Please help me solve Problem 2 on induction. Problem 2MotivationIn computer science, we often use induction to prove the correctness of a function - that is, we prove formally that the function doeswhat it is supposed to do. This is sometimes called "proving a function." For example, consider the Python function below, whichreverses an input string using recursion.def reverse_string(s):||||||reverse the string s. The first letter becomes the last letter, the second letter becomes the second-args:s, the string to be reversedreturns: the reversed string||||||if s == "":returnelse:return reverse_string(s[1:]) +s[0]Here it is in action.||||reverse_string("CSCI 0200")¹0020 ICSC'We got the right answer for this input! But...would we get the right answer on every possible input? Let's write a proof which willguarantee that we will.0C Problem StatementWe'll write a string with n characters as $₁8283 · Sn-2Sn-1Sn.Now we can state the thing we want to prove:Proposition: For any n E N, the result of calling the function reverse_string on the string $18283of s, that is, the string SnSn-15n-2 ··· S3S2S1.Prove this claim using induction.Note: The empty string € is the string with no elements at all; this string is its own reversal.Sn-2Sn-1Sn is the reversal

Given :-In the above question, a statement along with the code fragment is mentioned

Answered: Python function

Engineering

Computer Science

Python function

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 6PE

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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*.
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 12/4/2021
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.
For 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>>;}
write a recursive function that checks see if the first letter matches the last letter, return the middle letters and check until only 0 or 1 letters are left. It returns True or False. Here is python code that needs to be fixed # Returns the first character of the string str def firstCharacter(str): return str[:1] # Returns the last character of a string str def lastCharacter(str): return str[-1:] # Returns the string that results from removing the first # and last characters from str def middleCharacters(str): return str[1:-1] def isPalindrome(str): # base case #1 # base case #2 # recursive case pass def isPalindrome(string): reversedString = string[::-1] if reversedString == string: return True else: return False inputString = input() string = inputString.replace(" ", "") if isPalindrome(string): print(inputString,"is a palindrome") else: print(inputString,"is not a palindrome") if __name__ ==…
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 .
Given a string str and number n, write a program that recursively appends a copy of string str n times and returns the resulting string. For example: RecuriveCopy("a", 10) // -> "aaaaaaaaaaa" RecursiveCopy("blah", 5) // -> "blahblahblahblahblahblah" For this exercise, complete the following function. n is the number of copies to add to str: function RecursiveCopy(str, n) { // your code here } Part 2: Call RecursiveCopy Write another function that calls RecursiveCopy() and returns the following string output: "The resulting string [x] has [y] characters". [x] should be replaced by the result from RecursiveCopy) and [y] should be replaced by the number of characters in the resulting string. You may pick the arguments to RecursiveCopy in CountChars or have the user provide input. I will leave this up to you. function CountChars() { } // your code here // call RecursiveCopy(..) // returns a formatted string For example: console.log(CountChars()) // -> "The resulting string blahblahblahblah…
A palindrome is a sentence that contains the same sequence of letters reading it either forwards or backwards. A classic example is '1\.ble was I, ereI saw Elba." Write a recursive function that detects whether a string is apalindrome. The basic idea is to check that the first and last letters of thestring are the same letter; if they are, then the entire string is a palindromeif everything between those letters is a palindrome.There are a couple of special cases to check for. If either the first orlast character of the string is not a letter, you can check to see if the restof the string is a palindrome with that character removed. Also, when youcompare 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 andthen tells whether or not it is a palindrome. Here's another classic fortesting: '1\. man, a plan, a canal, Panama!"
Write a recursive function called that takes a string of single names separated by spaces and prints out all possible combinations (permutations), each combination on a new line. When the input is: Alice Bob Charlie then the output is: Alice Bob Charlie Alice Charlie Bob Bob Alice Charlie Bob Charlie Alice Charlie Alice Bob Charlie Bob Alice Here is my original code that needs to be fixed: def all_permutations(permList, nameList): # TODO: Implement method to create and output all permutations of the list of names. if nameList == len(permList) - 1: return nameList else: for x in range(permList, len(nameList)): permList[nameList], permList[x] = permList[x], permList[name_List] return all_permutations(permList, nameList + 1) permList[nameList], permList[x] = permList[x], permList[name_List] if __name__ == "main": nameList = input().split(' ') permList = [] all_permutations(permList, nameList)
c++ A palindrome is a string that reads the same both forward and backward. For example, the string "madam" is a palindrome. Write a program that uses a recursive function to check whether a string is a palindrome. Your program must contain a value-returning recursive function that returns true if the string is a palindrome and false otherwise. Do not use any global variables; use the appropriate parameter.
Fibonacci numbers are a sequence of integers, starting with 1, where the value of each number is the sum of the two previous numbers, e.g. 1, 1, 2, 3, 5, 8, etc. Write a function called fibonacci that takes a parameter, n, which contains an integer value, and have it return the nth Fibonacci number. (There are two ways to do this: one with recursion, and one without.)