# Combination Sum Problem Solution

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.

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 :

```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.```

## Problem Solution In Python

``````class Solution:
def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
candidates.sort()
res = []
self.helper(0, candidates, target, [], 0, res)
return res

def helper(self, i, candidates, target, cur, temp, res):
for j in range(i, len(candidates)):
if temp + candidates[j] == target:
res.append(cur + [candidates[j]])
return
elif temp + candidates[j] < target:
self.helper(j, candidates, target, cur + [candidates[j]], temp + candidates[j], res)
else:
return
``````

## Problem Solution In Java

``````class Solution {

public List<List<Integer>> combinationSum(int[] candidates, int target)
{
List<List<Integer>> scombo = new ArrayList<>();
tryCombo(candidates, target, 0, new ArrayList<>(), scombo);
return scombo;
}

public void tryCombo(int[] candidates, int target, int idxCandidate, List<Integer> currentCombo, List<List<Integer>> combos)
{
if (target == 0)
{
return;
}
if (target < 0)
{
return;
}

for (int i = idxCandidate; i < candidates.length; i++)
{
int cur = candidates[i];
if (target - cur < 0)
{
continue;
}

List<Integer> list = new ArrayList<>(currentCombo);

tryCombo(candidates, target - cur, i, list, combos);
}
}
}
``````

## Problem Solution In C++

``````class Solution {
public:
vector<vector<int>> combinationSum(vector<int>& candidates, int target) {
vector<vector<int>> res;
vector<int> r;
combin(res,r,candidates,target,0);
return res;
}
void combin(vector<vector<int>> &res, vector<int> r, vector<int>& c, int t, int s){
if(s == t){
cout<<s<<endl;
sort(r.begin(),r.end());
if(res.size()<=0){
res.push_back(r);
}else{
bool flag =false;
for(int i=0; i < res.size(); i++){
if(r == res[i]){
flag = true;
break;
}
}
if(!flag){
res.push_back(r);
}
}

}else if(s < t){
for(int i = 0; i <c.size(); i++ ){
int sum = s+ c[i];
r.push_back(c[i]);
combin(res, r,c,t,sum);
r.pop_back();
}
}
}
};
``````

## Problem Solution In C

``````#define SIZE 125
int** combinationSum(int* candidates, int candidatesSize, int target, int** columnSizes, int* returnSize) {
int** ret=(int**)malloc(SIZE*sizeof(int*));
int count=0;
int tamp_returnSize=0;
int** tamp_columnSizes=(int**)malloc(sizeof(int*));
columnSizes[0]=(int*)malloc(SIZE*sizeof(int));
if(candidatesSize<1||target<0){
*returnSize=0;
free(ret);
free(tamp_columnSizes);
return NULL;
}
for(int i=0;i<candidatesSize;i++){
if(target-candidates[i]==0){
ret[count]=(int*)malloc(sizeof(int));
columnSizes[0][count]=1;
ret[count][0]=candidates[i];
count++;
continue;
}
int** tamp=combinationSum(&candidates[i], candidatesSize-i, target-candidates[i], tamp_columnSizes, &tamp_returnSize);
for(int k=0;k<tamp_returnSize;k++){
ret[count]=(int*)malloc((tamp_columnSizes[0][k]+1)*sizeof(int));
columnSizes[0][count]=tamp_columnSizes[0][k]+1;
ret[count][0]=candidates[i];
for(int j=0;j<tamp_columnSizes[0][k];j++){
ret[count][j+1]=tamp[k][j];
}
count++;
}
free(tamp);
}
free(tamp_columnSizes);
*returnSize=count;
return ret;
}``````