I am having trouble understanding how exactly this code works:

int length = 1;
int x = 234567545;
while (x /= 10)
 length++;

It is supposed to count the number of digits in the int variable. I don't get how the while loop is working. Does the loop just go to zero and stop by default? Also, why is the length starting at 1?

There are three things that might be suspicious for you if you are a C++ beginner:

First thing might be operator /=, which combines an integral division (i.e. without remainder), with an assignment. So x /= 10 actually is the same as x = x / 10.

Second, each expression in C++ has - after having been evaluated - a value. For an assignment like (x = 0), the result is the value of x after the assignment, i.e. 0 in this case.

Third, a condition like if (x) ... with x being of integral type has in C++ the same meaning as if(x != 0), i.e. it is false if x equals 0, and it is true if x is anything else but 0.

All together: while ( x /= 10 ) means assign x the value of an integral division by 10 and then compare the value to 0. If 0 is reached, the loop ends.

BTW: length starts with 1, because any number, even 0, comprises at least one digit.

x /= 10 continuously divides x by 10, which will make it 0 eventually and cause the while loop to terminate due to 0 being interpreted as false (and any other value than 0 as true).

The reason it starts at length = 1 is because there is always at least 1 digit in the number: if x was from 0 to 9 inclusive, then x /= 10 would cause x to become 0 immediately, meaning nothing inside the loop would execute. Therefore, if length started at 0, it would never get to be incremented to 1 which would be wrong if x was a single digit large.

Manually calculating this example by hand:

1. 234567545 / 10 = 23456754, which is true, so the while loop continues and length becomes 2.




2. 23456754 / 10 = 2345675, true. length becomes 3.




3. 2345675 / 10 = 234567, true. length becomes 4.




4. 234567 / 10 = 23456, true. length becomes 5.




5. 23456 / 10 = 2345, true. length becomes 6.




6. 2345 / 10 = 234, true. length becomes 7.




7. 234 / 10 = 23, true. length becomes 8.




8. 23 / 10 = 2, true. length becomes 9.




9. 2 / 10 = 0, false. The while loop stops with length equal 9.

The loop

while (x /= 10) 
 length++;

will go until the result of x /= 10 evaluates to false, since 0 means false it will go until x /= 10 is 0. Integer division truncates, ensuring the condition will be reached. This can be illustrated by adding a simple debug statement, i.e.

while (x /= 10) 
 length++;
 std::cout << length << " " << x << std::endl;

Which outputs

2 23456754
3 2345675
4 234567
5 23456
6 2345
7 234
8 23
9 2

Integer division will truncate the remainder, so continually dividing a number with integer division will inevitably result in zero.

Dividing a number n by 10 while incrementing a counter i once for each time the resulting quotient (stored back into n) is not zero will result in the i containing the number of digits for the base-10 representation of n.

It helps to understand two parts:

• what is "/="


• when does the loop terminate

Explain "/="

This:

x /= 10

is the same as:

x = x / 10

Explain when the loop terminates

The while loop terminates, when the condition is false. And 0 is equivalent to false.

while (condition) 
 length++;

So x is, with every pass through the loop, divided by 10, until is is 0. That terminates the loop.

So, the condition is two things at the same time:

• it is a value, that is compared to 0. The loop continues until this
  evaluates to 0.


• it is an assignment: x gets a new value with every evaluation. It's divided by 10, so it converges to 0.

This is a bit of stupidity you'll often see in C/C++, taking advantage of the fact that TRUE is implemented as non-zero, and FALSE as zero*. So x is repeatedly divided by 10, and the expression eventually becomes zero, so the loop stops.

Though confusing, this works - until the day someone in a hurry changes x from an int to a double :-) Much clearer and less failure-prone to write "while (x /= 10 >= 1)", or even to put the math inside the loop body rather than in the condition.

*IMHO one of the few shortcomings of C is that it didn't have an explicit logical type, as FORTRAN did.