*To*: mathgroup@smc.vnet.net*Subject*: [mg10638] prograMing: ReplacePart problem*From*: Xah Lee <xah@best.com>*Date*: Tue, 27 Jan 1998 03:10:03 -0500

"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