<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:
    vector<int> temp;

    int merge(vector<int>& nums, int start, int mid, int end){
        int i = start, j = mid+1, cn = 0;
        int n = nums.size();
        
        while(i <= mid && j <= end){
            if(nums[i] <= nums[j]){
                temp.push_back(nums[i++]);
            }
            else{
                temp.push_back(nums[j++]);
                cn += mid - i + 1;
            }
        }

        while(i <= mid){
            temp.push_back(nums[i++]);
        }
        while(j <= end){
            temp.push_back(nums[j++]);
        }

        for(int x = start; x <= end; x++){
            nums[x] = temp[x-start];
        }
        temp.clear();
        return cn;
    }

    int mergesort(vector<int>& nums, int start, int end){
        //base case
        if(start >= end){
            return 0;
        }

        int mid = start + (end-start)/2;
        long long cn = 0;
        cn += mergesort(nums, start, mid);
        cn += mergesort(nums, mid+1, end);
        cn += merge(nums, start, mid, end);
        return cn;
    }

    bool isIdealPermutation(vector<int>& nums) {
        int n = nums.size();
        int local = 0; 

        for(int i=0; i<n-1; i++){
            if(nums[i] > nums[i+1]){
                local++;
            }
        }

        int global = mergesort(nums, 0, n-1);

        return global == local;
    }
};
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