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From: Oscar Benjamin <oscar.j.benjamin@gmail.com>
Date: Sun, 9 Feb 2014 14:30:55 +0000
Subject: Re: Sort one sequence by O(n) in time and O(1) in space
To: Wesley <nispray@gmail.com>
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Xref: csiph.com comp.lang.python:65761

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@gmail.com> wrote:
> 2014=C4=EA2=D4=C29=C8=D5 =CF=C2=CE=E79:41=D3=DA "Oscar Benjamin" <oscar.j=
.benjamin@gmail.com>=D0=B4=B5=C0=A3=BA
>
>> On 9 February 2014 12:13, Wesley <nispray@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 =A3=ACthe 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