Question

TITLE

RECURSIVE FUNCTIONS - THREE SMALL PROGRAMS in C++

INTRODUCTION

Recursion is a programming technique in which a function calls itself. It is another way of implementing repetitive computations, which we have previously associated with loops. When called to solve a problem, a recursive function passes a smaller version (or versions) of the problem to another instance (or instances) of itself, then uses the results returned by the recursive call or calls to build or complete a solution to the original problem.

DESCRIPTION

Design, implement, and document recursive functions to solve the three problems described below; test those functions by calling them from appropriate main functions; and document the resulting programs and their functions. Note that you will write three small programs.

Keep in mind the questions that arise in designing recursive algorithms:

• What is/are smaller but identical problem(s)?
• How will the smaller solution(s) be used to solve the larger problem?
• What is/are the base case(s)?

EXPONENTIATION

Write and exercise a recursive function exp(x,n) that returns the value of the double x raised to the non-negative integer power n. A run of a program that exercises this function might look like this:

          Enter a real value: 2.4
          Enter an integer: 3
          2.4^3 = 13.824
        

Remember that any non-zero value raised to the power 0 is 1.

DETERMINE IF A VALUE IS PRESENT IN AN ARRAY

Implement and test a recursive function present(a,n,k) that returns TRUE if the value k is present in the array a[0..n-1], FALSE if it is not. Read values from a file into the array. Read values to test from the terminal. Terminate the program with an input of 0.

If the values read into the array are [14, 66, 34, 51, 44, 16, 29, 33], then a run of the program might look like this:

        Data file name -> vals.dat
        Test value -> 51
            Present
        Test value -> 63
            Not present
        Test value -> 29
            Present
        Test value -> 0
          

IDENTIFY PALINDROMES

As we saw in Project 1, a palindrome is a string in which the letters read the same in both directions, disregarding non-letters and capitalization. For example, "Eva, can I see bees in a cave?" is this kind of palindrome.

This time, solve the problem of the previous project with a recursive function, say pal(a,low,high). This function will return a boolean value. Note that you can re-use the rest of your program from the first project.

HINT: Count the letters as they are read in.

HINT: Use an array of characters rather than the string type.

Answer 1

Hi,

Note: I've written all functions in one program. U can copy the code separately for each functionality, there is no dependency of variable.

exp(double x,unsigned int n) : recursively calculates the x^n.

1. n is even then x^(n/2) * x^(n/2) will be calculated

2. n is odd the x * x^(n/2) * x^(n/2) will be calculated.

int findElement(int arr[] , int start , int end , int value): Recursively check each index for value in arr.

bool pal(char arr[] , int start , int end) : stored all characters from given input(ignored spaces . , etc). Recursively compared arr[start] == arr[end] if matching called pal function otherwise returned false.

C++ code:

//Program starts here

#include <iostream>
#include<bits/stdc++.h>
#include <fstream>
#include<stdio.h>
#include <stdlib.h>
using namespace std;

double exp(double x,unsigned int n){
if (n == 0)
return 1;
else if (n % 2 == 0) //if n is even number
return exp(x, n / 2) * exp(x, n / 2);
else
return x * exp(x, n / 2) * exp(x, n / 2); //if n is odd number
}

int findElement(int arr[] , int start , int end , int value){
if(start == end)//end of array, no element found
return 0;
if(arr[start] == value)//if value equals to current index(start) value and given value
return 1;
//else search from the next index.
return findElement(arr, start+1 , end , value);//start incremented
}

bool pal(char arr[] , int start , int end){
if(start == end){//incase of odd size
return true;
}
else if (start > end)//both indexes crosses each other, in case of even size
return true;
if(arr[start] != arr[end])
return false;
return pal(arr,start+1 , end-1);//end and start index charatcers compared.
}

int main() {
  
//Power of x^n
double x ;
unsigned int n;//n is non-negative number.
cout << "Enter x:";
cin >> x;
cout << "Enter n:";
cin >> n;
cout << x << "^" << n<<" = " <<exp(x,n) << endl;//recursive function

//array element search
cout << "enter file name:";
string s;
cin >> s;
ifstream file(s.c_str());//ifstream constructor accepts a const char* as the filename, otherwise we can use ifstream file(s)
string line;
getline(file,line);//Input give as one line only
stringstream ss(line);
int num=0;
int arr[100];
int i = 0;
while(ss >> num){//reading one by one number using string stream.
arr[i] = num;
cout << arr[i] << " ";
i++;
}
cout << endl;
int test;
while(1){
cout << "Test value --> ";
cin >> test;
if(test == 0)//test value = 0, terminates program
break;
if(findElement(arr,0 , i , test))
cout << "Present" << endl;
else
cout << "Not present" << endl;
}

//Palindrome.
string word;
cin.ignore();//to ignore new line
getline(cin,word);//will read the line from input
// cout << word;
char characters[1000];//Only storing characters from words ignoring . , space etc...
int j = 0;//for characters count
for(int i = 0; i < word.length(); i++){
if((word[i] >= 'A' && word[i] <= 'Z') ||(word[i] >= 'a' && word[i] <= 'z'))
characters[j++] = tolower(word[i]);//storing only characters and all characters converted to lower case.
}

if(pal(characters , 0 , j-1)){
cout << "palindrome" << endl;
}
else{
cout << "Not a palindrome" << endl;
}

}

//End of the program