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question:Write a function in Python that takes an integer `n` and returns a list containing the first `n` prime numbers. Your solution should be efficient and consider the time complexity of the algorithm used to find prime numbers.

answer:def is_prime(num): Helper function to determine if a number is prime. if num <= 1: return False if num == 2: return True if num % 2 == 0: return False for i in range(3, int(num**0.5) + 1, 2): if num % i == 0: return False return True def first_n_primes(n): Returns a list of the first n prime numbers. primes = [] num = 2 while len(primes) < n: if is_prime(num): primes.append(num) num += 1 return primes

question:Write a Python function named `merge_and_sort` that takes two lists of integers as input. The function should merge the two lists into one and sort the resulting list in ascending order. The function should handle cases where the input lists are empty or contain negative numbers. **Function signature:** ```python def merge_and_sort(list1: List[int], list2: List[int]) -> List[int]: pass ``` **Examples:** ```python # Example 1 list1 = [1, 4, 6] list2 = [2, 5, 3] print(merge_and_sort(list1, list2)) # Output: [1, 2, 3, 4, 5, 6] # Example 2 list1 = [-1, -4, 0] list2 = [3, -2, 1] print(merge_and_sort(list1, list2)) # Output: [-4, -2, -1, 0, 1, 3] # Example 3 list1 = [] list2 = [5, 7, 3] print(merge_and_sort(list1, list2)) # Output: [3, 5, 7] ``` # Constraints: - The lists `list1` and `list2` can contain up to 1000 integers each. - Each integer in the lists can range from `-10^6` to `10^6`.

answer:from typing import List def merge_and_sort(list1: List[int], list2: List[int]) -> List[int]: Merges two lists of integers and returns the sorted list. :param list1: First list of integers. :param list2: Second list of integers. :return: Merged and sorted list of integers. merged_list = list1 + list2 merged_list.sort() return merged_list

question:Given an integer, determine whether it is a T-prime or not. A T-prime is a number that is the square of a prime number. For example, 4 is a T-prime because it is equal to 2^2, where 2 is a prime number. # Input - A single integer n, where 1 leq n leq 10^{12}. # Output - Output "YES" if the number is a T-prime. Otherwise, output "NO". # Example Input 49 Output YES Input 10 Output NO

answer:import math def is_prime(n): Check if a number n is a prime number if n <= 1: return False if n <= 3: return True if n % 2 == 0 or n % 3 == 0: return False i = 5 while i * i <= n: if n % i == 0 or n % (i + 2) == 0: return False i += 6 return True def is_t_prime(n): Check if a number n is a T-prime if n <= 0: return "NO" sqrt_n = int(math.isqrt(n)) if sqrt_n * sqrt_n == n and is_prime(sqrt_n): return "YES" return "NO"

question:Create a Python function that receives a string and returns a new string where every duplicate character is removed, but only keeps the first occurrence of each character. Your function should maintain the order of characters as they first appear in the input. Make sure to handle both uppercase and lowercase characters as distinct. Example input/output: ```python # Example input input_str = "Google" # Expected output output_str = "Gogle" ``` ```python # Example input input_str = "Development" # Expected output output_str = "Devlopmnt" ```

answer:def remove_duplicates(input_str): Returns a new string where every duplicate character is removed, but only keeps the first occurrence of each character. Maintains the order of characters as they first appear in the input. seen = set() output_str = [] for char in input_str: if char not in seen: seen.add(char) output_str.append(char) return ''.join(output_str)