<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 {
private:
    long long localInversions(vector<int>& nums) {
        long long count = 0;
        for (int i = nums.size()-1; i >= 0; i--) {
            if (i+1 < nums.size() && nums[i] > nums[i+1]) count++;
        }
        return count;
    }

    void globalInversions(vector<int>& nums, int s, int e, long long& total) {
        if (s >= e) {
            return;
        } else {
            vector<int> vec(e-s+1);
            int mid = s +(e-s)/2;
            globalInversions(nums, s, mid, total);
            globalInversions(nums, mid+1, e, total);
            int i = s, j = mid+1;
            int ptr = 0;
            while (i <= mid && j <= e) {
                if (nums[i] <= nums[j]) {
                    vec[ptr] = nums[i];
                    i++;
                } else {
                    total += (mid-i+1);
                    vec[ptr] = nums[j];
                    j++;
                }
                ptr++;
            }
            while (i <= mid) {
                vec[ptr++] = nums[i++];
            }
            while (j <= e) {
                vec[ptr++] = nums[j++];
            }
            for (int d = 0; d < vec.size(); d++) {
                nums[d+s] = vec[d];
            }
        }
    }
public:
    bool isIdealPermutation(vector<int>& nums) {
        long long total = 0;
        long long local = localInversions(nums);
        globalInversions(nums, 0, nums.size() - 1, total);
        return total == local;
    }
};
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