Question

Write functions for each of the following problems. Each problem should be solved by
writing a recursive function. Your final program should not have any loops in it.

(a) Write a function that uses recursion to raise a number to a power. The function should
take two arguments, the number to be raised to the power (floating point) and the
power (a non-negative int). (10
Points)
(b) Write a boolean function named isMember that takes two arguments: an array of type
char and a value. It should return true if the value is found in the array, or false if the
value is not found in the array. (10 Points)

(c) A palindrome is any word, phrase, or sentence that reads the same forwards or
backwards. Here are some palindromes:
Level
Civic
Pot top
A man a plan a canal Panama

note:your final programme must not have any loops, do it with recursion, the language must be c++, and kindly explain it in simple words in the form of comments before each part

Answer 1

To be as simple as possible we are designing functions sensitive to the input.

for example:

• power function does not handle the case if input is negative.
• isPalindrome function must provide length to avoid null character '\0' and also case sensitive and doesn't handle the case of whitespaces.

#include <iostream>

using std::cout;

float power(float a, int n){
  float temp;                 //to hold intermidiate results
  if(n == 0) return 1;        // base case

  temp = power(a, n/2);

  if(n % 2 == 0)              // if power is even
    return temp * temp;
  else{                       // if power is odd
    if(n > 0)
      return a * temp * temp;
    else
      return (temp * temp) / a;
  }

}

bool isMember(char a[], char val, int i, int l){
  if (i == l)                 // array is traversed completely
    return false;
  if (a[i] == val)            // element to be search is found at index i
    return true;
  return isMember(a, val, i + 1, l); // recursively search in remaining array
}

bool isPalindrome(char a[], int i, int l){

    if (i == l)                 // base case: If only one character is there
    return true;

    if (a[i] != a[l])           // if first and last characters do not match
    return false;               // string cannot be a palindrome

    if (i < l + 1)              // recursively check if middle array is palindrome
    return isPalindrome(a, i + 1, l - 1);

    return true;
}

int main(){
  float a = 2.5;
  int n = 3;

  char arr[] = {'h','e','l','l','o', '\0'};
  char pal[] = {'p','o','t','t','o','p','\0'};
  int p = sizeof(pal) / sizeof(pal[0]);
  int l = sizeof(arr) / sizeof(arr[0]);

  cout << power(a, n) << std::endl;

  cout << isMember(arr, 'i', 0, l) << std::endl;

  cout << isPalindrome(pal, 0, p - 2);

  return 0;
}