Combination Sum II

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Given a collection of candidate numbers candidates (which may contain duplicates) and a target number target, find all unique combinations in candidates where the candidate numbers sum to target. Each number in candidates may only be used once in the combination.

Example 1
Input: candidates = [10,1,2,7,6,1,5], target = 8
Output: [[1,1,6],[1,2,5],[1,7],[2,6]]
Explanation: 1+1+6=8, 1+2+5=8, 1+7=8, 2+6=8.
Example 2
Input: candidates = [2,5,2,1,2], target = 5
Output: [[1,2,2],[5]]

Solution Approach

Sort the array first. The key difference from Combination Sum I is that each element can only be used once (recurse with i+1) and we must skip duplicates at the same tree level to avoid duplicate combinations.

  • Sort candidates to bring duplicates adjacent and enable pruning.
  • In the loop, skip if i > start && candidates[i] == candidates[i-1].
  • Recurse with i+1 (not i) since each element is used at most once.
  • Prune when candidates[i] > remaining.
Java
import java.util.*;

class Solution {
    public List<List<Integer>> combinationSum2(int[] candidates, int target) {
        Arrays.sort(candidates);
        List<List<Integer>> result = new ArrayList<>();
        backtrack(candidates, target, 0, new ArrayList<>(), result);
        return result;
    }

    private void backtrack(int[] candidates, int remaining,
                           int start, List<Integer> current,
                           List<List<Integer>> result) {
        if (remaining == 0) {
            result.add(new ArrayList<>(current));
            return;
        }
        for (int i = start; i < candidates.length; i++) {
            if (candidates[i] > remaining) break;
            // Skip duplicates at the same depth level
            if (i > start && candidates[i] == candidates[i - 1]) continue;
            current.add(candidates[i]);
            backtrack(candidates, remaining - candidates[i], i + 1, current, result);
            current.remove(current.size() - 1);
        }
    }
}
Complexity Analysis:

Time complexity: O(2^n) in the worst case since each element is either included or excluded.
Space complexity: O(n) for the recursion stack.