【第三轮】8.3-8.9 CareerCup 9.4

9.4 Write a method to return all subsets of a set.

回复解法可以按照以下格式来

【解题思路】
【时间复杂度】
【空间复杂度】
【gist link】
---------------OPTional，如果觉得test case比较好，欢迎写出来分享----------------------
【test case】

【解题思路】
build on subsets of the first n-1 items by adding item n to them
simple approach: combinatoric! iterate from 0 to 2^n-1, translate from binary representation to subsets
【时间复杂度】
O(2^N)
【空间复杂度】
O(1) if print in process
O(2^N) if store all subsets
【gist link】
https://gist.github.com/d6b93616fc4188fae134
【test case】
input: 1 2 3
output:
(empty subset)
1
2
1 2
3
1 3
2 3
1 2 3

【解题思路】
Recurson. The subsets of n element is just add the n-th element to all the subsets containing previous (n-1) elemnts.

【时间复杂度】
O(2^n)

【空间复杂度】
O(2^n)

【gist link】
https://gist.github.com/happyWinner/51c1887f3c0d58232988

【解题思路】
Iterative building larger subset based on small subsets, adding new elem in.

PS: I prefer the binary string interpretation in the book's answer, it's neat

【时间复杂度】
O(2^N) since this is the number of subset

【空间复杂度】
O(2^N)

【gist link】
https://gist.github.com/chrislukkk/5de217155d2418327e82

【解题思路】My understanding is that to build a hash table and put all possible combinations in each element

【时间复杂度】
O(2^N)
【空间复杂度】
O(2^N)
【gist link】
https://gist.github.com/bitcpf/9b9c5c1ed4401d15a3ef