The following questions are related to regular expression and regular language: (i) Let r,, r2, r be regular expressions. Find all the regular ones from the following expressions: a·p, r³, r* · 0, (r*)), r + r2 – r, (4) +r + 12, n+r, ÷ r,, r*), (r, r2), {rn + r2}, a+¢ (ii) Let E= {a, b}. Given regular expressions r = a*b*, r' = ba*ab* + (ab)* (ba)* and Ir" = (a* + b)b(a + b)*,- nd L(r), L(r"), and L(r"), the languages defined by r, r', r", respectively. (iii) Let E = {a, b}. Given the language L = {aam b"b, (ba)*, bb: n, m 2 0 and h 2 1}, find the regular expression r such that L(r) = L.

In C programing Write a recursive function that returns the product of the digits of its integer input parameter, n. You may assume that n is non-negative. For example, productDigits(243) should return 24, since 2 x 4 x 3 = 24.int productDigits (int n) {

Write a recursive function that returns both the smallest and the largest element in an int array. Also, write a program to test your function.

The 4th problem mimics the situation where eagles flying in the sky can be spotted and counted.FindEagles: a recursive function that examines and counts the number of objects (eagles) in aphotograph. The data is in a two-dimensional grid of cells, each of which may be empty (value 0) orfilled (value 1 to 9). Maximum grid size is 50 x 50. The filled cells that are connected form an object(eagle). Two cells are connected if they are vertically, horizontally, or diagonally adjacent. Thefollowing figure shows 3 x 4 grids with 3 eagles. 0 0 1 21 0 0 01 0 3 1 FindEagle function takes as parameters the 2-D array and the x-y coordinates of a cell that is a part ofan eagle (non-zero value) and erases (change to 0) the image of an eagle. The function FindEagleshould return an integer value that counts how many cells has been counted as part of an eagle and havebeen erased. The following sample data has two pictures, the first one is 3 x 4, and the second one is 5 x 5 grids. Notethat your program…