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CHAPTER 14 TREE-STRUCTURED DATA
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Implementing TREESORT
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I now show how TREESORT might be implemented.1 The intention is, of course, that this implementation code should be provided as part of the DBMS but if it isn t, then it could be provided by some application programmer and then invoked as if it were part of the DBMS after all. Note: I make no claim that the following code is particularly efficient; my primary concern is just to show that TREESORT is indeed implementable. There are some fairly obvious improvements that could be made if desired (as doubtless they would be in practice). Essentially what we have to do is (a) build the tree from the input list and then (b) build the output list from the tree. Here then is the code to build the tree (which I ll assume is initially empty): VAR I INTEGER ; VAR N INTEGER ; VAR X INTEGER ; /* node number within TREE */ /* total number of nodes */ /* current value from INLIST */
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IF NOT ( IS_EMPTY ( INLIST ) ) THEN BEGIN ; N := COUNT ( INLIST ) ; DO I := 1 TO N ; BEGIN ; X := V FROM ( TUPLE FROM ( INLIST WHERE P = I ) ) ; INSERT TREE RELATION { TUPLE { ID I, V X, LEFT 0, RIGHT 0 } } ; IF I > 1 THEN CALL ADD_TO_TREE ( 1 ) ; END IF ; END ; END DO ; END ; END IF ; OPERATOR ADD_TO_TREE ( M INTEGER ) ; BEGIN ; VAR T TUPLE { ID INTEGER, V INTEGER, LEFT INTEGER, RIGHT INTEGER } ; T := TUPLE FROM ( TREE WHERE P = M ) ; IF X ( V FROM T ) THEN IF ( LEFT FROM T ) = 0 THEN UPDATE TREE WHERE P = M ( LEFT := I ) ; ELSE CALL ADD_TO_TREE ( LEFT FROM T ) ; END IF ;
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1. Barring explicit statements to the contrary, all coding examples in the body of this chapter are expressed in a self-explanatory language called Tutorial D. As you might know, Tutorial D is the language used for examples by Hugh Darwen and myself in our book Databases, Types, and the Relational Model: The Third Manifesto, 3rd edition (Addison-Wesley, 2006).
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CHAPTER 14 TREE-STRUCTURED DATA
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ELSE IF ( RIGHT FROM T ) = 0 THEN UPDATE TREE WHERE P = M ( RIGHT := I ) ; ELSE CALL ADD_TO_TREE ( RIGHT FROM T ) ; END IF ; END IF ; END ; END OPERATOR ; And here s the code to build the output list, which, like the tree, I ll assume is initially empty: IF N > 0 THEN BEGIN ; I := 0 ; CALL INORDER ( 1 ) ; END ; END IF ; OPERATOR INORDER ( M INTEGER ) ; BEGIN ; VAR T TUPLE { ID INTEGER, V INTEGER, LEFT INTEGER, RIGHT INTEGER } ; I := I + 1 ; T := TUPLE FROM ( TREE WHERE P = M ) ; IF ( LEFT FROM T ) 0 THEN CALL INORDER ( LEFT FROM T ) ; END IF ; INSERT OUTLIST RELATION { TUPLE { P I, V ( V FROM T ) } } ; IF ( RIGHT FROM T ) 0 THEN CALL INORDER ( RIGHT FROM T ) ; END IF ; END ; END OPERATOR ;
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Note: This subsection can be skipped on a first reading. It s a little bit of a digression from the main thrust of this chapter, but I think I should say something about the integrity constraints that apply to relvar TREE. Please note, however, that I m not saying the constraints I m going to show would need to be stated explicitly in practice;2
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2. A good thing, you might think, since (as we ll soon see) some of them are a little complex. But this observation raises another point: The complexities in question are not due to the fact that we ve chosen to represent the tree relationally they re inherent (for the most part) in the very nature of trees, and they need to be enforced somehow, regardless of whether the system is relational or otherwise.
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