マージソート

#include <iostream>
using namespace std;

void merge(int arr[], int beg, int mid, int end) {
  int output[end - beg + 1];
  int i = beg, j = mid + 1, k = 0;
  // add smaller of both elements to the output
  while (i <= mid && j <= end) {
    if (arr[i] <= arr[j]) {
      output[k] = arr[i];
      k += 1;
      i += 1;
    } else {
      output[k] = arr[j];
      k += 1;
      j += 1;
    }
  }
  // remaining elements from first array
  while (i <= mid) {
    output[k] = arr[i];
    k += 1;
    i += 1;
  }
  // remaining elements from the second array
  while (j <= end) {
    output[k] = arr[j];
    k += 1;
    j += 1;
  }
  // copy output to the original array
  for (i = beg; i <= end; i += 1) {
    arr[i] = output[i - beg];
  }
}

void mergeSort(int arr[], int beg, int end) {
  if (beg < end) {
    int mid = (beg + end) / 2;
    // divide and conquer
    mergeSort(arr, beg, mid);      // divide : first half
    mergeSort(arr, mid + 1, end);  // divide: second half
    merge(arr, beg, mid, end);     // conquer
  }
}
int main() {
  int n = 6;
  int arr[6] = {5, 3, 4, 2, 1, 6};
  cout << "Input array: ";
  for (int i = 0; i < n; i++) {
    cout << arr[i] << " ";
  }
  cout << "\n";
  mergeSort(arr, 0, n - 1);  // Sort elements in ascending order
  cout << "Output array: ";
  for (int i = 0; i < n; i++) {
    cout << arr[i] << " ";
  }
  cout << "\n";
}

T(n) = 2T(n/2) + θ(n)