C++ Coding Test Course, Finding the Sum of Numbers

Problem Definition

Write a program to calculate the sum of the integers from 1 to a given natural number N.

For example, if N is 5, the output should be 15, which is the result of 1 + 2 + 3 + 4 + 5.

Input and Output

Input

A single integer N (1 ≤ N ≤ 100,000) is given.

Output

The sum of the integers up to N is printed in one line.

Problem-Solving Process

Step 1: Understanding the Algorithm

To find the sum of numbers, you can generally use a loop, adding each number while iterating up to the given natural number N. However, using a mathematical formula can provide a more efficient solution.

Step 2: Mathematical Approach

The formula for the sum from 1 to N is as follows:

Sum = N * (N + 1) / 2

Using this formula, we can solve the problem with O(1) time complexity. The space complexity also remains O(1).

Step 3: Implementing C++ Code

Now let’s move on to the implementation step. Below is the C++ code to solve the problem.

#include <iostream>
using namespace std;

int main() {
    int N;
    cout << "Please enter the value of N: ";
    cin >> N;

    // Sum calculation using the formula
    long long sum = static_cast(N) * (N + 1) / 2;
    
    cout << "The sum of integers from 1 to " << N << " is: " << sum << "." << endl;

    return 0;
}

        

Step 4: Example Input and Output

After carefully reviewing the code, let’s check if the results are correct with a few examples.

Example 1:

Input: 5

Output: The sum of integers from 1 to 5 is: 15.

Example 2:

Input: 10

Output: The sum of integers from 1 to 10 is: 55.

Example 3:

Input: 100

Output: The sum of integers from 1 to 100 is: 5050.

Optimization Strategies

This problem has been solved using a mathematical formula with O(1), so no further optimization is necessary. However, if the range of input data is reduced, using loops to calculate the sum may become inefficient.

For example, if N is very large, using a loop can take a long time and may result in a timeout error. The mathematical formula is especially useful in resolving such issues.

Anticipated Questions and Answers

Q1: What if N is negative?

A1: The conditions for this problem restrict N to be a natural number greater than or equal to 1, so negative input will not be provided. It’s advisable to thoroughly check the input range.

Q2: Can this be implemented in languages other than C++?

A2: Yes, the algorithm for calculating the sum of numbers can be similarly applied in other programming languages. However, the code needs to be adjusted to fit the syntax of each language.

Q3: Are there no variations of this problem?

A3: This problem is a basic sum problem. If you want a variation, you could consider problems that sum only even or odd numbers, for example.