# 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

```java
```