Combination Sum

Given a set of candidate numbers (C) and a target number (T), find all unique combinations inC where the candidate numbers sums to T.

The same repeated number may be chosen from C unlimited number of times.

Note:

• All numbers (including target) will be positive integers.
• Elements in a combination (a₁, a₂, � ,a_k) must be in non-descending order. (ie, a₁ ?a₂ ? � ? a_k).
• The solution set must not contain duplicate combinations.

For example, given candidate set 2,3,6,7 and target 7,
A solution set is:
[7]

[2, 2, 3]

DFS solution:

public class Solution {    public ArrayList<Integer> cur;public ArrayList<ArrayList<Integer>> res;public ArrayList<ArrayList<Integer>> combinationSum(int[] candidates,int target) {// Start typing your Java solution below// DO NOT write main() functionres = new ArrayList<ArrayList<Integer>>();cur = new ArrayList<Integer>();Arrays.sort(candidates);find(candidates, 0, cur, target);return res;}public void find(int[] candidates, int index, ArrayList<Integer> cur, int target){if(target == 0)res.add(new ArrayList<Integer>(cur));else{for(int i = index; i < candidates.length; i++){if(target >= candidates[i]){cur.add(candidates[i]);find(candidates, i, cur, target - candidates[i]);cur.remove(cur.size() - 1);}}}}}

DP solution: sum(target) = {sum(target-a[i]), a[i]}

import java.util.Hashtable;public class Solution {    public ArrayList<ArrayList<Integer>> combinationSum(int[] candidates,int target) {// Start typing your Java solution below// DO NOT write main() functionArrays.sort(candidates);Hashtable<Integer, ArrayList<ArrayList<Integer>>> sum = new Hashtable<Integer, ArrayList<ArrayList<Integer>>>();for(int i = 1; i <= target; i++){sum.put(i, new ArrayList<ArrayList<Integer>>());int size = candidates.length;for(int j = 0; j < size; j++){if(i < candidates[j])continue;else if(i == candidates[j]){ArrayList<Integer> x = new ArrayList<Integer>();x.add(i);sum.get(i).add(x);continue;}else{int temp = i - candidates[j];for(int k = 0; k < sum.get(temp).size(); k++){ArrayList<Integer> res = new ArrayList<Integer>(sum.get(temp).get(k));if(res.get(res.size() - 1) <= candidates[j]){res.add(candidates[j]);sum.get(i).add(res);}}}}}return sum.get(target);}}