<p>You are given an integer array <code>nums</code> of length <code>n</code> which represents a permutation of all the integers in the range <code>[0, n - 1]</code>.</p>

<p>The number of <strong>global inversions</strong> is the number of the different pairs <code>(i, j)</code> where:</p>

<ul>
	<li><code>0 &lt;= i &lt; j &lt; n</code></li>
	<li><code>nums[i] &gt; nums[j]</code></li>
</ul>

<p>The number of <strong>local inversions</strong> is the number of indices <code>i</code> where:</p>

<ul>
	<li><code>0 &lt;= i &lt; n - 1</code></li>
	<li><code>nums[i] &gt; nums[i + 1]</code></li>
</ul>

<p>Return <code>true</code> <em>if the number of <strong>global inversions</strong> is equal to the number of <strong>local inversions</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,0,2]
<strong>Output:</strong> true
<strong>Explanation:</strong> There is 1 global inversion and 1 local inversion.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,0]
<strong>Output:</strong> false
<strong>Explanation:</strong> There are 2 global inversions and 1 local inversion.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == nums.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt; n</code></li>
	<li>All the integers of <code>nums</code> are <strong>unique</strong>.</li>
	<li><code>nums</code> is a permutation of all the numbers in the range <code>[0, n - 1]</code>.</li>
</ul>

class Solution {
public:
    long long cnt = 0;

    void merge(vector<int>& nums, int low, int mid, int high) {
        int i = low;
        int j = mid + 1;
        vector<int> temp(high - low + 1);
        int k = 0;

        while (i <= mid && j <= high) {
            if (nums[i] <= nums[j]) {
                temp[k++] = nums[i++];
            } else {
                temp[k++] = nums[j++];
                cnt += (mid - i + 1); // Count inversions
            }
        }

        while (i <= mid) {
            temp[k++] = nums[i++];
        }
        while (j <= high) {
            temp[k++] = nums[j++];
        }

        for (int i = low; i <= high; i++) {
            nums[i] = temp[i - low];
        }
    }

    void mergeCount(vector<int>& nums, int low, int high) {
        if (low >= high) {
            return;
        }
        int mid = low + (high - low) / 2;
        mergeCount(nums, low, mid);
        mergeCount(nums, mid + 1, high);
        merge(nums, low, mid, high);
    }

    int localInversionCount(vector<int>& nums) {
        int cnt = 0;
        for (int i = 0; i < nums.size() - 1; i++) {
            if (nums[i] > nums[i + 1]) {
                cnt++;
            }
        }
        return cnt;
    }

    bool isIdealPermutation(vector<int>& nums) {
        int localCount = localInversionCount(nums);
        cnt = 0; // Reset the global count
        mergeCount(nums, 0, nums.size() - 1);
        return cnt == localCount;
    }
};

127196