05. Global and Local Inversions.cpp

/*
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.

Hint #1  
Where can the 0 be placed in an ideal permutation? What about the 1?
*/

class Solution
{
public:
  bool isIdealPermutation(vector<int> &A)
  {
    if (A.size() <= 1)
      return true;
    int Max = -1;
    for (int i = 0; i < A.size() - 2; ++i)
    {
      Max = max(Max, A[i]);
      if (Max > A[i + 2])
        return false;
    }
    return true;
  }
};