Global and Local Inversions — LeetCode 775 Python Solution

The problem

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

Input

nums = [1,0,2]

Output

true

Explanation

There is 1 global inversion and 1 local inversion.

Python solution

class Solution:
    def isIdealPermutation(self, nums: List[int]) -> bool:
        mx = 0
        for i in range(2, len(nums)):
            if (mx := max(mx, nums[i - 2])) > nums[i]:
                return False
        return True

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 775. Global and Local Inversions is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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