Power set

Problem

Backtracking approach:
TC:(2^n) i.e. exponential time complexity (Since we are left with two choice at every recursive call i.e. either to consider the value at 'index' or not that leads to 2 possible outcome, this will happen for n times)
SC:(2^n)*(n), n for temp ArrayList<>() and 2^n for the main ArrayList<>();

class Solution {
    public List<List<Integer>> subsets(int[] nums) {
        List<List<Integer>> list = new ArrayList<>();
        powerSet(nums,0,list,new ArrayList<Integer>());
        return list;
    }
    public void powerSet(int [] nums, int index , List<List<Integer>> list, List<Integer> l){
        //base case
        if(index ==nums.length){
            list.add(new ArrayList<>(l));
            return;
        }
        //take
        l.add(nums[index]); //consider the value at 'index'
        powerSet(nums,index+1,list,l);
        //dont take;
        l.remove(l.size()-1);// don't consider the value at 'index'
        powerSet(nums,index+1,list,l);
    }
}

---

Using Bit Manipulation:
TC: O(2^n)*n
SC: O(2^n)*n, (2^n for the main list, and n for the subset lists, well not all the subsets will be of size n but still we can assume that is the case)

pre-requisite: check if ith bit is set or not ( refer the Bit manipulation tips and tricks page for more details)
Intuition:
If all the no . subsets are represented as binary values,
for example : if n = 3 i.e. array having 3 value in it.
there will be 2^n = 8 subsets
8 subsets can also be represented as

index 2	index 1	index 0	subset number
0	0	0	0
0	0	1	1
0	1	0	2
0	1	1	3
1	0	0	4
1	0	1	5
1	1	0	6
1	1	1	7

We will take into consideration that if bit value is 1 then that index value in the nums[] should be taken into consideration for forming the subset.
This way we will be able to create all the subsets

class Solution {
    public List<List<Integer>> subsets(int[] nums) {
        List<List<Integer>> list = new ArrayList<>();
        int n = nums.length;
        int noOfSubset = 1<<n; // this is nothing but 2^n, i.e if there are n elements in the array, they will form 2^n subsets

        for(int num = 0;num<noOfSubset;num++){ /// all possible subsets numbers
            List<Integer> l = new ArrayList<>();
            for(int i =0;i<n;i++){// for the given subset number find which index value to pick 
                if((num & (1<<i))!=0) l.add(nums[i]); 
            }
            list.add(l);
        }
        return list;
    }
}

The above is the detailed content of Power set. For more information, please follow other related articles on the PHP Chinese website!