# Sort one sequence by O(n) in time and O(1) in space

Oscar Benjamin oscar.j.benjamin at gmail.com
Sun Feb 9 15:30:55 CET 2014

```Please reply to the list rather than directly to me so that other
people can see the answer to my question and offer you help.

On 9 February 2014 14:04, Ni Wesley <nispray at gmail.com> wrote:
> 2014年2月9日 下午9:41于 "Oscar Benjamin" <oscar.j.benjamin at gmail.com>写道：
>
>> On 9 February 2014 12:13, Wesley <nispray at gmail.com> wrote:
>> > Hi guys,
>> >    Here is one question related to algorithm.
>> > Details here:
>> >
>> > here is input sequence like a1,a2,...,an,b1,b2,...,bn ，the ax and bx
>> > always exist in pair. So, now, how to change the sequence to
>> > a1,b1,...,an,bn, with time complexity as O(n) and space as O(1).
>>
>> Do you mean that you have a list and you want to rearrange the
>> elements in-place without creating a new list?
>
> Yes

Okay so if you're going to do it with O(1) space then it's going to
have to be done with a whole bunch of swaps. Have a think with pen and
paper about how you could do a sequence of swaps that would rearrange
the order to the one that you want (it's actually a harder problem
than it looks at first glance). This is an example of what is known as
"transposition" and much information is available about algorithms for
doing this in-place:
http://en.wikipedia.org/wiki/In-place_matrix_transposition

Oscar

```