Subsets Pattern

When to use Subsets

• The problem asks for all subsets, all permutations, or all combinations of a small input.
• You need to generate every possible string that satisfies a structural constraint (parentheses, IP addresses, letter case).
• You can frame the answer as a sequence of include/exclude decisions on each input element.
• The input size is small (n <= 20 for subsets, n <= 10 for permutations) because the output is exponential.
• Counting alone is not enough — you must enumerate the actual combinations or paths.

Template

function subsets(nums) {
  const result = [[]];
  for (const num of nums) {
    const size = result.length;
    for (let i = 0; i < size; i++) {
      result.push([...result[i], num]);
    }
  }
  return result;
}

Common mistakes

• Iterating over `result` with a normal length read in the inner loop, which grows the array as you append and creates an infinite loop.
• Forgetting to make a shallow copy of the partial subset before pushing it into the result, which means every saved subset points to the same mutating array.
• On Subsets II, failing to sort the input first and skip duplicates — duplicates produce identical subsets that violate the unique-output requirement.
• Using the recursive include/exclude template without a depth parameter, causing the recursion to revisit indices.
• Pruning too aggressively in Combination Sum and missing valid combinations that use the same number multiple times.