LeetCode 829: Consecutive Numbers Sum Solution

Master LeetCode problem 829 (Consecutive Numbers Sum), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

829. Consecutive Numbers Sum

Hard

Math Enumeration

Problem Explanation

Explanation

To solve this problem, we can iterate through all possible lengths of consecutive numbers starting from 1. For each length, we calculate the sum of the sequence using the formula (length * (length + 1)) / 2. If this sum is divisible by n, then it means there is a valid solution. We can calculate the starting number of the sequence using the formula (n - sum) / length + 1.

Algorithm:

Initialize a variable count to 0 to store the number of ways.
Iterate length from 1 to n and for each length:
- Calculate the sum of the sequence using the formula (length * (length + 1)) / 2.
- Calculate the starting number of the sequence using the formula (n - sum) / length + 1.
- If the starting number is a positive integer, increment count.
Return count.

Time Complexity: O(n) Space Complexity: O(1)

Solution Code

class Solution {
    public int consecutiveNumbersSum(int n) {
        int count = 0;
        
        for (int length = 1; length <= n; length++) {
            double sum = (length * (length + 1)) / 2.0;
            int start = (int)((n - sum) / length) + 1;
            
            if (start > 0 && sum == n) {
                count++;
            }
        }
        
        return count;
    }
}

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