775. 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.

Rust Solution

struct Solution;

impl Solution {
    fn is_ideal_permutation(a: Vec<i32>) -> bool {
        let n = a.len();
        for i in 0..n {
            if (a[i] - i as i32).abs() > 1 {
                return false;
            }
        }
        true
    }
}

#[test]
fn test() {
    let a = vec![1, 0, 2];
    let res = true;
    assert_eq!(Solution::is_ideal_permutation(a), res);
    let a = vec![1, 2, 0];
    let res = false;
    assert_eq!(Solution::is_ideal_permutation(a), res);
}

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