JavaScript Coding Test Course, Finding the Sum of Consecutive Natural Numbers

Problem Description

The problem of finding the sum of consecutive natural numbers is one of the representative types of algorithm problems. Given a number N, what we want to find out is the number of combinations of consecutive natural numbers that can form the number N. In other words, this problem is about determining whether N can be expressed as the sum of multiple consecutive natural numbers.

Problem Definition

The problem can be summarized in the following format:

        Input:
        - Integer N (1 ≤ N ≤ 10^6)

        Output:
        - The number of ways to express N as the sum of consecutive natural numbers
    

Examples

Example 1

        Input: 15
        Output: 4
        Explanation: 15 can be expressed in the following ways:
        - 7 + 8
        - 4 + 5 + 6
        - 1 + 2 + 3 + 4 + 5
        - 15 (as the integer itself)
    

Example 2

        Input: 10
        Output: 2
        Explanation: 10 can be expressed in the following ways:
        - 1 + 2 + 3 + 4
        - 4 + 6
    

Problem Solution

To find the sum of consecutive natural numbers, a specific methodology is needed. Basically, the sum of two consecutive natural numbers follows a mathematical formula:

The sum of several numbers a, a+1, a+2, …, a+k can be expressed as:

        S = a + (a + 1) + (a + 2) + ... + (a + k)
          = (k + 1) * a + (0 + 1 + 2 + ... + k)
          = (k + 1) * a + (k * (k + 1) / 2)
    

At this point, S must equal N. Based on this, we can design an algorithm.

Algorithm Design

This problem can be efficiently approached using a sliding window algorithm with two pointers. The proposed method is as follows:

1. Set up a start pointer and an end pointer, both initialized to 1.
2. Initialize the current sum.
3. Move the end pointer to the right while adding the value of the end pointer to the sum.
4. If the current sum is less than N, continue moving the end pointer.
5. If the current sum equals N, increment the count of combinations and move the start pointer to the right to reduce the sum.
6. If the current sum is greater than N, move the start pointer to the right to reduce the sum.
7. Repeat until the end pointer is less than or equal to N.

Python Code Implementation

Now, let’s implement the algorithm described above in Python. Although the syntax differs from JavaScript, it will help in understanding the logic.

        
def count_consecutive_sum(N):
    count = 0
    start = 1
    end = 1
    current_sum = 0

    while end <= N:
        current_sum += end

        while current_sum > N:
            current_sum -= start
            start += 1

        if current_sum == N:
            count += 1

        end += 1

    return count
        
    

JavaScript Code Implementation

Now, let’s implement the same algorithm in JavaScript.

        
function countConsecutiveSum(N) {
    let count = 0;
    let start = 1;
    let end = 1;
    let currentSum = 0;

    while (end <= N) {
        currentSum += end;

        while (currentSum > N) {
            currentSum -= start;
            start++;
        }

        if (currentSum === N) {
            count++;
        }

        end++;
    }

    return count;
}
        
    

Conclusion

The problem of finding the sum of consecutive natural numbers is one of the basic algorithm problems, and can be effectively solved using mathematical approaches alongside the sliding window technique. This technique is a common topic in coding interviews, so being familiar with it will be beneficial.

References

Additional resources for studying algorithms include the following:

• Geeks for Geeks
• LeetCode
• HackerRank