Count the number of digits in the number

Problem

Given the integer, find the number of digits in the integer.

Solution

Method 1 - Brute force using loop
Keep dividing the number, until it is 0. This will give us the count of number.

Java code

public static int getSize(long number) {  
      int count = 0;  
      while (number > 0) {  
          count += 1;  
          number = (number / 10);  
      }  
      return count;  
}

Method 2 - Convert to string

int length = String.valueOf(number).length();

Method 3 - Log and floor

digits = floor( log10( number ) ) + 1;

ie. in java

 int length = (int)(Math.log10(number)+1);

Also, note that number > 0 , as we can’t take log of negative numbers.

Time complexity - O(n)
These all are O(n) solution. Can we do better?

Method 4 - Divide and conquer
We know that numbers have limits, and also when we do integer division, result tends to some int or 0 if divisor is greater than dividend.

So, lets use it to our advantage:

n = 1;  
if (i >= 100000000){i /= 100000000; n += 8;}  
if (i >= 10000){i /= 10000; n += 4;}  
if (i >= 100){i /= 100; n += 2;}  
if (i >= 10){i /= 10; n += 1;}

Here is a long but beautiful java code borrowed from here:

if (n < 100000)  
{  
 // 5 or less  
 if (n < 100)  
 {  
  // 1 or 2  
  if (n < 10)  
   return 1;  
  else  
   return 2;  
 }  
 else  
 {  
  // 3 or 4 or 5  
  if (n < 1000)  
   return 3;  
  else  
  {  
   // 4 or 5  
   if (n < 10000)  
    return 4;  
   else  
    return 5;  
  }  
 }  
}  
else  
{  
 // 6 or more  
 if (n < 10000000)  
 {  
  // 6 or 7  
  if (n < 1000000)  
   return 6;  
  else  
   return 7;  
 }  
 else  
 {  
  // 8 to 10  
  if (n < 100000000)  
   return 8;  
  else  
  {  
   // 9 or 10  
   if (n < 1000000000)  
    return 9;  
   else  
    return 10;  
  }  
 }  
}

Of-course we can make it compact if we use ?: ternary operator, below is the code upto 7 digits

return (n < 100000 ? (n < 100 ? (n < 10 ? 1 : 2) :   
          (n < 1000 ? 3 : (n < 10000 ? 4 : 5))) :   
          (n < 10000000 ? 6 : (n < 10000000 : 7 )))

Forgive me for that :P. Please post your comments if you have better idea.

References

Problem

Solution

See also