Solution: Generate Binary Numbers From 1 to n Using a Queue

Statement

Given a number n, generate a list of binary numbers from $1$ to n in the form of a string using a queue.

Constraints:

• $1\leq$ n $\leq 1000$

Solution

The algorithm for generating binary numbers up to a specified count using a queue is straightforward. It begins by placing the binary number "1" in the queue and creating an empty list to hold the generated binary numbers. In each iteration of the algorithm, a number is removed from the queue, added to the result list, and then two variations of that number are placed back into the queue by appending "0" and "1". This process is repeated until the desired number of binary numbers has been generated.

Below are the detailed steps of the algorithm:

1. Initialize an empty list result to store the binary numbers, and create an empty queue named queue.

2. Enqueue the integer 1 into the queue.

3. Start a loop that iterates n times, where n is the desired count of binary numbers. Inside the loop, perform the following steps:

   1. Dequeue an element from the queue, convert it to a string, and append it to the result list.

   2. Create two new strings, s1 and s2, by appending "0" and "1" respectively, to the dequeued string.

   3. Enqueue s1 and s2 back into the queue.

4. After the loop completes, return the result list containing the generated binary numbers.

Let’s look at the illustration below to better understand the solution: