Generate Binary Numbers from 1 to N

Generating binary numbers from 1 to a given number $nn$ is a fundamental problem in programming. This task can be solved using two main methods: with and without using a queue. Each approach has its own merits and use cases. Let’s dive into the details of both methods.

Method 1: Generating Binary Numbers Without Using a Queue

Overview

This is the most common approach for generating binary numbers. The binary equivalent of a number is calculated using modulo and division operations, with the results stored in an array.

Steps

Input: Specify the maximum number $nn$ up to which binary numbers are to be generated.
Modulo Operation: For each number, compute the remainder when divided by 2.
Division: Divide the number by 2 and repeat the modulo operation, storing remainders.
Reversal: Reverse the stored remainders to obtain the binary representation.
Output: Display the binary numbers from 1 to $nn$ .

Algorithm

Input the maximum value $nn$ .
For each number from 1 to nn:
- Perform modulo operation with 2.
- Store the remainder.
- Divide the number by 2 and repeat until the number becomes zero.
Reverse the remainders to get the binary number.
Print all binary numbers.

Code Example

# Function to generate binary numbers without a queue
def generate_binary_no_queue(n):
    result = []
    for num in range(1, n + 1):
        binary = ""
        temp = num
        while temp > 0:
            binary = str(temp % 2) + binary
            temp //= 2
        result.append(binary)
    return result

# Test case
n = 5
print("Binary numbers from 1 to", n, ":", generate_binary_no_queue(n))

Test Case

Input: 5
Output: ['1', '10', '11', '100', '101']

Method 2: Generating Binary Numbers Using a Queue

Overview

In this approach, a queue data structure is used to generate binary numbers. The process involves enqueueing and dequeueing operations to construct the binary numbers sequentially.

Steps

Input: Specify the maximum number $nn$ .
Initialize Queue: Enqueue the string “1” as the first binary number.
Iterate: For each number:
- Dequeue the front element.
- Print the dequeued element.
- Append “0” and “1” to the dequeued element and enqueue the results.
Repeat: Continue until $nn$ numbers are generated.

Algorithm

Input the maximum value $nn$ .
Initialize a queue and enqueue “1”.
While the number of generated binaries is less than nn:
- Dequeue the front element.
- Print the dequeued value.
- Append “0” and “1” to the dequeued value and enqueue them.
Output all generated binary numbers.

Code Example

from queue import Queue

# Function to generate binary numbers using a queue
def generate_binary_with_queue(n):
    q = Queue()
    q.put("1")
    result = []

    for _ in range(n):
        current = q.get()
        result.append(current)
        q.put(current + "0")
        q.put(current + "1")

    return result

# Test case
n = 5
print("Binary numbers from 1 to", n, ":", generate_binary_with_queue(n))

Test Case

Input: 5
Output: ['1', '10', '11', '100', '101']