public void sort(int[] a) {
    mergeSort(a, 0, a.length - 1);
  }

  // Use merge sort to sort the array between indexes left
  // and right.  Split the list in half, recursively
  // sort each half, and then merge the sorted halves
  // back together.
  private void mergeSort(int[] a, int left, int right) {

    if (left < right) {
      // Find the mid point.  Sort the first half and second
      // half separately.
      int middle = (left + right) / 2;
      mergeSort(a, left, middle);
      mergeSort(a, middle + 1, right);

      // Merge the sorted arrays together to form one sorted array.
      merge(a, left, middle, right);
  }

  // Merge the sorted lists a[left]..a[middle] and 
  // a[middle+1]..a[right] into one large sorted list
  // of a[left]..a[right].
  private void merge(int[] a, int left, int middle, int right) {

    // copy data into temp array
    int[] temp = new int[a.length];
    for (int i = left; i <= right; i++) {
      temp[i] = a[i];
    }

    int indexLeft = left;
    int indexRight = middle + 1;
    int endLeft = middle;
    int endRight = right;

    for (int target = left; target <= endRight; target++) {
      if (indexLeft > endLeft) {
        // Used up all the elements in left portion
        a[target] = temp[indexRight];
        indexRight++;
      } else if (indexRight > endRight) {
        // Used up all the elements in right portion
        a[target] = temp[indexLeft];
        indexLeft++;
      } else if (temp[indexLeft] < temp[indexRight]) {
        // Left value is less.  Use it.
        a[target] = temp[indexLeft];
        indexLeft++;
      } else {
        // Right value is less.  Use it.
        a[target] = temp[indexRight];
        indexRight++;
      }
    }
  }