Question

1- Write algorithm (in pseudo-code) for the following problem:

sum of the series: 1 +2+3+…+N

2- Convert an algorithm to a flowchart diagram.

3- Counting the primitive operations of the algorithm.

4- Determine algorithm complexity.

5- Write a complete C++ program for the previous algorithm where the program should contain the following:

 Display messages.  Input any number;  Display the series.  Display the sum of the series.

Answer 1

1. Algorithm()

1 Taking user Input = n

2 Initialize : sum = 0

3 for i = 1 to n do

4 sum =sum + i

5 return sum

2.Flowchart

3.Primitive Operation

Primitive operations are basic computations within an algorithm. evaluating an expression, assigning a value to a variable,calling a method, returning from a method , all these are the examples of primitive operations.

for taking user Input we are assuming that , It takes 1 primitive operation.

Algorithm ()	Number of primitive operations:
1 Taking user Input = n 2 Initialize : sum = 0 3 for i = 1 to n do 4 sum =sum + i 5 return sum	1 ( let) 1 2n 4n (including increment counter) 1

  total primitive Operation: 1+ 1+ 2n +4n + 1 = 6n +3

4.Complexity

Algorithm ()	complexity:
1 Taking user Input = n 2 Initialize : sum = 0 3 for i = 1 to n do 4 sum =sum + i 5 return sum	O(1) O(1) O(n) O(1) O(1)

Total time complexity = O(1) +O(1) + {O(n) *O(1) } + O(1) = O(n)

5. C++ program :

#include <iostream>

using namespace std;
int main()
{
int n, sum = 0;
// taking user input
cout << "Enter the input : ";
cin >> n;
//Displaying the series
cout << "Series :";
for (int i = 1; i <= n; ++i) {
cout << i<<" " ;
}
//calculating sum of the series using for loop
for (int i = 1; i <= n; ++i) {
sum += i;
}
//Displaying the sum
cout << "\nSum of the Series = " << sum;
return 0;
}

Output: