如何将一个数除3而不使用*、/、+、-、%等运算符?

号码可以有签名,也可以没有签名。


当前回答

好吧,我想我们都同意这不是一个现实世界的问题。为了好玩,这里是如何用Ada和多线程来做这件事:

with Ada.Text_IO;

procedure Divide_By_3 is

   protected type Divisor_Type is
      entry Poke;
      entry Finish;
   private
      entry Release;
      entry Stop_Emptying;
      Emptying : Boolean := False;
   end Divisor_Type;

   protected type Collector_Type is
      entry Poke;
      entry Finish;
   private
      Emptying : Boolean := False;
   end Collector_Type;

   task type Input is
   end Input;
   task type Output is
   end Output;

   protected body Divisor_Type is
      entry Poke when not Emptying and Stop_Emptying'Count = 0 is
      begin
         requeue Release;
      end Poke;
      entry Release when Release'Count >= 3 or Emptying is
         New_Output : access Output;
      begin
         if not Emptying then
            New_Output := new Output;
            Emptying := True;
            requeue Stop_Emptying;
         end if;
      end Release;
      entry Stop_Emptying when Release'Count = 0 is
      begin
         Emptying := False;
      end Stop_Emptying;
      entry Finish when Poke'Count = 0 and Release'Count < 3 is
      begin
         Emptying := True;
         requeue Stop_Emptying;
      end Finish;
   end Divisor_Type;

   protected body Collector_Type is
      entry Poke when Emptying is
      begin
         null;
      end Poke;
      entry Finish when True is
      begin
         Ada.Text_IO.Put_Line (Poke'Count'Img);
         Emptying := True;
      end Finish;
   end Collector_Type;

   Collector : Collector_Type;
   Divisor : Divisor_Type;

   task body Input is
   begin
      Divisor.Poke;
   end Input;

   task body Output is
   begin
      Collector.Poke;
   end Output;

   Cur_Input : access Input;

   -- Input value:
   Number : Integer := 18;
begin
   for I in 1 .. Number loop
      Cur_Input := new Input;
   end loop;
   Divisor.Finish;
   Collector.Finish;
end Divide_By_3;

其他回答

使用Linux shell脚本:

#include <stdio.h>
int main()
{
    int number = 30;
    char command[25];
    snprintf(command, 25, "echo $((%d %c 3)) ", number, 47);
    system( command );
    return 0;
}

请看我的另一个答案。

好吧,我想我们都同意这不是一个现实世界的问题。为了好玩,这里是如何用Ada和多线程来做这件事:

with Ada.Text_IO;

procedure Divide_By_3 is

   protected type Divisor_Type is
      entry Poke;
      entry Finish;
   private
      entry Release;
      entry Stop_Emptying;
      Emptying : Boolean := False;
   end Divisor_Type;

   protected type Collector_Type is
      entry Poke;
      entry Finish;
   private
      Emptying : Boolean := False;
   end Collector_Type;

   task type Input is
   end Input;
   task type Output is
   end Output;

   protected body Divisor_Type is
      entry Poke when not Emptying and Stop_Emptying'Count = 0 is
      begin
         requeue Release;
      end Poke;
      entry Release when Release'Count >= 3 or Emptying is
         New_Output : access Output;
      begin
         if not Emptying then
            New_Output := new Output;
            Emptying := True;
            requeue Stop_Emptying;
         end if;
      end Release;
      entry Stop_Emptying when Release'Count = 0 is
      begin
         Emptying := False;
      end Stop_Emptying;
      entry Finish when Poke'Count = 0 and Release'Count < 3 is
      begin
         Emptying := True;
         requeue Stop_Emptying;
      end Finish;
   end Divisor_Type;

   protected body Collector_Type is
      entry Poke when Emptying is
      begin
         null;
      end Poke;
      entry Finish when True is
      begin
         Ada.Text_IO.Put_Line (Poke'Count'Img);
         Emptying := True;
      end Finish;
   end Collector_Type;

   Collector : Collector_Type;
   Divisor : Divisor_Type;

   task body Input is
   begin
      Divisor.Poke;
   end Input;

   task body Output is
   begin
      Collector.Poke;
   end Output;

   Cur_Input : access Input;

   -- Input value:
   Number : Integer := 18;
begin
   for I in 1 .. Number loop
      Cur_Input := new Input;
   end loop;
   Divisor.Finish;
   Collector.Finish;
end Divide_By_3;

如果你提醒自己标准的学校除法方法,用二进制来做,你会发现在3的情况下,你只是在有限的一组值中除法和减法(在这种情况下,从0到5)。这些可以用switch语句处理,以摆脱算术运算符。

static unsigned lamediv3(unsigned n)
{
  unsigned result = 0, remainder = 0, mask = 0x80000000;

  // Go through all bits of n from MSB to LSB.
  for (int i = 0; i < 32; i++, mask >>= 1)
  {
    result <<= 1;
    // Shift in the next bit of n into remainder.
    remainder = remainder << 1 | !!(n & mask);

    // Divide remainder by 3, update result and remainer.
    // If remainder is less than 3, it remains intact.
    switch (remainder)
    {
    case 3:
      result |= 1;
      remainder = 0;
      break;

    case 4:
      result |= 1;
      remainder = 1;
      break;

    case 5:
      result |= 1;
      remainder = 2;
      break;
    }
  }

  return result;
}

#include <cstdio>

int main()
{
  // Verify for all possible values of a 32-bit unsigned integer.
  unsigned i = 0;

  do
  {
    unsigned d = lamediv3(i);

    if (i / 3 != d)
    {
      printf("failed for %u: %u != %u\n", i, d, i / 3);
      return 1;
    }
  }
  while (++i != 0);
}

没有反复检查这个答案是否已经发表。如果程序需要扩展到浮点数,可以将这些数字乘以所需精度的10*数,然后可以再次应用下面的代码。

#include <stdio.h>

int main()
{
    int aNumber = 500;
    int gResult = 0;

    int aLoop = 0;

    int i = 0;
    for(i = 0; i < aNumber; i++)
    {
        if(aLoop == 3)
        {
           gResult++;
           aLoop = 0;
        }  
        aLoop++;
    }

    printf("Reulst of %d / 3 = %d", aNumber, gResult);

    return 0;
}

我会用这段代码除所有正数,非浮点数。基本上你要把除数位向左对齐以匹配被除数位。对于被除数的每一段(除数的大小),你想要检查是否被除数的每一段大于除数,然后你想要左Shift,然后在第一个注册器中OR。这个概念最初是在2004年创建的(我相信是斯坦福大学),这里是一个C版本,它使用了这个概念。注:(我做了一点修改)

int divide(int a, int b)
{
    int c = 0, r = 32, i = 32, p = a + 1;
    unsigned long int d = 0x80000000;

    while ((b & d) == 0)
    {
        d >>= 1;
        r--;
    }

    while (p > a)
    {
        c <<= 1;
        p = (b >> i--) & ((1 << r) - 1);
        if (p >= a)
            c |= 1;
    }
    return c; //p is remainder (for modulus)
}

使用示例:

int n = divide( 3, 6); //outputs 2