> For the complete documentation index, see [llms.txt](https://mayanktyagi3111.gitbook.io/interview-prep/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mayanktyagi3111.gitbook.io/interview-prep/strings-arrays-and-2-pointers/global-and-local-inversions.md).

# Global and Local Inversions

We have some permutation `A` of `[0, 1, ..., N - 1]`, where `N` is the length of `A`.

The number of (global) inversions is the number of `i < j` with `0 <= i < j < N` and `A[i] > A[j]`.

The number of local inversions is the number of `i` with `0 <= i < N` and `A[i] > A[i+1]`.

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

**Example 1:**

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

**Example 2:**

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

**Note:**

* `A` will be a permutation of `[0, 1, ..., A.length - 1]`.
* `A` will have length in range `[1, 5000]`.
* The time limit for this problem has been reduced.

```java
// The local and global adjacent inversions are same
// therefore we are only looking for an inversion at min distance of 2
class Solution {
    public boolean isIdealPermutation(int[] A) {
        int cmax = 0;
        for (int i = 0; i < A.length - 2; ++i) {
            cmax = Math.max(cmax, A[i]);
            if (cmax > A[i + 2])
                return false;
        }
        return true;
    }
}
```


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