# Solving Leetcode Interviews in Seconds with AI: Find the Pivot Integer


	# Introduction
	In this blog post, we will explore how to solve the LeetCode problem "2485" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like [Chatmagic](https://www.chatmagic.app), we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

	# Problem Statement
	> Given a positive integer n, find the pivot integer x such that:  The sum of all elements between 1 and x inclusively equals the sum of all elements between x and n inclusively.  Return the pivot integer x. If no such integer exists, return -1. It is guaranteed that there will be at most one pivot index for the given input.   Example 1:  Input: n = 8 Output: 6 Explanation: 6 is the pivot integer since: 1 + 2 + 3 + 4 + 5 + 6 = 6 + 7 + 8 = 21.  Example 2:  Input: n = 1 Output: 1 Explanation: 1 is the pivot integer since: 1 = 1.  Example 3:  Input: n = 4 Output: -1 Explanation: It can be proved that no such integer exist.    Constraints:  1 <= n <= 1000  

	# Explanation
	Here's an efficient solution to find the pivot integer:

*   **Mathematical Approach:**  Instead of iterating and calculating sums repeatedly, we can use the formula for the sum of an arithmetic series. The sum of numbers from 1 to `x` is `x * (x + 1) / 2`, and the sum from 1 to `n` is `n * (n + 1) / 2`.  The sum from `x` to `n` can then be calculated as the difference between the sum from 1 to `n` and the sum from 1 to `x-1`.  We're looking for an `x` where sum(1 to x) = sum(x to n).
*   **Iterative Search:** Iterate through possible values of `x` from 1 to `n`. For each `x`, calculate the sum from 1 to `x` using the formula.  Then, calculate the sum from `x` to `n` also using the formula and compare.
*   **Early Exit:** As the problem states that there will be at most one pivot, we can immediately return once we find it.

*   **Runtime Complexity:** O(n), **Storage Complexity:** O(1)

	
	# Code
	```python
	def pivotInteger(n: int) -> int:
    """
    Finds the pivot integer x such that the sum of all elements between 1 and x inclusively
    equals the sum of all elements between x and n inclusively.

    Args:
        n: A positive integer.

    Returns:
        The pivot integer x. If no such integer exists, return -1.
    """

    total_sum = n * (n + 1) // 2

    for x in range(1, n + 1):
        sum_1_to_x = x * (x + 1) // 2
        sum_x_to_n = total_sum - (x - 1) * x // 2

        if sum_1_to_x == sum_x_to_n:
            return x

    return -1
	```