> Option C
Quick Check:
Recursing with start=i enables reuse of number i [OK]
Quick Trick:Reuse requires recursive calls with start index unchanged [OK]
Common Mistakes:
MISTAKES
Not changing start index to allow reuse
Allowing duplicates by mistake
Switching to DP unnecessarily
Trap Explanation:
PITFALL
Keeping start=i+1 forbids reuse; adding visited set prevents reuse; DP is overkill here.
Interviewer Note:
CONTEXT
Tests candidate's understanding of backtracking modifications for reuse constraints.
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