Given a limit N, we need to find out the count of binary digit numbers which are smaller than N. Binary digit numbers are those numbers which contains only 0 and 1 as their digits as 1, 10, 101 etc are binary digit numbers.
Input : N = 200 Output : 7 Count of binary digit number smaller than N is 7, enumerated below, 1, 10, 11, 110, 101, 100, 111
One simple way to solve this problem is to loop from 1 till N and check each number whether it is a binary digit number or not. If it is a binary digit number, increase the count of such numbers but this procedure will take O(N) time. We can do better, as we know that count of such numbers will be much smaller than N, we can iterate over binary digit numbers only and check whether generated numbers are smaller than N or not.
In below code, BFS like approach is implemented to iterate over only binary digit numbers. We start with 1 and each time we will push (t*10) and (t*10 + 1) into the queue where t is the popped element, if t is a binary digit number then (t*10) and (t*10 + 1) will also binary digit number, so we will iterate over these numbers only using queue. We will stop pushing elements in the queue when popped number crosses the N.
This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Find the sum of the series x(x+y) + x^2(x^2+y^2) +x^3(x^3+y^3)+ ... + x^n(x^n+y^n)
- Calculate the Discriminant Value
- Converting a Real Number (between 0 and 1) to Binary String
- Find coordinates of the triangle given midpoint of each side
- Find power of power under mod of a prime
- Generation of n numbers with given set of factors
- Reversible numbers
- Primitive root of a prime number n modulo n
- Smallest number with at least n digits in factorial
- Euler's Totient function for all numbers smaller than or equal to n
- Count of n digit numbers whose sum of digits equals to given sum
- Generate all unique partitions of an integer
- Write a program to add two numbers in base 14
- Number of ways to arrange a word such that all vowels occur together
- Find maximum value of x such that n! % (k^x) = 0
Improved By : Sanjit_Prasad