## Combination Sum II

06/26/2016 Array Backtracking

## Question

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

Each number in C may only be used once in the combination.

Note:

• All numbers (including target) will be positive integers.
• The solution set must not contain duplicate combinations.

For example, given candidate set [10, 1, 2, 7, 6, 1, 5] and target 8,

A solution set is:

[
[1, 7],
[1, 2, 5],
[2, 6],
[1, 1, 6]
]


## Solution

Result: Accepted Time: 12ms

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() || rest < 0) return ;
int last = ptr,i;
while(++last < cdd.size() && cdd[ptr] == cdd[last]);
dfs(cdd,sol,ret,last,rest);
for(i = 0;rest >= cdd[ptr] && i+ptr < last;i++)
{
sol.push_back(cdd[ptr]);
rest -= cdd[ptr];
dfs(cdd,sol,ret,last,rest);
}
while(i--)
sol.pop_back();
}
vector<vector<int>> combinationSum2(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: $O(n)$?