We can define an alphabet as a set of characters to be used in creating strings. Let A = {a,b} be an alphabet. We define A* to be all strings of length 0 or more made up only of letters in the alphabet A. (The length of a string is the number of characters in it.) (a) Write a recursive definition for A*. (b) Write a recursive definition for A* -A, i.e. all strings of length 1 or more that can be made with the letters in A.
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- Write a recursive function to print all the permutations of a string. For example, for the string abc, the printout is:abcacbbacbcacabcba(Hint: Define the following two functions. The second function is a helper function.def displayPermuation(s):def displayPermuationHelper(s1, s2): The first function simply invokes displayPermuation(" ", s). The secondfunction uses a loop to move a character from s2 to s1 and recursively invokes t with a new s1 and s2. The base case is that s2 is empty and prints s1 to the console.)Write a test program that prompts the user to enter a string and displays all its permutations.CodeW For fun X C Solved https://codeworkou... 臺亂 CodeWorkout X272: Recursion Programming Exercise: Is Reverse For function isReverse, write the two missing base case conditions. Given two strings, this function returns true if the two strings are identical, but are in reverse order. Otherwise it returns false. For example, if the inputs are "tac" and "cat", then the function should return true. Examples: isReverse("tac", "cat") -> true Your Answer: 1 public boolean isReverse(String s1, String s2) { 2. if > 3. 4. else if > return true; return false; 5. 6. else { String s1first = String s2last return s1first.equals (s2last) && 51. substring(0, 1); s2, substring(s2.length() 1); 7. 8. 6. isReverse(s1.substring(1), s2.substring(0, s2.length() 1)); { 12} 1:11AM 50°F Clear 12/4/2021Exercise 1: The number of combinations CR represents the number of subsets of cardi- nal p of a set of cardinal n. It is defined by C = 1 if p = 0 or if p = n, and by C = C+ C in the general case. An interesting property to nxC calculate the combinations is: C : Write the recursive function to solve this problem.
- This problem considers strings that can be made from the alphabetA= {‘a’, ‘b’, ‘c’}.a. Write a recursive definition for the set of strings that have at least one 'a' character.b. Write a recursive definition for the set of strings that do not start with the letter 'a'.Recursive Palindrome! Recall that a palindrome is a string that reads the same forward and backward. Write a recursive function is_palindrome (s:str) -> bool to check whether a string s is a palindrome. Here's a hint: think about how you can use is_palindrome(t), where t is a substring of s, to help you decide whether s is a palindrome. Your Answer: 1 # Put your answer here 2 SubmitFor function decToBinary, write the missing parts of the recursion case. This function should return a string that stores the binary equivalent for int variable num. Example: The binary equivalent of 13 may be found by repeatedly dividing 13 by 2. So, 13 in base 2 is represented by the string "1101". Examples: decToBinary(13) -> "1101" public String decToBinary (int num) { if (num < 2) return Integer.toString(num); else return <<Missing recursive call>> + <<Missing calculation>>;}
- A palindrome is a string that’s spelled the same way forward and backward. Examples of palindromes include “radar” and “able was i ere i saw elba.” Write a recursive function testPalindrome that returns true if a string is a palindrome, and false otherwise. Note that like an array , the square brackets ( [] ) operator can be used to iteratethrough the characters in a string .A palindrome is any word, phrase, or sentence that reads the same forward and backward. Here are some well-known palindromes:Able was I, ere I saw ElbaA man, a plan, a canal, PanamaDesserts, I stressedKayakWrite a bool function that uses recursion to determine if a string argument is a palindrome. The function should return true if the argument reads the same forward andbackward. Demonstrate the function in a program.3. A palindrome is a sentence that contains the same sequence of letters read-ing it either forwards or backwards. A classic example is "Able was I, ere I saw Elba." Write a recursive function that detects whether a string is a palindrome. The basic idea is to check that the first and last letters of the string are the same letter; if they are, then the entire string is a palindrome if everything between those letters is a palindrome. There are a couple of special cases to check for. If either the first or last character of the string is not a letter, you can check to see if the rest of the string is a palindrome with that character removed. Also, when you compare letters, make sure that you do it in a case-insensitive way. Use your function in a program that prompts a user for a phrase and then tells whether or not it is a palindrome. Here's another classic for testing: "A man, a plan, a canal, Panama!"
- Python Question QUESTION 1 Recursively count the occurrences of a substring. Implement a function that counts the number of times a target string occurs in the main string. In particular, provide the implementation for count(s, target), where 's' is the main string and 'target' is the substring you wish to count. Note that 'target' is not just a single character, but a substring of any length greater than zero (length guaranteed to be positive). Some of the sample cases include, but are not limited to, the following. Input: s= 'aaabbb', target = 'aa' Output: 2 Input: s= 'bbaaa', target = 'c' Output: 0 Input: s= 'abcbc', target='bcb' Output: 1 Input: s = 'aab', target='bbbb' Output: 0 Here are the constraints: • You mustn't use any of the string methods provided by Python. (Indexing is okay) • You must use recursion. • Write a paragraph detailing the base and recursive cases. Your answer should also include the *why* and *how*.a) Give a recursive definition for the set of all strings of a’s and b’s where n a’s followed by n b’s (where n= 0, 1, 2, 3, ...). (Assume, S is set of all strings of a’s and b’s. Then S = {λ, ab, aabb, aaabbb, ... ) b) Give a recursive definition for the set of all strings of 'a' 's and 'b' 's that ends with an 'ab'. (Assume, S is set of all strings of a’s and b’s. Then S = {ab, aab, bab, abab, baab, aaab, bbab, ... ).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.