How to resolve the algorithm Cyclops numbers step by step in the Python programming language

Published on 12 May 2024 09:40 PM
#Python

How to resolve the algorithm Cyclops numbers step by step in the Python programming language

Table of Contents

Problem Statement

A cyclops number is a number with an odd number of digits that has a zero in the center, but nowhere else. They are named so in tribute to the one eyed giants Cyclops from Greek mythology. Cyclops numbers can be found in any base. This task strictly is looking for cyclops numbers in base 10. There are many different classifications of cyclops numbers with minor differences in characteristics. In an effort to head off a whole series of tasks with tiny variations, we will cover several variants here.

(Note: there are no cyclops numbers between ten million and one hundred million, they need to have an odd number of digits)

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Cyclops numbers step by step in the Python programming language

This Python program generates and prints various types of cyclops numbers, which are numbers that contain a single instance of the digit 0. It also finds and prints prime cyclops numbers, blind prime cyclops numbers, and palindromic prime cyclops numbers.

Here is a detailed explanation of the program:

  1. Cyclops Numbers: Cyclops numbers are numbers that contain a single instance of the digit 0. The function generate_cyclops generates cyclops numbers by combining digits from 1 to 9. It iterates through digits of length d and d+1, skipping numbers that contain 0. Then, it combines the left and right digits to form a cyclops number.

  2. Prime Cyclops Numbers: Prime cyclops numbers are cyclops numbers that are prime numbers. The function generate_prime_cyclops uses the Sympy library's isprime function to check for primality.

  3. Blind Prime Cyclops Numbers: Blind prime cyclops numbers are prime cyclops numbers where removing the central digit (0) also results in a prime number. The function generate_blind_prime_cyclops checks for this property.

  4. Palindromic Cyclops Numbers: Palindromic cyclops numbers are cyclops numbers that are also palindromes. The function generate_palindromic_cyclops generates palindromic cyclops numbers by combining digits from 1 to 9 to create palindromic strings.

  5. Palindromic Prime Cyclops Numbers: Palindromic prime cyclops numbers are palindromic cyclops numbers that are also prime numbers. The function generate_palindromic_prime_cyclops uses the isprime function to check for primality.

  6. Printing and Output: The program prints the first 50 numbers for each type of cyclops number, using a custom function print50 for better formatting. It also finds and prints the first cyclops number after 10,000,000 for each type.

The program demonstrates the generation and properties of various types of cyclops numbers, showcasing their mathematical characteristics and providing examples for each type.

Source code in the python programming language

from sympy import isprime


def print50(a, width=8):
    for i, n in enumerate(a):
        print(f'{n: {width},}', end='\n' if (i + 1) % 10 == 0 else '')


def generate_cyclops(maxdig=9):
    yield 0
    for d in range((maxdig + 1) // 2):
        arr = [str(i) for i in range(10**d, 10**(d+1)) if not('0' in str(i))]
        for left in arr:
            for right in arr:
                yield int(left + '0' + right)


def generate_prime_cyclops():
    for c in generate_cyclops():
        if isprime(c):
            yield c


def generate_blind_prime_cyclops():
    for c in generate_prime_cyclops():
        cstr = str(c)
        mid = len(cstr) // 2
        if isprime(int(cstr[:mid] + cstr[mid+1:])):
            yield c


def generate_palindromic_cyclops(maxdig=9):
    for d in range((maxdig + 1) // 2):
        arr = [str(i) for i in range(10**d, 10**(d+1)) if not('0' in str(i))]
        for s in arr:
            yield int(s + '0' + s[::-1])


def generate_palindromic_prime_cyclops():
    for c in generate_palindromic_cyclops():
        if isprime(c):
            yield c


print('The first 50 cyclops numbers are:')
gen = generate_cyclops()
print50([next(gen) for _ in range(50)])
for i, c in enumerate(generate_cyclops()):
    if c > 10000000:
        print(
            f'\nThe next cyclops number after 10,000,000 is {c} at position {i:,}.')
        break

print('\nThe first 50 prime cyclops numbers are:')
gen = generate_prime_cyclops()
print50([next(gen) for _ in range(50)])
for i, c in enumerate(generate_prime_cyclops()):
    if c > 10000000:
        print(
            f'\nThe next prime cyclops number after 10,000,000 is {c} at position {i:,}.')
        break

print('\nThe first 50 blind prime cyclops numbers are:')
gen = generate_blind_prime_cyclops()
print50([next(gen) for _ in range(50)])
for i, c in enumerate(generate_blind_prime_cyclops()):
    if c > 10000000:
        print(
            f'\nThe next blind prime cyclops number after 10,000,000 is {c} at position {i:,}.')
        break

print('\nThe first 50 palindromic prime cyclops numbers are:')
gen = generate_palindromic_prime_cyclops()
print50([next(gen) for _ in range(50)], 11)
for i, c in enumerate(generate_palindromic_prime_cyclops()):
    if c > 10000000:
        print(
            f'\nThe next palindromic prime cyclops number after 10,000,000 is {c} at position {i}.')
        break

You may also check:How to resolve the algorithm Loops/Infinite step by step in the min programming language
You may also check:How to resolve the algorithm Twelve statements step by step in the Groovy programming language
You may also check:How to resolve the algorithm Loops/Foreach step by step in the Clojure programming language
You may also check:How to resolve the algorithm Horner's rule for polynomial evaluation step by step in the Erlang programming language
You may also check:How to resolve the algorithm Order by pair comparisons step by step in the AutoHotkey programming language