Example of Skip List source code

Материал из DRKB


{*

Example of Skip List source code for Pascal:

Skip Lists are a probabilistic alternative to balanced trees, as
described in the June 1990 issue of CACM and were invented by
William Pugh in 1987.

This file contains source code to implement a dictionary using
skip lists and a test driver to test the routines.

A couple of comments about this implementation:
  The routine randomLevel has been hard-coded to generate random
  levels using p=0.25. It can be easily changed.

  The insertion routine has been implemented so as to use the
  dirty hack described in the CACM paper: if a random level is
  generated that is more than the current maximum level, the
  current maximum level plus one is used instead.

The code, as presented, allows duplicate entries which act in a FIFO
manner. To disallow duplicates, the insert procedure needs to be modified
as indicated in the insert procedure.

The library includes an adaptation of the Unix C random number generator,
since the standard Pascal random number generator is unsuitable.

An attempt has been made to make sure that no integer overflow occurs
in the random number generator. However, this could not be tested.

randomBits is defined to be the number of bits returned by a call to
random(). For most all machines with 32-bit integers, this is 31 bits
as currently set.

The routines defined in this file are:

  init: defines terminator and initializes the random bit source

  newList: returns a new, empty list

  freeList(l): deallocates the list l

  randomLevel: Returns a random level

  insert(l,key,value): inserts the binding (key,value) into l. If
allowDuplicates is undefined, returns true if key was newly
inserted into the list, false if key already existed

  delete(l,key): deletes any binding of key from the l. Returns
false if key was not defined.

  search(l,key,value): Searches for key in l and returns true if found.
If found, the value associated with key is stored in value

*}


program test(input, output);

const
  sampleSize = 65536;

  (* The following constants are associated with the random number generator *)
  differentRandoms = 1073741824; (* 2^30 *)
  randomTableSize = 31; (* size of table used *)

  (* The follow constants are associated with the routines to procedure random levels *)
  ChunkSize = 4; (* ChunkSize = 1/p *)
  randomChucksInAWord = 15; (* = log(base ChunkSize) differentRandoms *)
  MaxLevel = 16;


type
  randomStuff = 0..maxint;
  keyType = 0..maxint;
  valueType = 0..maxint;
  levelNum = 1..MaxLevel;
  node = ^nodeRec;
  list = ^listRec;

  listRec = record
    level: Integer;
    header: node;
  end;

  nodeRec = record
    key: keyType;
    Value: valueType;
    case levelNum of
      1: (fwd1: array [1..1] of node;);
      2: (fwd2: array [1..2] of node;);
      3: (fwd3: array [1..3] of node;);
      4: (fwd4: array [1..4] of node;);
      5: (fwd5: array [1..5] of node;);
      6: (fwd6: array [1..6] of node;);
      7: (fwd7: array [1..7] of node;);
      8: (fwd8: array [1..8] of node;);
      9: (fwd9: array [1..9] of node;);
      10: (fwd10: array [1..10] of node;);
      11: (fwd11: array [1..11] of node;);
      12: (fwd12: array [1..12] of node;);
      13: (fwd13: array [1..13] of node;);
      14: (fwd14: array [1..14] of node;);
      15: (fwd15: array [1..15] of node;);
      16: (fwd: array [1..16] of node;)
  end;

var
  randomChunksLeft: Integer;
  randomBits: randomStuff;
  l: list;
  i, k: Integer;
  v: valueType;
  keys: array [1..sampleSize] of keyType;
  terminator: node;

  head, tail: Integer;
  randomTable: array[1..31] of randomStuff;


function randomNumber: Integer;
begin
  randomTable[head] := (randomTable[head] +
    randomTable[tail]) mod differentRandoms;
  head := (head mod randomTableSize) + 1;
  tail := (tail mod randomTableSize) + 1;
  randomNumber := randomTable[head];
end;

procedure initRandom;
begin
  head := 4;
  tail := 1;
  randomTable[1] := 1005175229;
  randomTable[2] := 143302914;
  randomTable[3] := 1027100827;
  randomTable[4] := 879468478;
  randomTable[5] := 755253631;
  randomTable[6] := 928858961;
  randomTable[7] := 331648406;
  randomTable[8] := 45248011;
  randomTable[9] := 26209743;
  randomTable[10] := 433832350;
  randomTable[11] := 944843483;
  randomTable[12] := 438263339;
  randomTable[13] := 813528929;
  randomTable[14] := 629457392;
  randomTable[15] := 618906479;
  randomTable[16] := 573714703;
  randomTable[17] := 766270699;
  randomTable[18] := 275680090;
  randomTable[19] := 436578616;
  randomTable[20] := 509842102;
  randomTable[21] := 649659208;
  randomTable[22] := 891701505;
  randomTable[23] := 24441858;
  randomTable[24] := 562763940;
  randomTable[25] := 980071615;
  randomTable[26] := 1011597961;
  randomTable[27] := 643279273;
  randomTable[28] := 241719451;
  randomTable[29] := 157584038;
  randomTable[30] := 1069844923;
  randomTable[31] := 471560540;
end;


function randomLevel: Integer;
var
  newLevel: Integer;
  shiftedBits: randomStuff;
  done: Boolean;

begin
  newLevel := 0;
  done := False;
  repeat
    shiftedBits := randomBits div ChunkSize;
    done := (shiftedBits * ChunkSize) <> randomBits;
    newLevel := newLevel + 1;
    randomBits := shiftedBits;
    randomChunksLeft := randomChunksLeft - 1;
    if randomChunksLeft = 0 then
    begin
      randomBits := randomNumber;
      randomChunksLeft := randomChucksInAWord;
    end;
  until done;
  if newLevel > MaxLevel then newLevel := MaxLevel;
  randomLevel := newLevel;
end;


procedure init;
begin
  new(terminator, 1);
  terminator^.key := (256 * 256 * 256 * 64 - 1) * 2 + 1;
  randomBits := randomNumber;
  randomChunksLeft := randomChucksInAWord;
end;

function newList: list;
var
  l: list;
  i: Integer;
begin
  new(l);
  l^.level := 1;
  new(l^.header, MaxLevel);
  for i := 1 to MaxLevel do l^.header^.fwd[i] := terminator;
  newList := l;
end;

procedure freeList(l: list);
var
  k: levelNum;
  done: Boolean;
  p: node;

begin
  p := l^.header^.fwd[1];
  while (p <> terminator) do
  begin
    k := 1;
    done := False;
    while not done do
    begin
      l^.header^.fwd[k] := p^.fwd[k];
      k := k + 1;
      if k > l^.level then done := True
      else
        done := l^.header^.fwd[k] <> p;
    end;
    case k - 1 of
      1: dispose(p, 1);
      2: dispose(p, 2);
      3: dispose(p, 3);
      4: dispose(p, 4);
      5: dispose(p, 5);
      6: dispose(p, 6);
      7: dispose(p, 7);
      8: dispose(p, 8);
      9: dispose(p, 9);
      10: dispose(p, 10);
      11: dispose(p, 11);
      12: dispose(p, 12);
      13: dispose(p, 13);
      14: dispose(p, 14);
      15: dispose(p, 15);
      16: dispose(p, 16)
    end;
    p := l^.header^.fwd[1];
  end;
  dispose(l^.header, MaxLevel);
  dispose(l);
end;

procedure insert(l: list; key: keyType; Value: valueType);
var
  k: levelNum;
  update: array[1..MaxLevel] of node;
  p, q: node;

begin
  p := l^.header;

  for k := l^.level downto 1 do
  begin
    q := p^.fwd[k];
    while q^.key < key do
    begin
      p := q;
      q := p^.fwd[k];
    end;
    update[k] := p;
  end;
  (* The insert routine currently allows duplicate entries. To make
    it update previous entries instead, put in the following code:

     if q^.key == key then begin
       q^.value = value;
       end;
     else
  *)

  begin

    k := randomLevel;
    if k > l^.level then
    begin
      k := l^.level + 1;
      l^.level := k;
      update[k] := l^.header;
    end;

    case k of
      1: new(q, 1);
      2: new(q, 2);
      3: new(q, 3);
      4: new(q, 4);
      5: new(q, 5);
      6: new(q, 6);
      7: new(q, 7);
      8: new(q, 8);
      9: new(q, 9);
      10: new(q, 10);
      11: new(q, 11);
      12: new(q, 12);
      13: new(q, 13);
      14: new(q, 14);
      15: new(q, 15);
      16: new(q, 16)
    end;
    q^.key := key;
    q^.Value := Value;

    for k := k downto 1 do
    begin
      p := update[k];
      q^.fwd[k] := p^.fwd[k];
      p^.fwd[k] := q;
    end;
  end;
end;

procedure Delete(l: list; key: keyType);
var
  k: levelNum;
  update: array[1..MaxLevel] of node;
  p, q: node;
  done: Boolean;

begin
  p := l^.header;

  for k := l^.level downto 1 do
  begin
    q := p^.fwd[k];
    while q^.key < key do
    begin
      p := q;
      q := p^.fwd[k];
    end;
    update[k] := p;
  end;

  if (q^.key = key) then
  begin
    k := 1;
    done := False;
    while not done do
    begin
      update[k]^.fwd[k] := q^.fwd[k];
      k := k + 1;
      if k > l^.level then done := True
      else
        done := update[k]^.fwd[k] <> q;
    end;

    case k - 1 of
      1: dispose(q, 1);
      2: dispose(q, 2);
      3: dispose(q, 3);
      4: dispose(q, 4);
      5: dispose(q, 5);
      6: dispose(q, 6);
      7: dispose(q, 7);
      8: dispose(q, 8);
      9: dispose(q, 9);
      10: dispose(q, 10);
      11: dispose(q, 11);
      12: dispose(q, 12);
      13: dispose(q, 13);
      14: dispose(q, 14);
      15: dispose(q, 15);
      16: dispose(q, 16)
    end;
  end;
end;

function search(l: list; key: keyType; var Value: valueType): Boolean;
var
  k: Integer;
  p, q: node;
begin
  p := l^.header;
  for k := l^.level downto 1 do
  begin
    q := p^.fwd[k];
    while q^.key < key do
    begin
      p := q;
      q := p^.fwd[k];
    end;
  end;
  if (q^.key <> key) then search := False
  else
  begin
    Value := q^.Value;
    search := True;
  end;
end;

begin
  initRandom;
  init;

  l := newList;

  for k := 1 to sampleSize do
  begin
    keys[k] := randomNumber;
    insert(l, keys[k], keys[k]);
  end;

  for i := 1 to 4 do
  begin
    for k := 1 to sampleSize do
      if not search(l, keys[k], v) then WriteLn('not found');
    for k := 1 to sampleSize do
    begin
      Delete(l, keys[k]);
      keys[k] := randomNumber;
      insert(l, keys[k], keys[k]);
    end;
  end;

  freeList(l);

end.


Source: http://algolist.manual.ru
ID: 04186