Subsets.txt

problem:
Given a set of distinct integers, S, return all possible subsets.

Note:

Elements in a subset must be in non-descending order.
The solution set must not contain duplicate subsets.
For example,
If S = [1,2,3], a solution is:

[
  [3],
  [1],
  [2],
  [1,2,3],
  [1,3],
  [2,3],
  [1,2],
  []
]

----------------------------------------------------------------

solution:
排列组合中的排列问题。
//思路一、二进制法。题目要求结果组合中数字按升序排列，因此刚开始需对数组排序。
vector<vector<int> > subsets(vector<int> &S)
{
    vector<vector<int> > ret;
    int n = S.size();
    if(n == 0)
        return ret;
    sort(S.begin(), S.end());
    int maxNum = 1 << n;
    for(int i = 0; i < maxNum; ++i)
    {
        vector<int> subset;
        int idx = 0;
        int j = i;
        while(j > 0)
        {
            if(j & 1)
                subset.push_back(S[idx]);
            j = j >> 1;
            ++idx;
        }
        ret.push_back(subset);
    }
    return ret;
}
 
//思路二、标志位法。题目要求结果组合中数字按升序排列，因此刚开始需对数组排序。
void subsets_aux(int idx, vector<int> &S, vector<vector<int> > &ret, vector<bool> &isVisited)
{
    if(idx == S.size())
    {
        vector<int> tmp;
        for(int i = 0; i < S.size(); ++i)
        {
            if(isVisited[i])
                tmp.push_back(S[i]);
        }
        ret.push_back(tmp);
        return;
    }
    isVisited[idx] = true;
    subsets_aux(idx + 1, S, ret, isVisited);
    isVisited[idx] = false;
    subsets_aux(idx + 1, S, ret, isVisited);
}
vector<vector<int> > subsets(vector<int> &S)
{
    vector<vector<int> > ret;
    if(S.size() == 0)
        return ret;
    sort(S.begin(), S.end());
    vector<bool> isVisited(S.size(), false);
    subsets_aux(0, S, ret, isVisited);
    return ret;
}