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Task/AVL-tree/Simula/avl-tree-1.simula
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Task/AVL-tree/Simula/avl-tree-1.simula
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CLASS AVL;
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BEGIN
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! AVL TREE ADAPTED FROM JULIENNE WALKER'S PRESENTATION AT ;
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! HTTP://ETERNALLYCONFUZZLED.COM/TUTS/DATASTRUCTURES/JSW_TUT_AVL.ASPX. ;
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! THIS PORT USES SIMILAR INDENTIFIER NAMES. ;
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! THE KEY INTERFACE MUST BE SUPPORTED BY DATA STORED IN THE AVL TREE. ;
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CLASS KEY;
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VIRTUAL:
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PROCEDURE LESS IS BOOLEAN PROCEDURE LESS (K); REF(KEY) K;;
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PROCEDURE EQUAL IS BOOLEAN PROCEDURE EQUAL(K); REF(KEY) K;;
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BEGIN
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END KEY;
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! NODE IS A NODE IN AN AVL TREE. ;
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CLASS NODE(DATA); REF(KEY) DATA; ! ANYTHING COMPARABLE WITH LESS AND EQUAL. ;
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BEGIN
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INTEGER BALANCE; ! BALANCE FACTOR ;
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REF(NODE) ARRAY LINK(0:1); ! CHILDREN, INDEXED BY "DIRECTION", 0 OR 1. ;
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END NODE;
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! A LITTLE READABILITY FUNCTION FOR RETURNING THE OPPOSITE OF A DIRECTION, ;
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! WHERE A DIRECTION IS 0 OR 1. ;
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! WHERE JW WRITES !DIR, THIS CODE HAS OPP(DIR). ;
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INTEGER PROCEDURE OPP(DIR); INTEGER DIR;
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BEGIN
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OPP := 1 - DIR;
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END OPP;
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! SINGLE ROTATION ;
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REF(NODE) PROCEDURE SINGLE(ROOT, DIR); REF(NODE) ROOT; INTEGER DIR;
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BEGIN
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REF(NODE) SAVE;
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SAVE :- ROOT.LINK(OPP(DIR));
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ROOT.LINK(OPP(DIR)) :- SAVE.LINK(DIR);
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SAVE.LINK(DIR) :- ROOT;
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SINGLE :- SAVE;
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END SINGLE;
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! DOUBLE ROTATION ;
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REF(NODE) PROCEDURE DOUBLE(ROOT, DIR); REF(NODE) ROOT; INTEGER DIR;
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BEGIN
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REF(NODE) SAVE;
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SAVE :- ROOT.LINK(OPP(DIR)).LINK(DIR);
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ROOT.LINK(OPP(DIR)).LINK(DIR) :- SAVE.LINK(OPP(DIR));
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SAVE.LINK(OPP(DIR)) :- ROOT.LINK(OPP(DIR));
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ROOT.LINK(OPP(DIR)) :- SAVE;
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SAVE :- ROOT.LINK(OPP(DIR));
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ROOT.LINK(OPP(DIR)) :- SAVE.LINK(DIR);
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SAVE.LINK(DIR) :- ROOT;
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DOUBLE :- SAVE;
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END DOUBLE;
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! ADJUST BALANCE FACTORS AFTER DOUBLE ROTATION ;
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PROCEDURE ADJUSTBALANCE(ROOT, DIR, BAL); REF(NODE) ROOT; INTEGER DIR, BAL;
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BEGIN
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REF(NODE) N, NN;
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N :- ROOT.LINK(DIR);
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NN :- N.LINK(OPP(DIR));
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IF NN.BALANCE = 0 THEN BEGIN ROOT.BALANCE := 0; N.BALANCE := 0; END ELSE
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IF NN.BALANCE = BAL THEN BEGIN ROOT.BALANCE := -BAL; N.BALANCE := 0; END
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ELSE BEGIN ROOT.BALANCE := 0; N.BALANCE := BAL; END;
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NN.BALANCE := 0;
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END ADJUSTBALANCE;
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REF(NODE) PROCEDURE INSERTBALANCE(ROOT, DIR); REF(NODE) ROOT; INTEGER DIR;
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BEGIN REF(NODE) N; INTEGER BAL;
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N :- ROOT.LINK(DIR);
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BAL := 2*DIR - 1;
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IF N.BALANCE = BAL THEN
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BEGIN
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ROOT.BALANCE := 0;
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N.BALANCE := 0;
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INSERTBALANCE :- SINGLE(ROOT, OPP(DIR));
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END ELSE
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BEGIN
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ADJUSTBALANCE(ROOT, DIR, BAL);
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INSERTBALANCE :- DOUBLE(ROOT, OPP(DIR));
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END;
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END INSERTBALANCE;
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CLASS TUPLE(N,B); REF(NODE) N; BOOLEAN B;;
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REF(TUPLE) PROCEDURE INSERTR(ROOT, DATA); REF(NODE) ROOT; REF(KEY) DATA;
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BEGIN
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IF ROOT == NONE THEN
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INSERTR :- NEW TUPLE(NEW NODE(DATA), FALSE)
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ELSE
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BEGIN
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REF(TUPLE) T; BOOLEAN DONE; INTEGER DIR;
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DIR := 0;
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IF ROOT.DATA.LESS(DATA) THEN
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DIR := 1;
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T :- INSERTR(ROOT.LINK(DIR), DATA);
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ROOT.LINK(DIR) :- T.N;
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DONE := T.B;
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IF DONE THEN INSERTR :- NEW TUPLE(ROOT, TRUE) ELSE
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BEGIN
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ROOT.BALANCE := ROOT.BALANCE + 2*DIR - 1;
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IF ROOT.BALANCE = 0 THEN
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INSERTR :- NEW TUPLE(ROOT, TRUE) ELSE
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IF ROOT.BALANCE = 1 OR ROOT.BALANCE = -1 THEN
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INSERTR :- NEW TUPLE(ROOT, FALSE)
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ELSE
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INSERTR :- NEW TUPLE(INSERTBALANCE(ROOT, DIR), TRUE);
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END;
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END;
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END INSERTR;
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! INSERT A NODE INTO THE AVL TREE. ;
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! DATA IS INSERTED EVEN IF OTHER DATA WITH THE SAME KEY ALREADY EXISTS. ;
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PROCEDURE INSERT(TREE, DATA); NAME TREE; REF(NODE) TREE; REF(KEY) DATA;
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BEGIN
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REF(TUPLE) T;
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T :- INSERTR(TREE, DATA);
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TREE :- T.N;
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END INSERT;
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REF(TUPLE) PROCEDURE REMOVEBALANCE(ROOT, DIR); REF(NODE) ROOT; INTEGER DIR;
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BEGIN REF(NODE) N; INTEGER BAL;
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N :- ROOT.LINK(OPP(DIR));
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BAL := 2*DIR - 1;
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IF N.BALANCE = -BAL THEN
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BEGIN ROOT.BALANCE := 0; N.BALANCE := 0;
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REMOVEBALANCE :- NEW TUPLE(SINGLE(ROOT, DIR), FALSE);
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END ELSE
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IF N.BALANCE = BAL THEN
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BEGIN ADJUSTBALANCE(ROOT, OPP(DIR), -BAL);
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REMOVEBALANCE :- NEW TUPLE(DOUBLE(ROOT, DIR), FALSE);
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END ELSE
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BEGIN ROOT.BALANCE := -BAL; N.BALANCE := BAL;
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REMOVEBALANCE :- NEW TUPLE(SINGLE(ROOT, DIR), TRUE);
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END
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END REMOVEBALANCE;
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REF(TUPLE) PROCEDURE REMOVER(ROOT, DATA); REF(NODE) ROOT; REF(KEY) DATA;
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BEGIN INTEGER DIR; BOOLEAN DONE; REF(TUPLE) T;
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IF ROOT == NONE THEN
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REMOVER :- NEW TUPLE(NONE, FALSE)
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ELSE
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IF ROOT.DATA.EQUAL(DATA) THEN
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BEGIN
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IF ROOT.LINK(0) == NONE THEN
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BEGIN
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REMOVER :- NEW TUPLE(ROOT.LINK(1), FALSE);
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GOTO L;
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END
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ELSE IF ROOT.LINK(1) == NONE THEN
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BEGIN
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REMOVER :- NEW TUPLE(ROOT.LINK(0), FALSE);
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GOTO L;
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END
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ELSE
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BEGIN REF(NODE) HEIR;
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HEIR :- ROOT.LINK(0);
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WHILE HEIR.LINK(1) =/= NONE DO
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HEIR :- HEIR.LINK(1);
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ROOT.DATA :- HEIR.DATA;
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DATA :- HEIR.DATA;
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END;
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END;
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DIR := 0;
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IF ROOT.DATA.LESS(DATA) THEN
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DIR := 1;
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T :- REMOVER(ROOT.LINK(DIR), DATA); ROOT.LINK(DIR) :- T.N; DONE := T.B;
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IF DONE THEN
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BEGIN
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REMOVER :- NEW TUPLE(ROOT, TRUE);
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GOTO L;
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END;
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ROOT.BALANCE := ROOT.BALANCE + 1 - 2*DIR;
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IF ROOT.BALANCE = 1 OR ROOT.BALANCE = -1 THEN
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REMOVER :- NEW TUPLE(ROOT, TRUE)
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ELSE IF ROOT.BALANCE = 0 THEN
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REMOVER :- NEW TUPLE(ROOT, FALSE)
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ELSE
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REMOVER :- REMOVEBALANCE(ROOT, DIR);
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L:
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END REMOVER;
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! REMOVE A SINGLE ITEM FROM AN AVL TREE. ;
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! IF KEY DOES NOT EXIST, FUNCTION HAS NO EFFECT. ;
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PROCEDURE REMOVE(TREE, DATA); NAME TREE; REF(NODE) TREE; REF(KEY) DATA;
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BEGIN REF(TUPLE) T;
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T :- REMOVER(TREE, DATA);
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TREE :- T.N;
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END REMOVEM;
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END.
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36
Task/AVL-tree/Simula/avl-tree-2.simula
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36
Task/AVL-tree/Simula/avl-tree-2.simula
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@ -0,0 +1,36 @@
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EXTERNAL CLASS AVL;
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AVL
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BEGIN
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KEY CLASS INTEGERKEY(I); INTEGER I;
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BEGIN
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BOOLEAN PROCEDURE LESS (K); REF(KEY) K; LESS := I < K QUA INTEGERKEY.I;
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BOOLEAN PROCEDURE EQUAL(K); REF(KEY) K; EQUAL := I = K QUA INTEGERKEY.I;
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END INTEGERKEY;
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PROCEDURE DUMP(ROOT); REF(NODE) ROOT;
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BEGIN
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IF ROOT =/= NONE THEN
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BEGIN
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DUMP(ROOT.LINK(0));
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OUTINT(ROOT.DATA QUA INTEGERKEY.I, 0); OUTTEXT(" ");
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DUMP(ROOT.LINK(1));
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END
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END DUMP;
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INTEGER I;
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REF(NODE) TREE;
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OUTTEXT("Empty tree: "); DUMP(TREE); OUTIMAGE;
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FOR I := 3, 1, 4, 1, 5 DO
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BEGIN OUTTEXT("Insert "); OUTINT(I, 0); OUTTEXT(": ");
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INSERT(TREE, NEW INTEGERKEY(I)); DUMP(TREE); OUTIMAGE;
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END;
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FOR I := 3, 1 DO
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BEGIN OUTTEXT("Remove "); OUTINT(I, 0); OUTTEXT(": ");
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REMOVE(TREE, NEW INTEGERKEY(I)); DUMP(TREE); OUTIMAGE;
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END;
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END.
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