Bitwise operations

collatz_conjecture.h

#ifndef COLLATZ_CONJECTURE_H
#define COLLATZ_CONJECTURE_H

#define ERROR_VALUE -1

int steps(int start);

#endif

collatz_conjecture.c

#include "collatz_conjecture.h"

int steps(int start)
{
   if (start < 1)
      return ERROR_VALUE;
   int step_count = 0;
   while (start != 1) {
      if (!(start & 1))
         start = start >> 1;
      else
         start = (start * 3) + 1;
      step_count++;
   }
   return step_count;
}

This approach starts by defining an ERROR_VALUE in the header file instead of using -1 as a magic number.

The steps function starts by checking if the input number is less than 1. If so, the function returns the ERROR_VALUE.

The counter variable is initialized to 0.

The while loop will iterate while the input number is not equal to 1. If the input number is already 1, the while loop will not execute and the function will return 0.

Inside the while loop, the input number is ANDed with 1. The falsiness of 0 is used by the logical NOT operator (!) to determine if the number is even.

• For example, if the number is 4, which is binary 100, then 100 is bitwise ANDed (&) with 001. Since 1 is not the rightmost digit in 100, the result of the AND is 000, determining that 4 is an even number.
• If the number is 5, which is binary 101, then 101 is ANDed with 001. Since 1 is the rightmost digit in 101, the result of the AND is 001, determining that 5 is an odd number.

If the number is even, then the number is set to half of itself. Instead of using division by 2, all of the bits in the number are shifted right (>>) once to halve the number.

• For example, if the number is 4, which is binary 100, then the bits in 100 are shifted right once to binary 010, which is decimal 2.
• If the number is 6, which is binary 110, then the bits in 110 are shifted right once to binary 011, which is decimal 3.

If the number is odd, then it is set to 3 times itself, plus 1.

Whether the number is even or odd, the loop increments the counter variable for each iteration.

After the input number is reduced to 1 in the whileloop, the loop is done and the function returns the value of the counter variable.