Re: newbie list question

• To: mathgroup at smc.vnet.net
• Subject: [mg115075] Re: newbie list question
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Thu, 30 Dec 2010 04:11:44 -0500 (EST)

```That fails, and Part throws an error, when l2's range is greater than that
of l1:

l1 = RandomInteger[{1, 10^4}, 5*10^5];
l2 = RandomInteger[{1, 10^5}, 10^3];
r1 = firstPositions2[l1, l2]; // Timing
r2 = firsts[l1, l2]; // Timing
r1 === r2

{1.35344, Null}

{0.093815, Null}

False

It fails without a Part error, if l1's range is greater:

l1 = RandomInteger[{1, 10^5}, 5*10^5];
l2 = RandomInteger[{1, 10^4}, 10^3];
r1 = firstPositions2[l1, l2]; // Timing
r2 = firsts[l1, l2]; // Timing
r1 === r2

{1.35791, Null}

{0.051834, Null}

False

When the ranges are equal, all is fine:

l1 = RandomInteger[{1, 10^6}, 5*10^5];
l2 = RandomInteger[{1, 10^6}, 10^3];
r1 = firstPositions2[l1, l2]; // Timing
r2 = firsts[l1, l2]; // Timing
r1 === r2

{1.29281, Null}

{0.102205, Null}

True

Bobby

On Wed, 29 Dec 2010 04:58:53 -0600, Carl Woll <carlw at wolfram.com> wrote:

> On 12/28/2010 5:53 AM, Daniel Lichtblau wrote:
>> ----- Original Message -----
>>
>>> From: "Gareth Edwards"<gareth.edwards at cubicmotion.com>
>>> To: mathgroup at smc.vnet.net
>>> Sent: Sunday, December 26, 2010 3:02:23 AM
>>> Subject: [mg114986] newbie list question
>>> Hi,
>>>
>>> Liking Mathematica a lot, but struggling with the early part of the
>>> learning curve, i.e. don't know what I don't know...
>>>
>>> What would be the neatest syntax for finding the first location of
>>> elements from one list in another? For example:
>>>
>>> listA = { 4,5,8,2,6,4 }
>>> listB = { 8,4,2 }
>>>
>>>
>>> I would like a function to return {3,1,4} in this case (the first
>>> location in A of each element in B)
>>>
>>> Many thanks!
>>>
>> Neatest is subject to debate. A straightforward and simple method is to
>> Map Position (of element in first list) over the second list.
>>
>> firstPositions1[l1_, l2_] := Flatten[Map[Position[l1, #, 1, 1]&, l2]]
>>
>> This will be fine provided the second list is not too large; it scales
>> as m1*m2 where mj is the length of list j. A method that is slower per
>> element of list2, but scales as O(m1+m2), is shown below.
>>
>> firstPositions2[l1_, l2_] := Module[
>>    {stor, elem, tab},
>>    tab = ConstantArray[0, Length[l2]];
>>    MapIndexed[If[! IntegerQ[stor[#1]], stor[#1] = #2[[1]]]&, l2];
>>    Do[
>>     elem = stor[l1[[j]]];
>>     If[IntegerQ[elem],
>>      stor[l1[[j]]] = False;
>>      tab[[elem]] = j;
>>      ], {j, Length[l1]}];
>>    tab]
>>
>> Quick test that these work.
>>
>> listA = {4, 5, 8, 2, 6, 4};
>> listB = {8, 4, 2};
>>
>> In[85]:= firstPositions1[listA, listB] ==
>>   firstPositions2[listA, listB] ==
>>   IntegerDigits[IntegerPart[100*Pi]]
>>
>> Out[85]= True
>>
>> If the second list has 10 or so elements, the second method is
>> noticeably slower than the first. But it does in fact scale much
>> better. Here we compare speed when second list is 1000 elements (not
>> necessarily unique).
>>
>> l1 = RandomInteger[10^6, 5*10^5];
>> l2 = RandomInteger[10^6, 10^3];
>>
>> In[73]:= Timing[pos1 = firstPositions1[l1, l2];]
>> Out[73]= {68.11000000000001, Null}
>>
>> In[74]:= Timing[pos2 = firstPositions2[l1, l2];]
>> Out[74]= {1.933999999999969, Null}
>>
>> Notice there is a difference in behavior beyond speed. If the second
>> list contains values not found in the first, the second result will
>> have zeros in those corresponding slots. I'm guessing this is probably
>> desirable behavior, as compared to omitting them altogether (since you
>> won't otherwise know what element in result corresponds to what element
>> in second list).
>>
>> In[75]:= pos1 == DeleteCases[pos2, 0]
>> Out[75]= True
>>
>> In[76]:= Length[pos1]
>> Out[76]= 379
>>
>> Daniel Lichtblau
>> Wolfram Research
>>
>>
>>
> If we assume that all of the list elements are positive integers, then
> the following is much faster:
>
> firsts[l1_, l2_] :=  Normal[SparseArray[Automatic, {Max[l1]}, 0, {1,
> {{0, Length[l1]}, List /@ l1}, Range[Length[l1]]}][[l2]]]
>
> Example:
>
> l1 = RandomInteger[{1, 10^6}, 5*10^5];
> l2 = RandomInteger[{1, 10^6}, 10^3];
>
> In[130]:= r1 = firstPositions2[l1, l2]; // Timing
> r2 = firsts[l1, l2]; // Timing
> r1 === r2
>
> Out[130]= {2.387, Null}
>
> Out[131]= {0.109, Null}
>
> Out[132]= True
>
> Carl Woll
> Wolfram Research
>
>

--
DrMajorBob at yahoo.com

```

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