void printgreater(int arr[], int n) // naive approach θ(n²)
{
    for (int i = 0; i < n; i++) // traverse the array
    {
        int count = 0;
        for (int j = 0; j < n; j++)
            if (j != i && arr[j] > arr[i])
                count++; // for every greater element found , increment the count

        cout << count << " ";
    }
}

void Printgreater(int arr[], int n) // efficient way O(nlogn)
{
    map<int, int> m; // map O(n)  auxiliary space
    for (int i = 0; i < n; i++)
        m[arr[i]]++; // Traverse the array, map the key & value

    int cum_freq = 0; // cumulative freq
    /*this cumulative frequency will hold
    the values of the number of greater elements */
    for (auto it = m.rbegin(); it != m.rend(); it++) // iterating through the map
    {
        int freq = it->second; // value stored to freq
        it->second = cum_freq; // cum.freq assigned to it.second of map
        cum_freq += freq;      // cum.freq incremented by the stored value
    }
    for (int i = 0; i < n; i++)
        cout << m[arr[i]] << " "; // print the cum.freq according to array elements
}

void PrintGreater(int arr[], int n) //efficient way O(nlogn)
{
    vector<int> temp(n); //vector ini

    for (int i = 0; i < n; i++)
    {
        temp[i] = arr[i]; //copy in temp 
    }
    sort(temp.begin(), temp.end()); //sort the temp

    for (int i = 0; i < n; i++)
    {

        auto it = upper_bound(temp.begin(), temp.end(), arr[i]); // iterator to upper bound of the ith element in sorted vector
        auto it1 = temp.end() - 1; //iterator to the end of the sorted vector

        if (it != temp.end()) //if upper bound is present 
            cout << it1 - it + 1 /*binary_search(temp.begin(), temp.end(), *it)*/ << " ";
        else
            cout << 0 << " "; //if upper bound is not present
    }
}

int main()
{
    int arr[] = {10, 2, 8, 5, 8}, n = 4;
    printgreater(arr, n); //θ(n²) TC  
    Printgreater(arr,n); // O(nlogn) TC , O(n) AS
    PrintGreater(arr,n); // O(nlogn) TC , O(n) AS
}