<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 global_inversions = 0;
    long long local_inversions = 0;
    vector<int> nums_copy;

    void merge(vector<int>& nums, int start1, int end1, int start2, int end2) {
        nums_copy.clear();
        int start1_copy = start1;
        int index = 0;
        while (start1 <= end1 && start2 <= end2) {
            if (nums[start2] < nums[start1]) {
                global_inversions = end1 - start1 + 1 + global_inversions;
                nums_copy.push_back(nums[start2++]);
            }

            else {
                nums_copy.push_back(nums[start1++]);
            }
        }

        while (start1 <= end1) {
            nums_copy.push_back(nums[start1++]);
        }

        while (start2 <= end2) {
            nums_copy.push_back(nums[start2++]);
        }

        index = 0;
        for (int i = start1_copy; i <= end2; i++)
            nums[i] = nums_copy[index++];
    }
    void mergeSort(vector<int>& nums, int start, int end) {
        if (start >= end)
            return;

        int mid = start + end;
        mid = mid >> 1;
        mergeSort(nums, start, mid);
        mergeSort(nums, mid + 1, end);
        merge(nums, start, mid, mid + 1, end);
    }
    bool isIdealPermutation(vector<int>& nums) {
        vector<int> nums_copy = nums;
        mergeSort(nums_copy, 0, nums.size() - 1);
        for (int i = 0; i < nums.size() - 1; i++)
            if (nums[i] > nums[i + 1])
                local_inversions++;

        return (global_inversions == local_inversions) ? true : false;
    }
};

// merge sort
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