Merge Sort

Merge Sort

Our next sorting algorithm proceeds as follows:

• First, our base case: If the array contains 0 or 1 elements, there is nothing to do. It is already sorted.
• If the array has two or more elements in it, we will break it in half, sort the two halves, and then go through and merge the elements.

The Java method to do it:

  public void sort(int[] array) {
     // create tempArray for use in merging
     int[] tempArray = new int[array.length];
     mergeSort(array, 0, array.length-1, tempArray);
    }

  /*
   * PRE: left and right are valid indexes of array.  
   *      tempArray.length == array.length
   * POST: Sorts array from left to right.
   */
  public void mergeSort(int[] array, int left, int right, int[] tempArray) {
    if (left < right) {
      int middle = (right + left) / 2;
      mergeSort(array, left, middle, tempArray);
      mergeSort(array, middle + 1, right, tempArray);
      merge(array, left, middle, right, tempArray);
    }
  }

The method merge takes the sorted elements in array[left..middle] and array[middle+1..right] and merges then together using the array tempArray, and then copies them back into array.

    
  /** PRE: left <= middle <= right and left,middle,right are valid 
   *  indices for array * tempArray.length == array.length 
   *  array[left..middle] and array[middle+1..right] must both be sorted.
   * POST: Merges the two halves (array[left..middle] and
   * array[middle+1..right]) together, and array[left..right] is then
   * sorted.
   */
   private void merge(int []array, int left, int middle,
                      int right, int[] tempArray) { 
     int indexLeft = left; 
     int indexRight = middle + 1; 
     int target = left;

    // Copy both pieces into tempArray.
    for (int i = left; i <= right; i++) {
      tempArray[i] = array[i];
    }
    
    // Merge them together back in array while there are
    // elements left in both halves.
    while (indexLeft <= middle && indexRight <= right) {
      if (tempArray[indexLeft] < tempArray[indexRight]) {
        array[target] = tempArray[indexLeft];
        indexLeft++;
      } else {
        array[target] = tempArray[indexRight];
        indexRight++;
      }
      target++;
    }

    // Move any remaining elements from the left half.
    while (indexLeft <= middle) {
      array[target] = tempArray[indexLeft];
      indexLeft++;
      target++;
    }

    // Move any remaining elements from the right half.
    while (indexRight <= right) {
      array[target] = tempArray[indexRight];
      indexRight++;
      target++;
    }
  }

Merge Sort