Combination_Sum.md

Combination Sum

Alias

• Leetcode (39): Combination Sum

Problem

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.

Examples

• Example 1
  • Input

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

  • Output

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

• 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

    []
    

Solutions

• Solution 1: Backtracking

  public List<List<Integer>> combinationSum(int[] candidates, int target) {
      List<List<Integer>> resultList = new ArrayList<>();
      Arrays.sort(candidates);
      backtrack(resultList, new ArrayList<>(), candidates, target, 0);
      return resultList;
  }
  
  private void backtrack(List<List<Integer>> resultList, List<Integer> tempList, int[] nums, int remain, int start){
      if(remain < 0) return;
      else if(remain == 0) resultList.add(new ArrayList<>(tempList));
      else { 
          for(int i = start; i < nums.length; i++){
              tempList.add(nums[i]);
              backtrack(resultList, tempList, nums, remain - nums[i], i); // not i + 1 because we can reuse same elements
              tempList.remove(tempList.size() - 1);
          }
      }
  }