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829. Consecutive Numbers Sum

MathEnumeration

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:

  1. Initialize a variable count to 0 to store the number of ways.
  2. 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.
  3. Return count.

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

View Leetcode Problem
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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