#include<iostream> 
using namespace std;

int GetTotal(int n);

void main() 
{ 
	int  num;

	cout<<"We will calculate the total of \n"
	    <<"the consecutive numbers,\n"
	    <<"starting from 1 to the number\n"
	    <<"that you enter."<<endl;
	cout<<"\n\nEnter the ending number."<<endl;
	cin>>num;

	cout<<"\n\nThe sum of 1, 2, ..., "<<num <<" is "
	    <<GetTotal(num)<<endl<<endl;
}

int GetTotal(int n)
{

  //??????????? 
//Design your own method to calculate the total from 1 to n.

}

Method One: Accumulation Way

int GetTotal(int n)
{
	int sum=0;				// one action

	for(int i=1; i<=n; i++)		// one action for initializing, n+1 actions for comparisons, n actions for increment
		sum = sum + i;		// one action for addition, another action for assignment.  Repeat them n times

	return sum;				// one action
}

// Total time = 1+(1+n+1+n)+n*2+1 = 4n+4 = O(n)

Method Two: Using Mathematical Formulas

int GetTotal(int n)
{
	int sum;

	sum = (1 + n) * n / 2; 	//one action for each operator, +,*, /.  another action for assignment.

	return sum;			// one action
}

// Total time = (3 + 1) + 1 = 4 = O(c)