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.

It is guaranteed that the number of unique combinations that sum up to target is less than 150 combinations for the given input.

Solution Approach

Refer Code for Algorithm.

Expected Time complexity: $O(n^2)$

Click - to see solution code

C++

class Solution {
    int target;
    vector<int> comb;
    vector<int> arr;
    vector<vector<int>> ans;
    int sm, n;

   public:
    void find(int indx) {
        if (sm == target) {
            ans.push_back(arr);
            return;
        }
        if (sm > target || indx >= n) return;
        find(indx + 1);

        for (int i = 1; i <= target / comb[indx]; i++) {
            arr.push_back(comb[indx]);
            sm += comb[indx];
            find(indx + 1);
        }

        for (int i = 1; i <= target / comb[indx]; i++) {
            arr.pop_back();
            sm -= comb[indx];
        }
    }

    vector<vector<int>> combinationSum(vector<int>& candidates, int target) {
        this->comb = candidates;
        this->target = target;
        this->n = candidates.size();
        this->sm = 0;
        find(0);
        return ans;
    }
};