Subsets

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],  []]

Analysis:

There are two ways to think about it. 

first:  each element in S could be selected or not selected.  we can use recursion.

second:  for n.th element,  the number of subsets is twice as large as that of subsets created by first n-1 elements.  we can use recursion or iteration.

class Solution:    # @param S, a list of integer    # @return a list of lists of integer        ## wu ##  recursive    def subsets(self, S):        if len(S)==0:            return [[]]                res = [[]]        S = sorted(S)        for elem in S:            newres = []            for elemres in res:                new = elemres[:]                new.append(elem)                newres.append(new)            res = res + newresHTere                return res        

Summary:

get the deeper understanding of recursion and iteration.  For iteration, it is usual that there is a for loop in it.  For recursion, we only have one function to enter the process and another function will call itself many times. Sometimes, there is a internal variable pass through all iterative funcitons.