Is Find the Pivot Integer easy or hard?

The problem is rated Easy because the constraints are small and the logic is straightforward. The main challenge is recognizing that the equality of two ranges leads to the equation x² = n(n+1)/2, which immediately gives the pivot in constant time.

Find the Pivot Integer Python/Java solution

Most implementations compute the total sum n(n+1)/2 and check whether its square root is an integer. Python uses math.sqrt or integer checks, while Java typically uses Math.sqrt and verifies that the square of the result equals the sum.

How to solve Find the Pivot Integer in O(1)?

Compute the total sum S = n(n+1)/2 using the arithmetic series formula. If an integer x exists such that x² = S, then x is the pivot integer. Check whether sqrt(S) is an integer and return it; otherwise return -1.

What is the best approach for Find the Pivot Integer?

The optimal approach uses an arithmetic formula derived from the sum of the first n integers. If S = n(n+1)/2 is the total sum, the pivot must satisfy x² = S. Compute S and check whether its square root is an integer. This gives an O(1) time and O(1) space solution.

Is Find the Pivot Integer asked at Google/Amazon/Meta?

The exact problem may appear less frequently, but the underlying pattern—using arithmetic series and prefix sum reasoning—is common in coding interviews at companies like Google, Amazon, and Meta. Interviewers often test whether candidates can derive mathematical shortcuts from cumulative sum conditions.

What data structure is used in Find the Pivot Integer?

No special data structure is required. The problem relies on mathematical properties of arithmetic series and the concept behind prefix sums. The optimized solution uses simple integer arithmetic and a square root check.

What is the time complexity of Find the Pivot Integer?

The brute force method runs in O(n^2) time because it recomputes sums for each candidate pivot. The optimized arithmetic solution runs in O(1) time since it only calculates n(n+1)/2 and checks whether the result is a perfect square.

Description Hints 2 Solution Video 27:25

2485. Find the Pivot Integer

Easy83.8% acceptance3 companies

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

Asked at 3 companies

Amazon

Google Meta

Topics

Math Prefix Sum

Hints open one at a time

Hint 1

Can you use brute force to check every number from 1 to n if any of them is the pivot integer?

Hint 2

If you know the sum of [1: pivot], how can you efficiently calculate the sum of the other parts?

27:25

Still stuck?Read 4 approaches, or watch a walkthrough.

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