775. Global and Local Inversions LeetCode Solution | Easy Approach

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Global and Local Inversion 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].

Global and Local Inversion Solutions

Time: O(n)
Space: O(n)

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