0775. Global and Local Inversions

https://leetcode.com/problems/global-and-local-inversions

Description

You are given an integer array nums of length n which represents a permutation of all the integers in the range [0, n - 1].

The number of global inversions is the number of the different pairs (i, j) where:

• 0 <= i < j < n

• nums[i] > nums[j]

The number of local inversions is the number of indices i where:

• 0 <= i < n - 1

• nums[i] > nums[i + 1]

Return true if the number of global inversions is equal to the number of local inversions.

Example 1:

**Input:** nums = [1,0,2]
**Output:** true
**Explanation:** There is 1 global inversion and 1 local inversion.

Example 2:

**Input:** nums = [1,2,0]
**Output:** false
**Explanation:** There are 2 global inversions and 1 local inversion.

Constraints:

• n == nums.length

• 1 <= n <= 105

• 0 <= nums[i] < n

• All the integers of nums are unique.

• nums is a permutation of all the numbers in the range [0, n - 1].

ac