Exercise 2.2

The formula for the Pentagonal numeric sequence is Pn=n*(3n-1)/2. This yields the sequence 1, 5, 12, 22, 35, and so on. Define a function to fill a vector of elements passed in to the function calculated to some user-specified position. Be sure to verify that the position specified is valid. Write a second function that, given a vector, displays its elements. It should take a second parameter identifying the type of numeric series the vector represents. Write a main() function to exercise these functions.

#include <vector> 


#include <string> 


#include <iostream> 


using namespace std; 





bool calc_elements( vector<int> &vec, int pos ); 


void display_elems( vector<int> &vec, 


                    const string &title, ostream &os=cout ); 





int main() 


{ 


    vector<int> pent; 


    const string title( "Pentagonal Numeric Series" ); 





    if ( calc_elements( pent, 0 )) 


         display_elems( pent, title ); 





    if ( calc_elements( pent, 8 )) 


         display_elems( pent, title ); 





    if ( calc_elements( pent, 14 )) 


         display_elems( pent, title ); 





    if ( calc_elements( pent, 138 )) 


         display_elems( pent, title ); 


} 





bool calc_elements( vector<int> &vec, int pos ) 


{ 


   if ( pos <= 0 || pos > 64 ){ 


        cerr << "Sorry. Invalid position: " << pos << endl; 


        return false; 


   } 


   for ( int ix = vec.size()+1; ix <= pos; ++ix ) 


         vec.push_back( (ix*(3*ix-1))/2 ); 





   return true; 


} 





void display_elems( vector<int> &vec, 


                    const string &title, ostream &os ) 


{ 


   os << '\n' << title << "\n\t"; 


   for ( int ix = 0; ix < vec.size(); ++ix ) 


         os << vec[ ix ] << ' '; 


   os << endl; 


} 

When compiled and executed, this program generates the following output:

Sorry. Invalid position: 0 





Pentagonal Numeric Series 


        1 5 12 22 35 51 70 92 





Pentagonal Numeric Series 


        1 5 12 22 35 51 70 92 117 145 176 210 247 287 


Sorry. Invalid position: 138