Re: reliably sort?
- To: mathgroup at smc.vnet.net
- Subject: [mg123727] Re: reliably sort?
- From: Ulrich Arndt <ulrich.arndt at data2knowledge.de>
- Date: Fri, 16 Dec 2011 05:54:15 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jca06e$a35$1@smc.vnet.net> <201112150955.EAA22951@smc.vnet.net>
Union and Sort seems not naturally connected to me. Union is a set
operation and according to the documentation it seems that the
implementation is using some sorting...
But there are other implementations which can be used for this set
operation which do not use sorting and seems to have some better
performance in some cases - will clearly depend on the underlying data!
In[169]: dim = 1000000;
list = RandomChoice[Range[299], dim];
(a = Union[list]); // Timing
(b = Tally[list][[All, 1]]); // Timing
a == Sort[b]
Out[171]= {0.222803, Null}
Out[172]= {0.003932, Null}
Out[173]= True
Ulrich
Am 15.12.2011 um 10:55 schrieb David Bailey:
> On 14/12/2011 11:10, Michael Stern wrote:
>> I have noticed that if combine two lists of date/data objects using
>> Union[], the result is sorted by date.
>>
>> For example
>>
>> In[]:= mins={{{2001, 1, 31}, 0.993268}, {{2002, 3, 31}, 1.01395},
>> {{2003, 6, 30},
>> 1.08647}, {{2005, 11, 30}, 1.14752}, {{2006, 9, 30},
>> 1.18938}, {{2007, 2, 28}, 1.19658}, {{2008, 1, 31},
>> 1.20432}, {{2011, 1, 31}, 1.37501}};
>> In[]:= maxs={{{2000, 10, 31}, 1.01816}, {{2001, 12, 31}, =
1.02714},
>> {{2004, 2, 29},
>> 1.12702}, {{2005, 3, 31}, 1.16986}, {{2010, 10, 31}, 1.39026}};
>>
>> In[]:= Union[maxs, mins]
>>
>> Out[]= {{{2000, 10, 31}, 1.01816}, {{2001, 1, 31},
>> 0.993268}, {{2001, 12, 31}, 1.02714}, {{2002, 3, 31},
>> 1.01395}, {{2003, 6, 30}, 1.08647}, {{2004, 2, 29},
>> 1.12702}, {{2005, 3, 31}, 1.16986}, {{2005, 11, 30},
>> 1.14752}, {{2006, 9, 30}, 1.18938}, {{2007, 2, 28},
>> 1.19658}, {{2008, 1, 31}, 1.20432}, {{2010, 10, 31},
>> 1.39026}, {{2011, 1, 31}, 1.37501}}
>>
>> Is this reliable behavior? Is there any case in which Union would /not/
>> return results that have been properly sorted by date?
>>
>> Thank you,
>>
>> -Michael Stern
> Sorting is part of the operation, and you can rely on the result being
> sorted.
>
> Mathematica obviously uses the most efficient way to perform the Union
> operation, which is to sort the entire set of elements, and then perform
> a scan through the elements, discarding adjacent duplicates.
>
> David Bailey
> http://www.dbaileyconsultancy.co.uk
>
>
- References:
- Re: Does Union[] reliably sort?
- From: David Bailey <dave@removedbailey.co.uk>
- Re: Does Union[] reliably sort?