<p>Given an integer array <code>nums</code>, return <em>the number of <strong>reverse pairs</strong> in the array</em>.</p>

<p>A <strong>reverse pair</strong> is a pair <code>(i, j)</code> where:</p>

<ul>
	<li><code>0 &lt;= i &lt; j &lt; nums.length</code> and</li>
	<li><code>nums[i] &gt; 2 * nums[j]</code>.</li>
</ul>

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

<pre>
<strong>Input:</strong> nums = [1,3,2,3,1]
<strong>Output:</strong> 2
<strong>Explanation:</strong> The reverse pairs are:
(1, 4) --&gt; nums[1] = 3, nums[4] = 1, 3 &gt; 2 * 1
(3, 4) --&gt; nums[3] = 3, nums[4] = 1, 3 &gt; 2 * 1
</pre>

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

<pre>
<strong>Input:</strong> nums = [2,4,3,5,1]
<strong>Output:</strong> 3
<strong>Explanation:</strong> The reverse pairs are:
(1, 4) --&gt; nums[1] = 4, nums[4] = 1, 4 &gt; 2 * 1
(2, 4) --&gt; nums[2] = 3, nums[4] = 1, 3 &gt; 2 * 1
(3, 4) --&gt; nums[3] = 5, nums[4] = 1, 5 &gt; 2 * 1
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution {
public:
    long long  count=0;
    void merge(vector<int  >&arr,int low,int mid,int high){
        int i=low;
        int j=mid+1;
        int k=0;
        vector<long long >output(high-low+1);
        while(i<=mid && j<= high){
            if(arr[i]<=arr[j]){
                output[k]=arr[i];
                i++;
                k++;
            }
            else{
                // if arr[j] <arr[i]
                output[k]=arr[j];
                j++;
                k++;
            }
        }
        while(i<=mid){
            output[k]=arr[i];
            k++;
            i++;
        }
        while(j<=high){
            output[k]=arr[j];
            k++;
            j++;
        }
        // overwrite the original array
        for(int i=low,m=0;i<=high;i++,m++){
            arr[i]=output[m];
        }
    }
    void  countPairs(vector<int  >&arr,int low,int mid,int high){
        // i goes from low to mid and right will go from mid+1 to the high denoting the other array
        int right=mid+1;
        for(int i=low;i<=mid;i++){
            // for each element of the first array we need to find the limit till which arr[i]>2*arr[right]
            while(right<=high && arr[i]>2*(long)arr[right]){
                right++;

            }
            count=count+(right-(mid+1));
        }
    }
    void mergesort(vector<int >&arr,int low,int high){
        if(low>=high){
            return;
        }
        int mid=(low+high)/2;
        // divde the array into two parts on the basis of mid
        mergesort(arr,low,mid);
        mergesort(arr,mid+1,high);
        // perform the operation bfore merging
        countPairs(arr,low,mid,high);
        merge(arr,low,mid,high);
    }
    int reversePairs(vector<int>& nums) {
        mergesort(nums,0,nums.size()-1);
        return count;
    }
};
132023