Some object is moving along a path in the plane. At n+1 points of time we have recorded the corresponding (x,y) positions of the object: (x0,y0), (x1,y1), ..., (xn,yn). The total length L of the path from (x0,y0) to (xn,yn) is the sum of all the individual line segments ((xi−1,yi−1) to (xi,yi), i=1,...,n): L=∑i=1n(xi−xi−1)2+(yi−yi−1)2−−−−−−−−−−−−−−−−−−−−−√. Write a function pathlength( x,y ) for computing L according to the formula. The arguments x and y hold all the x0,...,xn and y0,...,yn coordinates, respectively. (You may assume x and y are lists of the same length.) (This assignment is based on Langtangen, Exercise 3.17a.)

a) # include <iostream>

# include <conio.h>

# include <stdio.h>

# include <string.h>

using namespace::std;

bool IsPalindrome(const string& str)

{

   if (str.empty())

       return false;

   int i = 0;                // first characters

   int j = str.length() - 1; // last character

   while (i < j)

   {

       if (str[i] != str[j])

       {

           return false;

       }

       i++;

       j--;

   }

   return true;

}

int main()

{      

      string str;

      cout<<"Enter the string";

      getline(cin, str);

      bool a= IsPalindrome(str);

      if(a)

      {

          cout<<"Is in palindrome";

      }

      else

      {

          cout<<"Is not in palindrome";

      }

}

b) Modified version of function with full program to discard uppercase or lowercase is as below:

# include <iostream>

# include <conio.h>

# include <stdio.h>

# include <string.h>

using namespace::std;

bool IsPalindrome(const string& str)

{

   if (str.empty())

       return false;

   int i = 0;                // first characters

   int j = str.length() - 1; // last character

   while (i < j)

   {

       char a= tolower(str[i]);

       char b= tolower(str[j]);

       if (a != b)

       {

           return false;

       }

       i++;

       j--;

   }

   return true;

}

int main()

{      

      string str;

      cout<<"Enter the string";

      getline(cin, str);

      bool a= IsPalindrome(str);

      if(a)

      {

          cout<<"Is in palindrome";

      }

      else

      {

          cout<<"Is not in palindrome";

      }

}

Explanation:

Please check the answer section.