Smoothsort

│ English (en) │ français (fr) │

Smoothsort is a comparison-based sorting algorithm.

unit USmoothsortExtra.pas

unit USmoothsortExtra;

{$mode objfpc}{$H+}

interface


type
  // data type
 TItemSmoothsort = integer;

// comparison function
function IsAscendingSmoothsort(v1, v2: TItemSmoothsort): boolean;

implementation

// customizable comparison function
function IsAscendingSmoothsort(v1, v2: TItemSmoothsort): boolean; inline;
begin
   result := v1 <= v2;
end;

end.

unit USmoothsort.pas

unit USmoothsort;

interface
uses USmoothsortExtra;

// sorting function
procedure Smoothsort(var A: array of TItemSmoothsort);

implementation

// implementation of Djikstra's algorithm
procedure Smoothsort(var A: array of TItemSmoothsort);
var
  q, r,
  p, b, c,
  r1, b1, c1,
  N: integer;

  procedure up(var vb, vc: integer);
  var
    temp: integer;
  begin
    temp := vb;
    vb := vb + vc + 1;
    vc := temp;
  end;

  procedure down(var vb, vc: integer);
  var
    temp: integer;
  begin
    temp := vc;
    vc := vb - vc - 1;
    vb := temp;
  end;

  procedure sift;
  var
    r0, r2: integer;
    T: TItemSmoothsort;
  begin
    r0 := r1;
    T := A[r0];
    while b1 >= 3 do
      begin
        r2 := r1 - b1 + c1;
        if not IsAscendingSmoothsort(A[r1 - 1], A[r2]) then
          begin
            r2 := r1 - 1;
            down(b1, c1);
          end;
        if IsAscendingSmoothsort(A[r2], T) then b1 := 1
          else
            begin
              A[r1] := A[r2];
              r1 := r2;
              down(b1, c1);
            end;
      end; // of while b1 >= 3
    if r1 <> r0 then A[r1] := T;
  end;

  procedure trinkle;
  var
    p1, r2, r3, r0 : integer;
    T: TItemSmoothsort;
  begin
    p1 := p;
    b1 := b;
    c1 := c;
    r0 := r1;
    T := A[r0];
    while p1 > 0 do
      begin
        while (p1 and 1) = 0 do
          begin
            p1 := p1 shr 1;
            up(b1, c1);
          end; // of while (p1 and 1) = 0
        r3 := r1 - b1;
        if (p1 = 1) or IsAscendingSmoothsort(A[r3], T) then p1 := 0
          else // p1>1
            begin
              p1 := p1 - 1;
              if b1 = 1 then
                begin
                  A[r1] := A[r3];
                  r1 := r3;
                end
              else
                if b1 >= 3 then
                  begin
                    r2 := r1 - b1 + c1;
                    if not IsAscendingSmoothsort(A[r1 - 1], A[r2]) then
                      begin
                        r2 := r1 - 1;
                        down(b1, c1);
                        p1 := p1 shl 1;
                      end;
                    if IsAscendingSmoothsort(A[r2], A[r3]) then
                      begin
                        A[r1] := A[r3];
                        r1 := r3;
                      end
                    else
                      begin
                        A[r1] := A[r2];
                        r1 := r2;
                        down(b1, c1);
                        p1 := 0;
                      end;
                  end; // of if b1 >= 3
            end;  // of else  p1 > 1
      end;  // of while p1 > 0
    if r0 <> r1 then A[r1] := T;
    sift;
  end;

  procedure semitrinkle;
  var
    T: TItemSmoothsort;
  begin
    r1 := r - c;
    if not IsAscendingSmoothsort(A[r1], A[r]) then
      begin
        T := A[r];
        A[r] := A[r1];
        A[r1] := T;
        trinkle;
      end;
  end;

begin
  N := length(A);
  q := 1;
  r := 0;
  p := 1;
  b := 1;
  c := 1;

  //building tree
  while q < N do
    begin
      r1 := r;
      if (p and 7) = 3 then
        begin
          b1 := b;
          c1 := c;
          sift;
          p := ( p + 1 ) shr 2;
          up(b, c);
          up(b, c);
        end
      else
        if (p and 3) = 1 then
          begin
           if q + c < N then
             begin
                b1 := b;
                c1 := c;
                sift;
             end
             else trinkle;
           down(b, c);
           p := p shl 1;
           while b > 1 do
           begin
             down(b, c);
             p := p shl 1;
           end;  // of while b > 1
           p := p + 1;
          end;  // of if (p and 3) = 1
     q := q + 1;
     r := r + 1;
   end;
   r1 := r;
   trinkle;

   //bulding sorted array
   while q > 1 do
     begin
       q := q - 1;
       if b = 1 then
       begin
         r := r - 1;
         p := p - 1;
         while (p and 1) = 0 do
           begin
             p := p shr 1;
             up(b, c);
           end; // of while (p and 1) = 0
       end
       else
         if b >= 3 then
           begin
             p := p - 1;
             r := r - b + c;
             if p > 0 then semitrinkle;
             down(b, c);
             p := p shl 1 + 1;
             r := r + c;
             semitrinkle;
             down(b, c);
             p := p shl 1 + 1;
           end; // of if b >= 3
       //element q is done
     end;
   //element 0 is done
end;

end.

Example of the use

uses
  USmoothsort

  ...

var

  a: array[0..100] of integer; 


begin

  ...

  Smoothsort( a );