LeetCode 829: Consecutive Numbers Sum
LeetCode 829 Solution 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
countto 0 to store the number of ways. - Iterate
lengthfrom 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)
LeetCode 829 Solutions in Java, C++, Python
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;
}
}Interactive Code Editor for LeetCode 829
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