### Vinay Singh

#### Latest posts by Vinay Singh (see all)

- Sorting non boundary elements - February 19, 2016
- Circular Prime – Solution of ISC Computer Practical 2016 - February 18, 2016
- Array Pattern - February 15, 2016

A *unique number* can be defined as a positive integer without leading zeros, in which each digit occurs only once (no duplicate digit). There can be various methods to detect whether or not a given positive integer is a unique number or not. I won’t be discussing methods which requires the number to be converted into a string as that would be inefficient in terms of space and time.

The approach which I am going to demonstrate in this post is to use a single short (integer) variable to store the presence(or absence) of each digit of an integer instead of multiple flags or an array. Note that a short variable consist of 16 bits (i.e. binary digit 0 or 1) and in this case we only need 10 bits to store the presence (or absence) of each digit. The idea is to read a bit corresponding to the required digit, if it is already 1 that means that the digit is repeated and false is returned. If the bit read is 0 then it is set as 1 to denote the presence of that particular digit. The last digit is for 0, the second last bit is for digit 1 and so on.

The java program to implement the above mentioned logic for unique number is as follows:

class UniqueNumber{ public static boolean isUniqueNumber( int n ){ short status=0; byte digit; for( int temp=n; temp>0; temp/=10 ){ digit=(byte)(temp%10); if( (status & (1<<(digit))) >0 ) return false; else status |= 1<<(digit); } return true; } public static void main( String args[] ){ System.out.println(isUniqueNumber(1234)); //1234 is a unique number System.out.println(isUniqueNumber(12342));//12342 is not a unique number } }

The output of the above program to ascertain the unique number would be as follows:

true false

The expression

1<<(digit)

is for shifting 1 towards the left for required number of bits. For example, if digit is 0 the expression it would remain 0, if digit is 1 the expression would result in 10, if digit is 2 the expression would result in 100 and so on.

The expression

status & (1<<(digit))

is for extracting the required bit from the variable status. Note that a.1=1 according to boolean algebra.

The expression

status |= 1<<(digit)

is a short-hand for

status = status | 1<<(digit)

The purpose of the above line is to set a particular bit because a+1=1 according to boolean algebra.