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- Give a recursive definition for the set of all strings of a’s and b’s that begins with an a and ends in a b. Say, S = { ab, aab, abb, aaab, aabb, abbb, abab..} Let S be the set of all strings of a’s and b’s that begins with a and ends in a b. The recursive definition is as follows – Base:... Recursion: If u ∈ S, then... Restriction: There are no elements of S other than those obtained from the base and recursion of S.1. Analyze the word finder with wild card characters scenario to form the algorithm and compute the time complexity. You are given a list of characters with size n, m. You need to read character data provided as input into this list. There is also a list of p words that you need to find in the given problem. You can only search in left, right, up and down direction from a position. There are two wild characters *' and '+' ,if there is any instance of wild card characters for example '+' appears you can match whatever character in your word that you are searching at this position (only one character). Similarly, if you got wildcard *' you can skip any number of characters ( A sequence of characters not necessary same in between the characters) but the last character should be matched in the given data. This means you are not allowed to match a first and last character with *' wildeard. Input: The first line of the input will give you two integers n and m. From the next line you will get…Must be new solution and run on GNU Common Lisp! Using Lisp, write a program that solves the Missionaries and Cannibals problem that uses a DFS( depth first search). It should use (mac start end). Start is the current state (which can be (3 3 l) and End is the goal state (which can be (0 0 r). This should output the sequences of moves needed to reach the end state from the start state. This should print nil if there is no solution. For example, the call should be something like this! Call: (mac '(3 3 l) '(0 0 r)) Output: ((3 3 l) (2 2 r) (3 2 l) (3 0 r) (3 1 l) (1 1 r) (2 2 l) (0 2 r) (0 3 l) (0 1 r) (1 1 l) (0 0 r))
- The intersection of two sets contains the list of elements that are common to both, without repetition. As such, you are required to write an algorithm that finds and returns the intersection of two sets A and B. The sets A and B and the resulting intersection set are all lists. Assume the size of A is n and that of B is m. (a) Write an iterative algorithm that finds the intersection. (b) Prove the correctness of your algorithm; i.e. state its loop invariant and prove it by induc- tion. (c) Analyze the time complexity of your algorithm. (d) Think of a way to enhance the complexity of your algorithm by sorting both lists A and B before calculating their intersection. Write the enhanced version and prove that it has a better time complexity.Q4. Recursion Find how many possible combinations that a number can be decomposed into the multiple of integers (smaller than the number itself) by a recursion function.Suppose we have a positive number Y as input, and it need to be decomposed into the multiple of several integers, Yi, where each Yi, is smaller than Y(e.g., Y=Y1∗Y2∗ Y3∗...∗Yn). In addition, these decomposed integers can only be arranged in an ascending order (Y1The Lucas numbers are a series of numbers where the first two Lucas numbers (i.e., at indices 0 and 1) are 2 and 1 (respectively) and the kth Lucas number L_k (where k>1) is L_(k-1) + L_(k-2). Consider the following recursive definition for a function that is supposed to find the nth element of the Lucas numbers. Select the best option that identifies the line of code that prevents this function from running recursively and provides the correct code. Question options: line 5 should be return recursive_function(n-1) + recursive_function(n-2) line 3 should be return [2,1][n-1][n-2] line 3 should be return [2,1][n-1] line 2 should be if n <= 2: line 5 should be return recursive_function(n-1 + n-2) None of these options
- Using Lisp, implement a program that solves the Missionaries and Cannibals problem that uses a DFS( depth first search). The function call should use (mac start(this is the current state of the problem) end(this is the desired state)). So the problem should output sequences of moves to go from the start state to the desired state! For example, the call should be like: Call: (mac '(3 3 l) '(0 0 r)) Output: ((3 3 l) (2 2 r) (3 2 l) (3 0 r) (3 1 l) (1 1 r) (2 2 l) (0 2 r) (0 3 l) (0 1 r) (1 1 l) (0 0 r)) Please make sure this is able to be achieved using GNU Common Lisp!Consider the following recursive function: if b = 0, if 6 > a > 0, a f(b, a) f (b, 2.(a mod b)) otherwise. f(a, b) = Estimate the number of recursive applications required to compute f(a, b).Computer Science 1. Let Σ = {0, 1} be an alphabet.(a) Let w = 101 be a word over Σ. Compute |w|, the length of w.(b) List all of the words in Σ32. Let {a, b, c} be an alphabet. List all of the words in Σ23. Let Σ = {a, b} be an alphabet and let · denote concatenation. Compute (ba · ε) · abb,where ε is the empty word.4. Let Σ = {0, 1} be an alphabet and let L ⊆ {0, 1} ∗ be the language defined as L = {w ∈ {0, 1} ∗ |w = x10y, x, y ∈ {0, 1}∗}. (a) Determine whether 01 ∈ L.(b) Determine whether 0101 ∈ L. 5. Let Σ = {0, 1} be an alphabet and let L ⊆ Σ ∗ be the language consisting of all wordsover Σ that contain the substring 10. Construct a DFA that accepts L. Thank you in advance
- Using Lisp, implement a program that solves the Missionaries and Cannibals problem that uses a DFS( depth first search). The function call should use (mac start(this is the current state of the problem) end(this is the desired state)). So the problem should output sequences of moves to go from the start state to the desired state! For example, the call should be like: Call: (mac '(3 3 l) '(0 0 r)) Output: ((3 3 L) (2 2 R) (3 2 L) (3 0 R) (3 1 L) (1 1 R) (2 2 L) (0 2 R) (0 3 L) (0 1 R) (1 1 L) (0 0 R))Write an iterative function that determines the number of even elements in an array a of integers of size n. The function should return the number of elements that are even in array a of size n. Propose an appropriate prototype for your function and then write its code. Write a recursive function to solve the above problem. Propose an appropriate prototype for your function and then write its code.Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, then the pattern generated is: **** *** ** * ** *** ****