78. Subsets

Given a set of distinct integers, nums, return all possible subsets.

Note: The solution set must not contain duplicate subsets.

For example,
If nums = [1,2,3], a solution is:

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

---

 

 class Solution {
public:
    /*
    //时间复杂度 O（2^N）  空间复杂度O（n）
    void subset(vector<vector<int>>& result,vector<int>&path,int step,vector<int>&nums)
    {
        if(nums.size() == step)
        {
            result.push_back(path);
            return;
        }
       
        subset(result,path,step+1,nums);
        path.push_back(nums[step]);
        subset(result,path,step+1,nums);
        path.pop_back();
    }
   
   
    vector<vector<int>> subsets(vector<int>& nums) {
        vector<vector<int>> result;
        if(nums.size() == 0)
        {
            return result;
        }
       
        vector<int> path;
        subset(result,path,0,nums);
        
        return result;
       
    }
    */
   
   
    void subset(vector<vector<int>>& result,vector<bool>&selected,int step,vector<int>&nums)
    {
        //结束条件
        if(nums.size() == step)
        {
            vector<int> PathSubset;
            for(int i = 0; i < nums.size();i++)
            {
                if(selected[i] == true)
                {
                    PathSubset.push_back(nums[i]);   
                }
               
            }
            result.push_back(PathSubset);
            return;           
           
        }
       
       
        //不选step
        selected[step] = false;
        subset(result,selected,step+1,nums);
        //选择step
        selected[step] = true;
        subset(result,selected,step+1,nums);
    }
   
    //位向量法   开一个bool selected[n] 每个元素可以选或者不选
    vector<vector<int>> subsets(vector<int>& nums) {
       
        sort(nums.begin(),nums.end());
        vector<vector<int>> result;
        if(nums.size() == 0)
        {
            return result;
        }
       
        vector<bool> selected(nums.size(),false);
       
       
        subset(result,selected,0,nums);
        
        return result;
       
    }
   
   
   
};