The Runtime Theory
mediumLeetCode#backtracking#unbounded-choice

Combination Sum

Find unique combinations that sum to target when each positive candidate may be reused.

The Runtime Theory Team25 min read
Solve it

Solving happens on the judge — come back and mark it done

Sample cases

incandidates=[2,3,6,7], target=7

out[[2,2,3],[7]]

incandidates=[2], target=1

out[]

incandidates=[1], target=2

out[[1,1]]

Find unique combinations that sum to target when each positive candidate may be reused.

A good solution should

  • State the invariant or decision rule that makes the approach correct.
  • Explain the time and space complexity in terms of the input sizes and required output.
  • Handle empty, minimal, duplicate, and boundary-shaped inputs covered by the contract.

Reasoning prompt

Sort candidates to stop when values exceed the remaining target. Recurse from the same index to allow reuse without permutation duplicates.

Use the linked judge for the canonical problem. The examples above are compact TRT checks; write additional cases before submitting, especially for the boundary that tends to break your chosen invariant.

More practice in this topic

medium · backtrackingCombination Sum IImedium · backtrackingLetter Combinations of a Phone Numberhard · backtrackingN-Queens

One dispatch a week

The trace behind each problem, the tradeoff that explains it, and one technical dispatch per week — no noise.

One technical dispatch per week. No noise.

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