S.No Binary sequence
Given a number k, we have to design an algorithm to print kth binary sequence.
Initial approach (not efficient):
Starting from the sequence 0, this algorithm iterates k times.
To get the next sequence, in each iteration we do the following.
check the last index of 0 in the number
- If it is found change that to 1 and all the digits after that to 0
- If it is not found, the next sequence contains all 0 which is one digit longer than previous
Observe the following. we can have
‘2’ single digit numbers
‘4’ two digit numbers
‘8’ three digit numbers
‘2^i’ i digit numbers
We can find the number of digits in kth sequence by calculating the power of 2 which is less than k .
For example if k is 5, the smallest power (s) of 2 less thank k is 4. So kth sequence has 2 digits.
To form the the sequence we need to find the binary representation of
k – ( 2^1 + 2^2 + …+2^s)
This SPOJ problem is based on the above algorithm.
Here is the C++ program which implements this.