039. Combination Sum

At a Glance

• Topic: Array
• Pattern: Analyze Pattern
• Difficulty: Medium
• LeetCode: 039

Problem Statement

Given an array of distinct integers candidates and a target integer target, return a list of all unique combinations of candidates where the chosen numbers sum to target. You may return the combinations in any order.

The same number may be chosen from candidates an unlimited number of times. Two combinations are unique if the frequency of at least one of the chosen numbers is different.

The test cases are generated such that the number of unique combinations that sum up to target is less than 150 combinations for the given input.

Example 1:

Input: candidates = [2,3,6,7], target = 7 Output: [[2,2,3],[7]] Explanation: 2 and 3 are candidates, and 2 + 2 + 3 = 7. Note that 2 can be used multiple times. 7 is a candidate, and 7 = 7. These are the only two combinations.

Example 2:

Input: candidates = [2,3,5], target = 8 Output: [[2,2,2,2],[2,3,3],[3,5]]

Example 3:

Input: candidates = [2], target = 1 Output: []

Constraints:

1 <= candidates.length <= 30
2 <= candidates[i] ...

Approach & Solution Steps

• Brute — generate multisets — exponential waste.
• Optimal — DFS with start index, prune when sum > target — O(2^target) worst conceptual; tight in practice with pruning.

Optimal JS Solution

function combinationSum(candidates, target) {
  const result = [];
  const path = [];

  function dfs(startIndex, remaining) {
    if (remaining === 0) {
      result.push([...path]);
      return;
    }
    if (remaining < 0) {
      return;
    }
    for (let index = startIndex; index < candidates.length; index += 1) {
      path.push(candidates[index]);
      dfs(index, remaining - candidates[index]);
      path.pop();
    }
  }

  dfs(0, target);
  return result;
}

Edge Cases & Pitfalls

• Always consider empty or null inputs.
• Watch out for off-by-one index errors.