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// Write a program to sort the elements of an array using Merge Sort (The program should report the number of comparisons).

#include <iostream>
using namespace std;

void merge(int arr[], int left, int mid, int right, int &comparisons) {
    int n1 = mid - left + 1;
    int n2 = right - mid;

    int *L = new int[n1];
    int *R = new int[n2];

    for (int i = 0; i < n1; i++)
        L[i] = arr[left + i];
    for (int j = 0; j < n2; j++)
        R[j] = arr[mid + 1 + j];

    int i = 0, j = 0, k = left;

    while (i < n1 && j < n2) {
        comparisons++;
        if (L[i] <= R[j]) {
            arr[k] = L[i];
            i++;
        } else {
            arr[k] = R[j];
            j++;
        }
        k++;
    }

    while (i < n1) {
        arr[k] = L[i];
        i++;
        k++;
    }

    while (j < n2) {
        arr[k] = R[j];
        j++;
        k++;
    }

    delete[] L;
    delete[] R;
}

void mergeSort(int arr[], int left, int right, int &comparisons) {
    if (left < right) {
        int mid = left + (right - left) / 2;

        mergeSort(arr, left, mid, comparisons);
        mergeSort(arr, mid + 1, right, comparisons);
        merge(arr, left, mid, right, comparisons);
    }
}

int main() {
    int arr[] = {38, 27, 43, 3, 9, 82, 10};
    int n = sizeof(arr) / sizeof(arr[0]);
    int comparisons = 0;

    mergeSort(arr, 0, n - 1, comparisons);

    cout << "Sorted array: ";
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    cout << endl;
    cout << "Number of comparisons: " << comparisons << endl;

    return 0;
}
// Output:
// Sorted array: 3 9 10 27 38 43 82
// Number of comparisons: 14
// Time Complexity: O(n log n)
// Space Complexity: O(n)