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g0701_0800.s0775_global_and_local_inversions.readme.md Maven / Gradle / Ivy

775\. Global and Local Inversions

Medium

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]`.