Last Updated: 16 Dec, 2020
Generate Binary Numbers
Easy
Asked in companies
Your friend Ninja has been learning about binary numbers lately. In order to understand binary numbers with perfection, Ninja asks you to generate a list of binary numbers from 1 to ‘N’, which he can use later for reference.
For every integer Ninja gives, your task is to generate all the binary numbers from 1 to ‘N’.
Example:
Consider N = 5,
All the binary numbers from 1 to 5 are: 1, 10, 11, 100, 101.
Input format:
The very first line of input contains an integer ‘T’ denoting the number of test cases.
The first and the only line of every test case contains a positive integer ‘N’.
Output format:
For each test case, print ‘N’ space-separated binary numbers from 1 to ‘N’, in a separate line.
Print the output of each test case in a separate line.
Note:
You do not need to print anything, it has already been taken care of. Just implement the given function.
Constraints:
1 <= T <= 10
1 <= N <= 10 ^ 5
Time Limit: 1 sec
Approaches
The idea is to generate all the decimal numbers from 1 to N and convert each of them to their corresponding binary representation.
This can be done as follows:
- Loop through all the decimal numbers from 1 to N.
- During each iteration, convert the decimal number to its corresponding binary representation.
- The algorithm to convert a decimal number to binary is as follows:
- Divide the number by 2 and store its remainder.
- Repeat the previous step until the number is greater than 0.
- Now, create a string of the remainders in reverse of the order in which they were obtained.
- Print the string, which is the binary representation of your decimal number.
The idea is to recognize the pattern while generating the sequence of the binary numbers. The following image can help us identify the pattern easily.
→ The number in blue color represents the decimal form of the binary number present inside the circle:
- The first binary number, i.e. ‘1’ is generated manually.
- Now, if we append ‘0’ and ‘1’ to our previously generated number ‘1’, we get the next two binary numbers of the sequence, which are 10 and 11.
- Appending ‘0’ and ‘1’ to these two newly generated binary numbers gives us the next four binary numbers of the sequence, which are 100, 101, 110, 111.
- Hence, repeating the same procedure again, we can generate all the binary numbers in an efficient manner.
- So, in order to generate the required sequence, we can assume that we are performing a level-order traversal of the tree until we get all the numbers from 1 to N.
The algorithm for the approach is as follows:
- Create an empty queue to store the binary numbers.
- Enqueue with the first binary number which we want to generate i.e. ‘1’.
- Now, repeat the following steps until N numbers have been generated:
- Dequeue the front element of the queue. Store this element in a variable that says ‘E’.
- Print ‘E’.
- Append ‘0’ to the end of ‘E’ and push it back to the queue.
- Append ‘1’ to the end of ‘E’ and push it back to the queue.
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