Nogarede, G.

Riet, R.P.

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A note on automatic storage of arbitrary trees in Algol 60

Riet, R.P. van de

CWI's Institutional Repository

ma the m·a tisch REKENAFDEL i NG cen trum R.P. VAN DE R1ET, G. NOGAREDE A NOTE ON AUTOMATIC STORAGE OF ARBiTRARY TREES lN ALGOL 60 amsterdam NR 16/71 MEl 1971 REKENAFDEL i NG stichting mathematisch centrum R.P. VANDERIET, G. NOGAREDE A NOTE ON AUTOMATIC STORAGE OF ARBITRARY TREES IN ALGOL 60 NR 16/71 RA ~ MC MEI 2e boerhaavestraat 49 amsterdam 6 fl,~1. i(; 1,, :: t: ~ r·:r, ~}, i" ~ 1,.\ ~ 1·-J,·.:H c:1:: NI r'l>Uti -- ,t,,~~,.; fl-t\;)Att ,.,,,,..... PJun.ted at :the. Mathe.ma.ucal. Ce.ntl!.e., 49, 2e. Boe.Jtha.a.vu.tJta.a.;t, Am6t:.Vtdam. The. Ma.the.ma.tic.a£ Ce.ntl!.e, f;ounde.d :the 11-;th of, F e.bJt.U.aJLy 19 46, i,.1, a. non.-p,to 6U wt.U:.u-tlon a.,iJn.i.ng a.t :the. pJt.Omo.tion of; pu.tLe. ma:the.ma.tic.o a.nd ,Lu a.ppUc.a.ti..on.6. 1.t .i.A .6pon6oJt.e.d by the. Ne..:thvz.i.and.6 GovVtnme.n.t -th!tou.gh the. Ne:theJl.i.a.nd.6 01t.9a.ruza.uon 6oJt. :the. Adva.nc.e.me.n.t 06 Pu.Jte. Ru e.a.Jt.c.h (Z. W. 0}, by .the. Mun.i..upa.llty of; Am6.te.Jt.da.m, by :the. Un.i..vvu..Uy of, Am.6.teAdam, by :the. FtLe.e. Un.i..vvu,.ay at Am6.te.Jt.da.m, a.n.d by indu.-b.vuu. 0. Summary In this note a method is demonstrated for making an elegant ALGOL 60 program which stores a tree in a one-dimensional array. 1 . 'l'he nroblem Consider a set s of trees t; each tree being either an atom (representable by an integer) or the root of an arbitrary number n(n > 0) of other trees t., i == 1, ... ,n, t. Es. l l The trees are assumed to be pure in the sense that no two trees are subtrees of each other. It is supposed that the trees have to be stored once, have to be inspected often, but will not be changed or deleted. In that case the following storage organization may be chosen. Declare the integer array INF[ 1: bound]. If t is an atom, then store the integer representing this atom in INP[ t], where t 1 s some appropriate value, called the location of t; otherwise, if t is the root of n trees t., with locations t., i = 1, ... ,n, l l fill n+ 1 consecutive array elements INF[ t], ... ,INF[ t+n] as follows: IN Flt J : == t+n+ 1 and for 1 -- i , ... ,n: if t. lS a root then INF[t+i] := t. ' otherwise ) l t+i - t. and INF[ t+i J contains the integer representing the atom t. , l 1 where t lS again some appropriate value, called the location of t. A tree consisting of d atoms and M roots will occupy N+2M places in INF. For the storage of this tree a program has to be written which performs the N+2M necessary assignments. For any given tree it is not too difficult to write down these assignment statements; the order of which has to be chosen judiciously however. 1'he problem is to construct auxiliary procedures, which perform the assignment statements, by means of which for every arbitrary tree a rrogra:m can be made with a structure reflecting directly the structure of this tree. In section 3 the solution the solution of the problem will be given 1r1 the form of the procedures STORE' TREE and L, which store an arbitrary tree consisting of at least one root. Before doing this it is necessary to introduce, in the next section, me&-ns for treating lists with a variable nwnber of elements as actual pG.rarn,,ters in procedure statements. 2. 2 Lists of variable length as :earameter Consider a set of lists, each list consisting of a variable number n of elements ei' l = 1, ... ,n; these elements have to be treated by a standard process p in the ordering e 1, ••• ,e . Before treating the n elements, an initialization process PO has to be executed which uses the number n. A way of programming this in ALGOL 60, where it is not allowed to have a variable number of actual para.meters in a procedure statement, is the following: Declare the procedure L: Boolean procedure L(first,ei); Boolean first; integer ei; begin comment count the nwriber of elements; cnt := cnt+l; if first then P 0; P; L := false end L The list (e 1 ,e2 , ... ,en) is then treated by the statement: L( ..• L(L(true, el), e2), e ) • n 3. Storage of trees A procedure STORE TREE and a procedure L are given now, by means of which the tree of the following example is stored in the array INF. Note that STORE TREE stores trees consisting of at least one root. 3. 1 • Example In the ALGOL 60 program of section 3.2. the following tree t is stored. In bracketed form: t = ( 100,200, ( 300, ( ( 400 , 5 00) ,600) , 700) , ( 800 ,900) ) . 'I'wo-dimensionally t looks like: 3 100 200 300 400 t = 500 600 700 800 900 3.2. The ALGOL 60 program begin integer ptr,fill ptr,t; integer array INF[1:1000]; 1nteger procedure STORE TREE(list); Boolean list; begin S'TtffiE TREE:• fill ptr:• ptr:• ptr + 1; if list then; enaSTORE ~; Boolean procedure L(first,inf); Boolean first; integer inf; begin in~eger toe fill ptr; :i;rtr:• ptr + 1; if first then oegin INF[1'II'1 ptr] :• ptr + 1; fill ptr:• fill ptr + 1; if ptr > 1 000 then EXIT ena; --roe fill ptr:• fill ptr; INF[loc fill ptr]:• inf; fill ptr:• loc fill ptr + 1; L:= false ~L; 4 ptr:= O; t:= STORE TREE(L(L(L(L(true, 100), -200), STORE TREE(L(L{L(true, 300), --STORE TREE(L(L(true, STORE TRE'Ef[tr,(true, 400), -500))), 600))), 700))), STORE TREE(L(L(true, 800), -900)))); NI.CR; FRINTI'EXT(-{:the contents of INF is displayed. Each line contains the information of one, :i•oot:}); t:= O; fill ptr:3 l; fort:= t + 1 while t < ptr do begin if t = fill ptr"then -- - -beginNLCR; fill ptr~[fill ptr] end; ~(2,0,t); FIXT(3,0,INF[t]); SPATI'.E;f5) end end the contents of INF is displayed. Each line contains the information of one root 1 +6 2 +100 3 +200 4 +6 6 +10 7 +300 8 +10 9 +700 10 +13 11 +13 12 +600 1 3 +16 14 +400 1 5 +500 16 +19 17 +800 18 +900 5 +16 

A note on automatic storage of arbitrary trees in Algol 60

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