C# Coding Test Course, Finding the Sum of Consecutive Natural Numbers

1. Problem Description

Your task is to solve the problem of “Finding the Sum of Consecutive Natural Numbers”. This problem requires finding the number of ways to sum consecutive natural numbers to reach a given number N. In other words, find the number of cases where N can be expressed as a sum of two or more consecutive natural numbers.

2. Problem Examples

Example Input 1

N = 9

Example Output 1

3

Explanation: 9 can be expressed as (4+5), (2+3+4), (1+2+3+4).

Example Input 2

N = 15

Example Output 2

4

Explanation: 15 can be expressed as (7+8), (4+5+6), (1+2+3+4+5), (1+2+3+4+5+6).

3. Approach

To solve the problem, we can use the following approach. First, we need to determine the range of possible starting values for the sum of consecutive natural numbers. Let the starting value be start. If this value exceeds N, the sum will always be less than N, thus going beyond the range.
Additionally, when there are k consecutive natural numbers, their sum can be expressed as follows: 

sum = start + (start + 1) + (start + 2) + ... + (start + (k - 1))

By simplifying the above equation:

sum = k * start + (0 + 1 + 2 + ... + (k - 1)) = k * start + (k * (k - 1)) / 2

Therefore, we can derive the start value using this equation. This will help identify all possible consecutive cases for the natural number N.

4. Algorithm Implementation

Here is the code implemented in C#:


using System;

class Program
{
    static void Main()
    {
        int N = 9; // Example input
        int count = 0;

        for (int k = 2; k <= N; k++) // k represents the number of consecutive natural numbers
        {
            // start is (N - k * (k - 1) / 2) / k
            int start_sum = N - (k * (k - 1)) / 2;
            if (start_sum > 0 && start_sum % k == 0)
            {
                count++;
            }
        }

        Console.WriteLine(count); // Example output
    }
}

The above code implements a method to find the sum of two or more consecutive natural numbers for the given number N. The variable k indicates the number of consecutive natural numbers, and calculations are performed to check the starting point. The count increases if the starting point is positive and divisible by k.

5. Time Complexity Analysis

The time complexity of the above algorithm is O(N). Considering that the value of k loops from 2 to N, it increases linearly, resulting in a complexity proportional to N. This specific problem can be calculated relatively quickly even when the size of the input value N increases.

6. Conclusion

The problem of finding the sum of consecutive natural numbers is a common question in coding tests, requiring basic mathematical approaches along with programming thinking. To enhance problem-solving skills, you can input various values of N and check the resulting outputs to improve understanding.
By solving the problem of finding the sum of consecutive natural numbers, you can enhance your basic syntax skills in C# and improve your problem-solving abilities for real coding tests.

7. Additional Practice Problems

If you want more practice after solving this problem, try the following challenges.

  • Given N, find the sum of all natural numbers less than N.
  • Given two natural numbers A and B, find the sum of natural numbers from A to B.
  • Given the number of consecutive natural numbers, and the sum S of these consecutive numbers, find all possible combinations of A (the starting number).