Algorithms and Data Structures

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N.Wirth. Algorithms and Data Structures. Oberon version 184 key: INTEGER; p: Page END; PageRec = RECORD m: INTEGER; (*no. of entries on page*) p0: Page; e: ARRAY 2*N OF Entry END; VAR root: Page; W: Texts.Writer; PROCEDURE search (x: INTEGER; VAR p: Page; VAR k: INTEGER); VAR i, L, R: INTEGER; found: BOOLEAN; a: Page; BEGIN a := root; found := FALSE; WHILE (a # NIL) & ~found DO L := 0; R := a.m; (*binary search*) WHILE L < R DO i := (L+R) DIV 2; IF x
N.Wirth. Algorithms and Data Structures. Oberon version 185 FOR i := a.m TO R+1 BY -1 DO a.e[i] := a.e[i-1] END; a.e[R] := u; INC(a.m) ELSE (*overflow; split a into a, b and assign the middle entry to v*) NEW(b); IF R < N THEN (*insert in left pate a*) v := a.e[N-1]; FOR i := N-1 TO R+1 BY -1 DO a.e[i] := a.e[i-1] END; a.e[R] := u; FOR i := 0 TO N-1 DO b.e[i] := a.e[i+N] END ELSE (*insert in right page b*) DEC(R, N); IF R = 0 THEN v := u ELSE v := a.e[N]; FOR i := 0 TO R-2 DO b.e[i] := a.e[i+N+1] END; b.e[R-1] := u END; FOR i := R TO N-1 DO b.e[i] := a.e[i+N] END END; a.m := N; b.m := N; b.p0 := v.p; v.p := b END END END END END insert; PROCEDURE underflow (c, a: Page; s: INTEGER; VAR h: BOOLEAN); (*a = underflow page, c = ancestor page, s = index of deleted entry in c*) VAR b: Page; i, k: INTEGER; BEGIN (*h & (a.m = N-1) & (c.e[s-1].p = a) *) IF s < c.m THEN (*b := page to the right of a*) b := c.e[s].p; k := (b.m-N+1) DIV 2; (*k = nof items available on page b*) a.e[N-1] := c.e[s]; a.e[N-1].p := b.p0; IF k > 0 THEN (*balance by moving k-1 items from b to a*) FOR i := 0 TO k-2 DO a.e[i+N] := b.e[i] END; c.e[s] := b.e[k-1]; b.p0 := c.e[s].p; c.e[s].p := b; DEC(b.m, k); FOR i := 0 TO b.m-1 DO b.e[i] := b.e[i+k] END; a.m := N-1+k; h := FALSE ELSE (*merge pages a and b, discard b*) FOR i := 0 TO N-1 DO a.e[i+N] := b.e[i] END; DEC(c.m); FOR i := s TO c.m-1 DO c.e[i] := c.e[i+1] END; a.m := 2*N; h := c.m < N END ELSE (*b := page to the left of a*) DEC(s); IF s = 0 THEN b := c.p0 ELSE b := c.e[s-1].p END;
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Algorithms and Data Structures

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