Google Treasure Hunt 2008 素数

[ahjoe]

题目：连续 5 个素数之和
连续 13 个素数之和
连续 275 个素数之和
连续 1187 个素数之和
求出同时符合以上4个条件的数。

技巧：用数组里的一个位保存一个数是否是素数。
结果：5615741
计算用时：17秒 (AMD 2600+)

unit GoogleHunt5u;

interface

uses
  Windows, Messages, SysUtils, Classes, Graphics, Controls, Forms, Dialogs,
  StdCtrls, Spin, SearchDir;

type
  TForm1 = class(TForm)
    Button1: TButton;
    Edit1: TEdit;
    Label3: TLabel;
    Label2: TLabel;
    Edit3: TEdit;
    procedure Button1Click(Sender: TObject);
    procedure FormCreate(Sender: TObject);
  private
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

function IsPrime(V: DWORD): Boolean;

implementation

{$R *.DFM}

var
  bitArr: array [0..HIGH(DWORD) div 32] of DWORD;

  InitMax: DWORD = 3;

function IsPrimeFromBit(V: DWORD): Boolean;
var
  p: integer; // 下标
  m: integer; // 余
  mask: DWORD;
begin
  if V = DWORD(-1) then
    sleep(0); // ERROR
  while InitMax < V do
  begin
    if IsPrime(InitMax + 2) then
    begin
      Inc(InitMax, 2);
      p := InitMax shr 5;
      m := InitMax and $1F;
      mask := 1 shl m;
      bitArr[p] := bitArr[p] or mask;
    end
    else
      Inc(InitMax, 2);
  end;
  p := V shr 5;
  m := V and $1F;
  if m = 0 then
  begin
    Result := False;
    Exit;
  end;
  mask := 1 shl m;
  if p < 0 then
    Sleep(1);
  Result := bitArr[p] and mask <> 0;
end;

function IsPrime(V: DWORD): Boolean;
var
  i: integer;
  max: DWORD;
begin
  max := Round(Sqrt(V));
  i := 3;
  while i <= max do
  begin
    if IsPrimeFromBit(i) then
    if V mod i = 0 then
    begin
      Result := False;
      Exit;
    end;
    Inc(i);
  end;
  Result := True;
end;

function NprePrime(V: DWORD; n: integer): integer;
begin
  if IsPrimeFromBit(V) then
    Dec(n, 2)
  else
    Dec(n);
  Dec(V);
  while n > 0 do
  begin
    if IsPrimeFromBit(V) then
    begin
      Dec(n);
      if n = 0 then
      begin
        Result := V;
        Exit;
      end;
    end;
    Dec(V);
    if V = 2 then
    begin
      Result := V;
      Exit;
    end
  end;
end;

function GetNextPrime(V: DWORD): DWORD;
begin
  Inc(V);
  while not IsPrimeFromBit(V) do
  begin
    Inc(V);
  end;
  Result := V;
end;

function SumNPrime(V: DWORD; n: integer): DWORD;
begin
  Result := V;
  Dec(n);
  while n > 0 do
  begin
    V := GetNextPrime(V);
    Inc(Result, V);
    Dec(n);
  end;
end;

function IsNPrimeSum(V: DWORD; n: integer): Boolean;
var
  stV: DWORD;
  sumN: DWORD;
begin
  stV:= NprePrime((V div n), n);
  repeat
    sumN := SumNPrime(stV, n);
    stV := GetNextPrime(stV);
  until sumN >= V;
  Result := sumN = V;
end;

procedure TForm1.Button1Click(Sender: TObject);
label repgo;
const
  Cnt1 = 5;
  Cnt2 = 13;
  Cnt3 = 275;
  Cnt4 = 1187;
var
  stV: DWORD;
  st: DWORD;
begin
  st := GetTickCount();
  stV := SumNPrime(2, Cnt4);
  while True do
  begin
    Edit1.Text := 'Calc... ' + IntToStr(stV);
    Application.ProcessMessages();
    if IsNPrimeSum(stV, Cnt1) then
    if IsNPrimeSum(stV, Cnt2) then
    if IsNPrimeSum(stV, Cnt3) then
    if IsNPrimeSum(stV, Cnt4) then
    begin
      Edit1.Text := IntToStr(stV);
      Break;
    end;
    if stV and 1 = 0 then // 偶数
      Inc(stV)
    else
      Inc(stV, 2);
  end;
  st := GetTickCount() - st;
  Edit3.Text := IntToStr(st div 1000);
end;

procedure TForm1.FormCreate(Sender: TObject);
begin
  FillChar(bitArr, sizeof(bitArr), 0);
  bitArr[0] := $C; // 2,3 are Prime
end;

end.