Exercise 3D Write a function sundaram which implements this algorithm. You should check the results by comparing the final list to that produced by the sieve of Eratosthenes, and for the avoidance of doubt, the output of sundaram (5) should be [ 3,5,7,11].

Remains code.  Implement regular expression matching with support for '.' and '*'. '.' Matches any single character.'*' Matches zero or more of the preceding element. The matching should cover the entire input string (not partial). The function prototype should be:bool is_match(const char *s, const char *p) Some examples:is_match("aa","a") → falseis_match("aa","aa") → trueis_match("aaa","aa") → falseis_match("aa", "a*") → trueis_match("aa", ".*") → trueis_match("ab", ".*") → trueis_match("aab", "c*a*b") → true""" def is_match(str_a, str_b):    """Finds if `str_a` matches `str_b`     Keyword arguments:    str_a -- string    str_b -- string    """    len_a, len_b = len(str_a) + 1, len(str_b) + 1    matches = [[False] * len_b  for _ in range(len_a)]     # Match empty string with empty pattern    matches[0][0] = True     # Match empty string with .*    for i, element in enumerate(str_b[1:], 2):        matches[0][i] = matches[0][i - 2] and element == '*'     for i, char_a in…

Generate a python code with commenting and correct codeformatting.The program should work and display correct outputs.

Write a function lis_rec(arr) that outputs the length of the longest increasing sequence and the actual longest increasing sequence. This function should use divide and conquer strategy to the solve the problem, by using an auxiliary function that is recursive. For example, one possibility is to define a recursive function, lis_rec(arr, i, prev), that takes the array arr, an index i, and the previous element index prev of LIS (which is part of the array arr before index i), and returns the length of the LIS that can be obtained by considering the subarray arr[i:]. Write a dynamic programming version ofthe function, lis_dp(arr), that outputs the length of the longest increasing sequence and the actual longest increasing sequence by using a table to store the results of subproblems in a bottom-up manner. Test the performance of the two functions on arrays of length n = 100, 500, 1000, 5000, 10000. Compare the running times and memory usage of the two functions.