Divide a number by 3 without using *, /, +, -, % operators

cdividedivisionmath

How would you divide a number by 3 without using *, /, +, -, %, operators?

The number may be signed or unsigned.

Best Answer

This is a simple function which performs the desired operation. But it requires the + operator, so all you have left to do is to add the values with bit-operators:

// replaces the + operator
int add(int x, int y)
{
    while (x) {
        int t = (x & y) << 1;
        y ^= x;
        x = t;
    }
    return y;
}

int divideby3(int num)
{
    int sum = 0;
    while (num > 3) {
        sum = add(num >> 2, sum);
        num = add(num >> 2, num & 3);
    }
    if (num == 3)
        sum = add(sum, 1);
    return sum; 
}

As Jim commented this works, because:

n = 4 * a + b
n / 3 = a + (a + b) / 3
So sum += a, n = a + b, and iterate
When a == 0 (n < 4), sum += floor(n / 3); i.e. 1, if n == 3, else 0

Related Solutions

How to determine the size of the array in C

Executive summary:

int a[17];
size_t n = sizeof(a)/sizeof(a[0]);

Full answer:

To determine the size of your array in bytes, you can use the sizeof operator:

int a[17];
size_t n = sizeof(a);

On my computer, ints are 4 bytes long, so n is 68.

To determine the number of elements in the array, we can divide the total size of the array by the size of the array element. You could do this with the type, like this:

int a[17];
size_t n = sizeof(a) / sizeof(int);

and get the proper answer (68 / 4 = 17), but if the type of a changed you would have a nasty bug if you forgot to change the sizeof(int) as well.

So the preferred divisor is sizeof(a[0]) or the equivalent sizeof(*a), the size of the first element of the array.

int a[17];
size_t n = sizeof(a) / sizeof(a[0]);

Another advantage is that you can now easily parameterize the array name in a macro and get:

#define NELEMS(x)  (sizeof(x) / sizeof((x)[0]))

int a[17];
size_t n = NELEMS(a);

C++ – How to detect unsigned integer multiply overflow

I see you're using unsigned integers. By definition, in C (I don't know about C++), unsigned arithmetic does not overflow ... so, at least for C, your point is moot :)

With signed integers, once there has been overflow, undefined behaviour (UB) has occurred and your program can do anything (for example: render tests inconclusive).

#include <limits.h>

int a = <something>;
int x = <something>;
a += x;              /* UB */
if (a < 0) {         /* Unreliable test */
  /* ... */
}

To create a conforming program, you need to test for overflow before generating said overflow. The method can be used with unsigned integers too:

// For addition
#include <limits.h>

int a = <something>;
int x = <something>;
if ((x > 0) && (a > INT_MAX - x)) /* `a + x` would overflow */;
if ((x < 0) && (a < INT_MIN - x)) /* `a + x` would underflow */;

// For subtraction
#include <limits.h>
int a = <something>;
int x = <something>;
if ((x < 0) && (a > INT_MAX + x)) /* `a - x` would overflow */;
if ((x > 0) && (a < INT_MIN + x)) /* `a - x` would underflow */;

// For multiplication
#include <limits.h>

int a = <something>;
int x = <something>;
// There may be a need to check for -1 for two's complement machines.
// If one number is -1 and another is INT_MIN, multiplying them we get abs(INT_MIN) which is 1 higher than INT_MAX
if ((a == -1) && (x == INT_MIN)) /* `a * x` can overflow */
if ((x == -1) && (a == INT_MIN)) /* `a * x` (or `a / x`) can overflow */
// general case
if (a > INT_MAX / x) /* `a * x` would overflow */;
if ((a < INT_MIN / x)) /* `a * x` would underflow */;

For division (except for the INT_MIN and -1 special case), there isn't any possibility of going over INT_MIN or INT_MAX.

Best Answer

Related Solutions

How to determine the size of the array in C

C++ – How to detect unsigned integer multiply overflow

Related Topic