subsets.py

# Time:  O(n * 2^n)
# Space: O(1)

# 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],
#   []
# ]

class Solution(object):
    def subsets(self, nums):
        """
        :type nums: List[int]
        :rtype: List[List[int]]
        """
        nums.sort()
        result = [[]]
        for i in xrange(len(nums)):
            size = len(result)
            for j in xrange(size):
                result.append(list(result[j]))
                result[-1].append(nums[i])
        return result


# Time:  O(n * 2^n)
# Space: O(1)
class Solution2(object):
    def subsets(self, nums):
        """
        :type nums: List[int]
        :rtype: List[List[int]]
        """
        result = []
        i, count = 0, 1 << len(nums)
        nums.sort()
        
        while i < count:
            cur = []
            for j in xrange(len(nums)):
                if i & 1 << j:
                    cur.append(nums[j])
            result.append(cur)
            i += 1
            
        return result


# Time:  O(n * 2^n)
# Space: O(1)
class Solution3(object):
    def subsets(self, nums):
        """
        :type nums: List[int]
        :rtype: List[List[int]]
        """
        return self.subsetsRecu([], sorted(nums))
    
    def subsetsRecu(self, cur, nums):
        if not nums:
            return [cur]
        
        return self.subsetsRecu(cur, nums[1:]) + self.subsetsRecu(cur + [nums[0]], nums[1:])


if __name__ == "__main__":
    print Solution().subsets([1, 2, 3])