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2485. Find the Pivot Integer

Difficulty Topics

Description

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

Solution

find-the-pivot-integer.py
class Solution:
    def pivotInteger(self, n: int) -> int:
        prefix = [0]
        for x in range(1, n + 1):
            prefix.append(prefix[-1] + x)

        for i in range(1, n + 1):
            if prefix[i - 1] == prefix[-1] - prefix[i]:
                return i

        return -1