S´ erie d’exercices #1 IFT2030 17 janvier 2006 1
1 Simula % Jean Vaucher % http://www.iro.umontreal.ca/~vaucher/Simula/Software/containers.sim ref(Container) procedure SORT; begin Boolean procedure precede(E1,E2); ref(element) E1, E2; precede := E1.key < E2.key; if numElements > 1 then Quicksort(1, numElements, precede); Sort :- Owner; end; ref(Container) procedure ORDER(precede); Boolean procedureprecede; begin if numElements > 1 then quicksort(1,numElements, precede ); Order :- Owner; end; procedure Quicksort(L,R,precede); integer L,R; Boolean procedure precede; begin integer i,j; ref(element) x, Mid; Mid :- A ( (L+R) // 2 ); j := R; i := L; while i < j do begin while precede( a(i), Mid ) do i := i+1; while precede( Mid , a(j)) do j := j-1; if i<=j then begin x :- A(i); A(i) :- A(j); a(j) :- x; i := i+1; j := j-1; end ; end; if L < j then QuickSort(L,j,precede); if i < R then QuickSort(i,R,precede); end; 2
2 Fortran C http://www.fortran.com/fortran/quick_sort1.f C C From HDK@psuvm.psu.edu Thu Dec 8 15:27:16 MST 1994 C C The following was converted from Algol recursive to Fortran iterative C by a colleague at Penn State (a long time ago - Fortran 66, please C excuse the GoTo’s). The following code also corrects a bug in the C Quicksort algorithm published in the ACM (see Algorithm 402, CACM, C Sept. 1970, pp 563-567; also you younger folks who weren’t born at C that time might find interesting the history of the Quicksort C algorithm beginning with the original published in CACM, July 1961, C pp 321-322, Algorithm 64). Note that the following algorithm sorts C integer data; actual data is not moved but sort is affected by sorting C a companion index array (see leading comments). The data type being C sorted can be changed by changing one line; see comments after C declarations and subsequent one regarding comparisons(Fortran C 77 takes care of character comparisons of course, so that comment C is merely historical from the days when we had to write character C compare subprograms, usually in assembler language for a specific C mainframe platform at that time). But the following algorithm is C good, still one of the best available. SUBROUTINE QSORTI (ORD,N,A) C C==============SORTS THE ARRAY A(I),I=1,2,...,N BY PUTTING THE C ASCENDING ORDER VECTOR IN ORD. THAT IS ASCENDING ORDERED A C IS A(ORD(I)),I=1,2,...,N; DESCENDING ORDER A IS A(ORD(N-I+1)), C I=1,2,...,N . THIS SORT RUNS IN TIME PROPORTIONAL TO N LOG N . C C C ACM QUICKSORT - ALGORITHM #402 - IMPLEMENTED IN FORTRAN 66 BY C WILLIAM H. VERITY, WHV@PSUVM.PSU.EDU C CENTER FOR ACADEMIC COMPUTING C THE PENNSYLVANIA STATE UNIVERSITY C UNIVERSITY PARK, PA. 16802 C IMPLICIT INTEGER (A-Z) C DIMENSION ORD(N),POPLST(2,20) INTEGER X,XX,Z,ZZ,Y C C TO SORT DIFFERENT INPUT TYPES, CHANGE THE FOLLOWING C SPECIFICATION STATEMENTS; FOR EXAMPLE, FOR FORTRAN CHARACTER C USE THE FOLLOWING: CHARACTER *(*) A(N) C INTEGER A(N) C 3
NDEEP=0 U1=N L1=1 DO 1 I=1,N 1 ORD(I)=I 2 IF (U1.LE.L1) RETURN C 3 L=L1 U=U1 C C PART C 4 P=L Q=U C FOR CHARACTER SORTS, THE FOLLOWING 3 STATEMENTS WOULD BECOME C X = ORD(P) C Z = ORD(Q) C IF (A(X) .LE. A(Z)) GO TO 2 C C WHERE "CLE" IS A LOGICAL FUNCTION WHICH RETURNS "TRUE" IF THE C FIRST ARGUMENT IS LESS THAN OR EQUAL TO THE SECOND, BASED ON "LEN" C CHARACTERS. C X=A(ORD(P)) Z=A(ORD(Q)) IF (X.LE.Z) GO TO 5 Y=X X=Z Z=Y YP=ORD(P) ORD(P)=ORD(Q) ORD(Q)=YP 5 IF (U-L.LE.1) GO TO 15 XX=X IX=P ZZ=Z IZ=Q C C LEFT C 6 P=P+1 IF (P.GE.Q) GO TO 7 X=A(ORD(P)) IF (X.GE.XX) GO TO 8 GO TO 6 7 P=Q-1 GO TO 13 C C RIGHT C 4
8 Q=Q-1 IF (Q.LE.P) GO TO 9 Z=A(ORD(Q)) IF (Z.LE.ZZ) GO TO 10 GO TO 8 9 Q=P P=P-1 Z=X X=A(ORD(P)) C C DIST C 10 IF (X.LE.Z) GO TO 11 Y=X X=Z Z=Y IP=ORD(P) ORD(P)=ORD(Q) ORD(Q)=IP 11 IF (X.LE.XX) GO TO 12 XX=X IX=P 12 IF (Z.GE.ZZ) GO TO 6 ZZ=Z IZ=Q GO TO 6 C C OUT C 13 CONTINUE IF (.NOT.(P.NE.IX.AND.X.NE.XX)) GO TO 14 IP=ORD(P) ORD(P)=ORD(IX) ORD(IX)=IP 14 CONTINUE IF (.NOT.(Q.NE.IZ.AND.Z.NE.ZZ)) GO TO 15 IQ=ORD(Q) ORD(Q)=ORD(IZ) ORD(IZ)=IQ 15 CONTINUE IF (U-Q.LE.P-L) GO TO 16 L1=L U1=P-1 L=Q+1 GO TO 17 16 U1=U L1=Q+1 U=P-1 17 CONTINUE IF (U1.LE.L1) GO TO 18 5
C C START RECURSIVE CALL C NDEEP=NDEEP+1 POPLST(1,NDEEP)=U POPLST(2,NDEEP)=L GO TO 3 18 IF (U.GT.L) GO TO 4 C C POP BACK UP IN THE RECURSION LIST C IF (NDEEP.EQ.0) GO TO 2 U=POPLST(1,NDEEP) L=POPLST(2,NDEEP) NDEEP=NDEEP-1 GO TO 18 C C END SORT C END QSORT C END 6
3 Forth \ http://www.tinyboot.com/quiksort.txt anew wilsort \ ---------------------------------------------------------- \ Wil Baden’s sorter \ Set PRECEDES for different datatypes or sort order. DEFER PRECEDES ’ < IS PRECEDES \ For sorting character strings in increasing order: : SPRECEDES ( addr addr -- flag ) >R COUNT R> COUNT COMPARE 0< ; : IPRECEDES ( addr addr -- flag ) < ; ’ SPRECEDES IS PRECEDES : EXCHANGE ( addr_1 addr_2 -- ) DUP @ >R OVER @ SWAP ! R> SWAP ! ; : -CELL ( -- n ) -1 CELLS ; : CELL- ( addr -- addr’ ) 1 CELLS - ; : PARTITION ( lo hi -- lo_1 hi_1 lo_2 hi_2 ) 2DUP OVER - 2/ -CELL AND + @ >R ( R: median) 2DUP BEGIN ( lo_1 hi_2 lo_2 hi_1) SWAP BEGIN DUP @ R@ PRECEDES WHILE CELL+ REPEAT SWAP BEGIN R@ OVER @ PRECEDES WHILE CELL- REPEAT 2DUP > NOT IF 2DUP EXCHANGE >R CELL+ R> CELL- THEN 2DUP > UNTIL ( lo_1 hi_2 lo_2 hi_1) R>DROP SWAP ROT ( lo_1 hi_1 lo_2 hi_2) ; : QSORT ( lo hi -- ) PARTITION ( lo_1 hi_1 lo_2 hi_2) 2OVER 2OVER - + ( . . . . lo_1 hi_1+lo_2-hi_2) < IF 2SWAP THEN ( lo_1 hi_1 lo_2 hi_2) 2DUP < IF RECURSE ELSE 2DROP THEN 2DUP < IF RECURSE ELSE 2DROP THEN ; : SORT ( addr n -- ) DUP 2 < IF 2DROP EXIT THEN 1- CELLS OVER + ( addr addr+{n-1}cells) QSORT ( ) ; \ ---------------------------------------------------------- 7
4 Algol 68 CO Lifted from the Algol 68 Genie documentation at http://www.xs4all.nl/~jmvdveer/algol.html CO BEGIN MODE NODE = STRUCT (INT k, TREE smaller, larger), TREE = REF NODE; TREE empty tree = NIL; PROC add = (REF TREE root, INT k) VOID: IF root IS empty tree THEN root := HEAP NODE := (k, NIL, NIL) ELSE IF k < k OF root THEN add (smaller OF root, k) ELSE add (larger OF root, k) FI FI; PROC write = (TREE root) VOID: IF root ISNT NIL THEN write (smaller OF root); print ((whole (k OF root, 0), " ")); write (larger OF root) FI; TREE root := empty tree; WHILE INT n = read int; n > 0 DO add (root, n) OD; write (root) END CO $Id: sort.a68,v 1.1 2006/01/17 02:55:31 haguenad Exp $ CO 8
5 Java /* Code by Manuel Hermenegildo, http://clip.dia.fi.upm.es/Projects/ParForce/Final_review/slides/intro/node4.html */ static void sort(int a[], int lo0, int hi0) { int lo = lo0; int hi = hi0; if (lo >= hi) { return; } int mid = a[(lo + hi) / 2]; while (lo < hi) { while (lo<hi && a[lo] < mid) { lo++; } while (lo<hi && a[hi] >= mid) { hi--; } if (lo < hi) { int T = a[lo]; a[lo] = a[hi]; a[hi] = T; } } if (hi < lo) { int T = hi; hi = lo; lo = T; } sort(a, lo0, lo); sort(a, lo == lo0 ? lo+1 : lo, hi0); } static void sort(int a[]) { sort(a, 0, a.length-1); } 9
6 Haskell sort :: [Int] -> [Int] sort [] = [] sort (h:t) = sort [x | x <- t, x < h] ++ [h] ++ sort [x | x <- t, x > h] 10
7 C Expliquer en quoi la norme ANSI C laisse ind´ efinie la s´ emantique des parties de programmes suivantes : 1. x % y 2. short x; x = 20000; x = x + x; 3. int x = 0; f(x, x, x, x = 1); 4. f(1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2) $Id: demo01.tex,v 1.2 2006/01/17 16:25:07 haguenad Exp $ 11
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