library.py

## Module of Python functions utilized across various solutions.

def digits(integer):
    return [ int(x) for x in str(integer) ]

def digits_to_number(t):
    """Converts a tuple of digits to an integer, e.g. (4, 7, 1) -> 471."""
    return int(str().join(map(str, t)))

def is_prime(n):
    if n % 2 == 0:
        return False
        
    for i in range(3, int(n**0.5)+2, 2):
        if n % i == 0:
            break
    else:
        return True

    return False

def primes_up_to(n):
    # Use the Sieve of Eratosthenes
    # https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
    #
    # Create a boolean array "prime[0..n]" and initialize
    # all entries it as true. A value in prime[i] will
    # finally be false if i is not a prime, else true.
    prime = [ True for i in range(n + 1) ]
    
    prime[0]= False
    prime[1]= False
    
    p = 2
    while (p * p <= n):
          
        # If prime[p] is not changed, then it is a prime
        if prime[p]:
              
            # Update all multiples of p
            for i in range(p * 2, n + 1, p):
                prime[i] = False
        
        p += 1

    return [ p for p in range(n+1) if prime[p] ]

import signal
import time
from functools import wraps

def timed(timeout_seconds=None):
    def decorator(func):
        @wraps(func)
        def wrapper(*args, **kwargs):
            if timeout_seconds is not None:  # If timeout is specified
                def timeout_handler(signum, frame):
                    raise TimeoutError("Function execution exceeded the time limit.")
                
                # Set the timeout signal handler
                signal.signal(signal.SIGALRM, timeout_handler)
                signal.alarm(timeout_seconds)  # Set the timeout duration
            
            try:
                start_time = time.time()  # Start timing
                result = func(*args, **kwargs)  # Execute the function
                elapsed_time = time.time() - start_time  # Calculate elapsed time
                return result, elapsed_time
            except TimeoutError as e:
                ## print(f"Timeout occurred: {e}")
                return None, None
            finally:
                if timeout_seconds is not None:
                    signal.alarm(0)  # Cancel the alarm
        return wrapper
    return decorator