## Combination Sum

06/26/2016 Array Backtracking

## Question

Given a set of candidate numbers (C) and a target number (T), find all unique combinations in C 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.

• 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]
]


## Solution

Result: Accepted Time: 20ms

Here should be some explanations.

class Solution {
public:
void dfs(vector<int> & cdd,vector<int> &sol,vector< vector<int>> &ret,int ptr,int rest)
{
if(!rest)
return ret.push_back(sol);
if(ptr >= cdd.size()) return ;
dfs(cdd,sol,ret,ptr+1,rest);
int i;
for(i = 0 ; rest >= cdd[ptr];i++)
{
sol.push_back(cdd[ptr]);
rest -= cdd[ptr];
dfs(cdd,sol,ret,ptr+1,rest);
}
while(i--) sol.pop_back();
}
vector<vector<int>> combinationSum(vector<int>& cdd, int target) {
vector<vector<int>> ret;
vector<int> sol;
sort(cdd.begin(),cdd.end());
dfs(cdd,sol,ret,0,target);
return ret;
}
};


Complexity Analytics

• Time Complexity: $O(n!)$
• Space Complexity: $O(n)$?