Re: Maximum in a list

• To: mathgroup at smc.vnet.net
• Subject: [mg97259] Re: [mg97209] Maximum in a list
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Mon, 9 Mar 2009 01:07:06 -0500 (EST)
• References: <200903081050.FAA21521@smc.vnet.net>

```Oopsy, the second version (returning the FIRST element with maximum second
sub-element) should be:

Clear[select]
select[s_List] := s[[Ordering[Reverse@s[[All, 2]],1]]]

Bobby

On Sun, 08 Mar 2009 12:07:11 -0500, DrMajorBob <btreat1 at austin.rr.com>
wrote:

> Here's a simple method:
>
> mylist = {{1, 2}, {3, 4}, {8, 3}};
> select[s_List] := s[[Ordering[s[[All, 2]], -1]]]
>
> mylist = RandomInteger[{1, 4}, {50, 2}]
> select@mylist
>
> {{3, 3}, {1, 2}, {4, 1}, {1, 3}, {4, 3}, {1, 4}, {1, 2}, {1, 4}, {1,
>    3}, {3, 4}, {4, 2}, {3, 1}, {2, 1}, {3, 3}, {3, 4}, {4, 2}, {4,
>    4}, {2, 1}, {4, 2}, {4, 3}, {1, 3}, {3, 2}, {2, 2}, {4, 2}, {2,
>    4}, {1, 4}, {4, 1}, {4, 3}, {3, 1}, {3, 1}, {3, 4}, {2, 1}, {3,
>    3}, {4, 1}, {3, 1}, {4, 3}, {3, 4}, {4, 4}, {2, 1}, {4, 3}, {3,
>    1}, {4, 2}, {1, 1}, {3, 2}, {1, 2}, {2, 1}, {4, 1}, {1, 2}, {3,
>    3}, {1, 4}}
>
> {{1, 4}}
>
> "select" returns the LAST element for which the second element is
> maximum, which may not be what you want. If you want the FIRST such
> element, change "select" to
>
> Clear[select]
> select[s_List] := s[[Ordering[Reverse@s[[All, 2]], -1]]]
>
> select@mylist
>
> {{1, 2}}
>
> For either of those, you could add First@ to get only the element,
> rather than a list with only that element:
>
> Clear[select]
> select[s_List] := First@s[[Ordering[Reverse@s[[All, 2]], -1]]]
>
> select@mylist
>
> {1, 2}
>
> If you want ALL pairs for which the second element is maximum, then:
>
> Clear[select]
> select[s_List] := Extract[s, Position[s[[All, 2]], Max@s[[All, 2]]]]
>
> select@mylist
>
> {{1, 4}, {1, 4}, {3, 4}, {3, 4}, {4, 4}, {2, 4}, {1, 4}, {3, 4}, {3,
>    4}, {4, 4}, {1, 4}}
>
> If you want the same thing without repeats, you can do it with:
>
> Clear[select]
> select[s_List] :=
>   Union@Extract[s, Position[s[[All, 2]], Max@s[[All, 2]]]]
>
> select@mylist
>
> {{1, 4}, {2, 4}, {3, 4}, {4, 4}}
>
> or
>
> Clear[select, unsortedUnion]
> unsortedUnion[s_List] := Tally[s][[All, 1]]
> select[s_List] :=
>   unsortedUnion@Extract[s, Position[s[[All, 2]], Max@s[[All, 2]]]]
>
> select@mylist
>
> {{1, 4}, {3, 4}, {4, 4}, {2, 4}}
>
> or
>
> Clear[select]
> select[s_List] :=
>   DeleteDuplicates@Extract[s, Position[s[[All, 2]], Max@s[[All, 2]]]]
>
> select@mylist
>
> {{1, 4}, {3, 4}, {4, 4}, {2, 4}}
>
> Bobby
>
> On Sun, 08 Mar 2009 05:50:59 -0500, pacotomi <pacotomi at orange.fr> wrote:
>
>> Hi,
>>  Suppose a list
>>
>> mylist={{1,2},{3,4},{8,3}}
>>
>> I would like to extract the element {i,j} of mylist for which j is max
>> (here, it is the second one {3,4}).
>>
>> Somebody could help me, please?
>>
>> Pacotomi
>>
>>
>>
>>
>
>
>

--
DrMajorBob at bigfoot.com

```

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