//This program is intended to demonstrate simple serial programming where a vectors element gets modified serially. 
//
#include <iostream>
#include <vector>
#include <cmath>

using std::cout;
using std::endl;
using std::vector;

void increase_magnitude(float *starting_address,unsigned int size_vec, float mag_multiplyer)
{
  //the variable *starting_address is a pointer which will point to (or contain address of), the first element of the array.
  for (int i=0;i<size_vec;i++)
  {
    //let us multiply the whole vector by 2
    //since we have address of first element of vector, we can take its value by use of *
    *starting_address=*starting_address * 2;
    //now we shall increase its address by 1.
    starting_address+=1;

  }

  //in this way at the same memory location we will have modified the vector.

}

float magnitude_finder(float *starting_address_vec,unsigned int size)
{
  //This function will return the magnitude of the vector. 
  float sum=0.0;
  for (int i=0;i<size;i++)
  {
    sum+=pow((*starting_address_vec),2);
  }
 return pow(sum,0.5); 
}


int main(int argc, char *argv[])
{
  unsigned int N=1<<31; //the number implies 31 zeroes in front of 1. So it is 2^31.
  vector<float> vec(N); //whenever we declare an vector, it has undefined size(if we don't provide the size). Unless we declare it with some size. 
  //declaring vector of finite size; vector<int> v(100);
  /* vector<int>v1(100); */
  //declaring vector without size; vector<int> vec;

  //let us define a pointer to integer vector
  //let us fill the vector with N natural numbers(1,2,.......N).
  cout<<N<<endl;

  for (int i=0;i<N;i++)
  {
      vec[i]=i;
  }

  float *ptr_to_vec=&vec[0]; //giving address of first element. Or we can just write: 

  //we shall modify the vector by multiply it with some real number. 
  //Real numbers are stored in float data types(require 4byte per real number) and double data types(8bytes).
  float multiplier=4.0;

  //Let us find the magnitude before changing the vector, 
  float mag_before=magnitude_finder(ptr_to_vec,N);
  increase_magnitude(ptr_to_vec,N,multiplier);
  float mag_after=magnitude_finder(ptr_to_vec,N);
  float ratio_of_magnitudes=mag_after/mag_before;
  cout<<"the final vector has magnitude "<<ratio_of_magnitudes<<" times the earlier one"<<endl<<"which should be equal to "<<pow(multiplier,0.5)<<endl;
  return 0;
}

```
Output:

2147483648
the final vector has magnitude -nan times the earlier one
which should be equal to 2

```

Remarks: The magnitude can't handle large numbers in float data type, one must use double or long double.