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

这是Python中的,基本上,字符串比较和一个状态机。

def divide_by_3(input):
  to_do = {}
  enque_index = 0
  zero_to_9 = (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
  leave_over = 0
  for left_over in (0, 1, 2):
    for digit in zero_to_9:
      # left_over, digit => enque, leave_over
      to_do[(left_over, digit)] = (zero_to_9[enque_index], leave_over)
      if leave_over == 0:
        leave_over = 1
      elif leave_over == 1:
        leave_over = 2
      elif leave_over == 2 and enque_index != 9:
        leave_over = 0
        enque_index = (1, 2, 3, 4, 5, 6, 7, 8, 9)[enque_index]
  answer_q = []
  left_over = 0
  digits = list(str(input))
  if digits[0] == "-":
    answer_q.append("-")
  digits = digits[1:]
  for digit in digits:
    enque, left_over = to_do[(left_over, int(digit))]
    if enque or len(answer_q):
      answer_q.append(enque)
  answer = 0
  if len(answer_q):
    answer = int("".join([str(a) for a in answer_q]))
  return answer

其他回答

log(pow(exp(number),0.33333333333333333333)) /* :-) */

这是经典的2进制除法算法

#include <stdio.h>
#include <stdint.h>

int main()
{
  uint32_t mod3[6] = { 0,1,2,0,1,2 };
  uint32_t x = 1234567; // number to divide, and remainder at the end
  uint32_t y = 0; // result
  int bit = 31; // current bit
  printf("X=%u   X/3=%u\n",x,x/3); // the '/3' is for testing

  while (bit>0)
  {
    printf("BIT=%d  X=%u  Y=%u\n",bit,x,y);
    // decrement bit
    int h = 1; while (1) { bit ^= h; if ( bit&h ) h <<= 1; else break; }
    uint32_t r = x>>bit;  // current remainder in 0..5
    x ^= r<<bit;          // remove R bits from X
    if (r >= 3) y |= 1<<bit; // new output bit
    x |= mod3[r]<<bit;    // new remainder inserted in X
  }
  printf("Y=%u\n",y);
}

这真的很简单。

if (number == 0) return 0;
if (number == 1) return 0;
if (number == 2) return 0;
if (number == 3) return 1;
if (number == 4) return 1;
if (number == 5) return 1;
if (number == 6) return 2;

(当然,为了简洁起见,我省略了一些程序。)如果程序员厌倦了把这些都输入,我相信他或她可以编写一个单独的程序来为他生成这些。我碰巧认识一个能大大简化他工作的人。

使用itoa转换为以3为基数的字符串。去掉最后一个小调,转换回10进制。

// Note: itoa is non-standard but actual implementations
// don't seem to handle negative when base != 10.
int div3(int i) {
    char str[42];
    sprintf(str, "%d", INT_MIN); // Put minus sign at str[0]
    if (i>0)                     // Remove sign if positive
        str[0] = ' ';
    itoa(abs(i), &str[1], 3);    // Put ternary absolute value starting at str[1]
    str[strlen(&str[1])] = '\0'; // Drop last digit
    return strtol(str, NULL, 3); // Read back result
}

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