Hello, coding test preparation students! Today, we will solve a problem that involves finding the minimum value that satisfies two conditions in a given range, using prime numbers and palindrome numbers. This problem is one of the common topics in algorithm problem solving and will greatly help in writing efficient code. Let’s take a look at the problem together.
Problem Definition
Write a function to find the minimum value that satisfies the following conditions:
- Given natural number
Nis provided as input, where1 <= N <= 10,000. - Find the palindrome numbers among the prime numbers less than or equal to
N. - Return the minimum value among the found prime numbers.
For example, when N = 31, the prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and the palindrome numbers among these are 2, 3, 5, 7, 11. Therefore, 11 is the minimum value.
Process of Solving the Problem
To solve the problem, we will proceed through the following steps:
- Step 1: Define a function to find the prime numbers less than or equal to the given
N. - Step 2: Check for palindrome numbers among the found primes.
- Step 3: Return the minimum value among the palindrome primes.
Step 1: Finding Prime Numbers
To find prime numbers, we will use the Sieve of Eratosthenes algorithm. This algorithm is one of the efficient methods for finding prime numbers, with a time complexity of O(n log log n). This will allow us to find all prime numbers up to the given N.
Implementation of the Sieve of Eratosthenes Algorithm
def sieve_of_eratosthenes(n):
primes = []
is_prime = [True] * (n + 1)
is_prime[0], is_prime[1] = False, False
for i in range(2, int(n**0.5) + 1):
if is_prime[i]:
for j in range(i * i, n + 1, i):
is_prime[j] = False
for i in range(n + 1):
if is_prime[i]:
primes.append(i)
return primesStep 2: Checking for Palindrome Numbers
Once we have found the prime numbers, we need to find the palindrome numbers among them. A palindrome number is a number that reads the same forwards and backwards. For example, 121 and 12321 are palindromes. A function to check this would look like the following:
def is_palindrome(num):
return str(num) == str(num)[::-1]Step 3: Returning the Minimum Value
Finally, we will write a function that finds and returns the minimum value among the found palindrome numbers. We can use the min() function for easy calculation of the minimum value.
def find_smallest_palindrome_prime(n):
primes = sieve_of_eratosthenes(n)
palindrome_primes = [p for p in primes if is_palindrome(p)]
if not palindrome_primes:
return None # Return None if there are no palindrome numbers
return min(palindrome_primes)Complete Code
When we put together all the above steps, the final code looks like this:
def sieve_of_eratosthenes(n):
primes = []
is_prime = [True] * (n + 1)
is_prime[0], is_prime[1] = False, False
for i in range(2, int(n**0.5) + 1):
if is_prime[i]:
for j in range(i * i, n + 1, i):
is_prime[j] = False
for i in range(n + 1):
if is_prime[i]:
primes.append(i)
return primes
def is_palindrome(num):
return str(num) == str(num)[::-1]
def find_smallest_palindrome_prime(n):
primes = sieve_of_eratosthenes(n)
palindrome_primes = [p for p in primes if is_palindrome(p)]
if not palindrome_primes:
return None
return min(palindrome_primes)
# Example usage
N = 31
result = find_smallest_palindrome_prime(N)
print(f"The minimum palindrome prime number less than or equal to {N} is: {result}")Conclusion
Through this lecture, we have understood the concepts of prime numbers and palindrome numbers and practiced how to solve problems using them. We were able to write efficient code using the Sieve of Eratosthenes to find primes and a simple algorithm to check if the number is a palindrome. I hope this will help you advance your algorithmic thinking and coding skills.
In the future, let’s work on various problems together and endeavor to prepare for coding tests. Thank you!