[Algorithm] How to find all the subsets of an n-element set T?

Posted 2021-01-07 chiyeung

There are two direction for us to solve this problem.

(1) Recursion

Recursive step: T[0] conbines with findsubsets(T[1:])

Final step: if len(T)==0: return [[]]

Code:

#Recursive method
def findsubsets(T):
	if len(T)==0:
		return [[]]

	answer=[]
	
	for sets in findsubsets(T[1:]):
		answer.append(sets)
		new=sets[:]+[T[0]]
		answer.append(new)
	
	return answer

　　

(2) Noncursive method

In this method, we can use stack and queue to help us solve this problem.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Algorithm: 

Input: an n-element set T

Output: all the subsets of T

1. define an empty stack S

2. define an empty queue Q

3. S.push([])

4. S.push([T[0]])

5. for all the elements a in T[1:]:

6.　　 while S is not empty:

7.　　　　x=S.pop()

8.　　　　Q.enqueue(x)

9.　　　　x=x+[[a]]

10.　　     Q.enqueue(x)

11.　　if a is not the final element in T:

12.　　　　while Q is not empty:

13.　　　　　　S.push(Q.dequeue())

14. return Q

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 

Code:

def findsubsets2(T):
	Q=ArrayQueue()
	S=ArrayStack()

	S.push([])
	S.push([T[0]])

	for i in T[1:]:
		while (len(S)!=0):
			x=S.pop()
			Q.enqueue(x)
			x=x+[[i]]
			Q.enqueue(x)

		if i!=T[-1]:
			while (len(Q)!=0):
				S.push(Q.dequeue())
        return Q._data