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MathGroup Archive 1998

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prograMing: ReplacePart problem



"Scott Morrison" <scott@morrison.fl.net.au> wrote:

> I have a list of pairs of the form:
> gt»3,5},{{},6},{7,{}},{{},{}},{{},56},{{},3}};
>
> The empty lists inside pairs are being used as placeholders. I want to
> replace these with the elements of b: bº1,a2,a3,a4,a5,a6};
> hopefully resulting in the list
> {{3,5},{a1,6},{7,a2},{a3,a4},{a5,56},{a6,3}}
>
> I had thought that ReplacePart could do this

This is an interesting problem. Many people already gave solutions.
Here
 I'll generalize this problem a bit.

Problem: Suppose you have an expression that contains n "slots" that
you
 want to fill-in using another list of length n. How to do it?

The problem is not completly specified above because the correspondence
 between slots in expr and replacementList is not clear. Since
Mathematica
 expressions are just trees, each slot has an index. The length of
slot's
 index may or may not be used to determine the replacement order. For
 example, should a slot with index {1,1,1} come before or after another
slot
 with index {1,2}? Anyhow, ReplaceParts should be the right function to
 solve this problem. The current four-argument-form behavior of
ReplaceParts
 is probably a bug. Here's a substitute.

Clear[ReplaceMultiplePart];
ReplaceMultiplePart::"usage"  "ReplaceMultiplePart[expr,newPartList,positionIndexList] replaces
parts of
 expr corresponding positionIndexList with newPartList. Usage Example:
ReplaceMultiplePartPart[f[1,2,3],{hal,x},{{0},{2}}]";

ReplaceMultiplePart[expr_,newParts_List,posIndexes_List]:
Fold[ReplacePart[#1,Sequence@@#2]&,expr,Transpose[{newParts,posIndexes}]];

Now we can use ReplaceMultiplePart to solve the generalized problem.

In[23]:Clear[aTree,replacementList];
aTreeûg[slot,{slot,p}][slot,slot],slot,m,slot[slot]];
replacementListºnge@7;

In[24]:pos˜sition[aTree,slot,Infinity,Heads->True]

Out[24]{{1,0,1},{1,0,2,1},{1,1},{1,2},{2},{4,0},{4,1}}

In[25]:(*assuming the order returned by Position is the desired one*)
ReplaceMultiplePart[aTree,replacementList,pos]

Out[25]f[g[1,{2,p}][3,4],5,m,6[7]]

 Xah, xah@best.com
 http://www.best.com/~xah/Wallpaper_dir/c0_WallPaper.html
 Mathematics, when viewed from the right angle, can be as boring as one
 could imagine.    --Mathematcian's lore




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