Global and Local Inversions
You are given an integer array nums of length n which represents a permutation of all the integers in the range [0, n - 1].
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:
The number of local inversions is the number of indices i where:
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 <= 10^5
- 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].
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