Re: Find Position of many elements in a large list.

• To: mathgroup at smc.vnet.net
• Subject: [mg127695] Re: Find Position of many elements in a large list.
• From: Peter Pein <petsie at dordos.net>
• Date: Wed, 15 Aug 2012 03:35:46 -0400 (EDT)
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```Am 14.08.2012 11:05, schrieb benp84 at gmail.com:
> I have a sorted, 1-dimensional list X of 1,000,000 integers, and a sorted, 1-dimensional list Y of 10,000 integers.  Most, but not all, of the elements of Y are also elements of X.  I'd like to know the positions of the elements in X that are also in Y.  What's the fastest way to compute this?
>
> I have an algorithm in mind but it requires lots of custom code and I'm wondering if there's a clever way to do it with built-in functions.  Thanks.
>

Well, using the fact that the huge list (x) is sorted, I got a faster one.

binpos[xl_, y0_] :=
Block[{mid = BitShiftRight[Length[xl]], sel, pos},
If[mid === 0,
Boole[xl === {y0}],
If[xl[[mid]] <= y0, sel = Drop; pos = mid, sel = Take; pos = 0];
pos + binpos[sel[xl, mid], y0]
]];
Reap[Fold[Drop[#1, Sow[binpos[##]]] &, x, Intersection[x, y]]][[2,
1]] // Accumulate

needs only 20% of the time needed by
Position[x,Alternatives@@Intersection[x,y]]//Flatten

I'm sure, this can be slightly optimized.
Peter

```

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