13.9. Mergesort Concepts¶

13.9.1. Mergesort Concepts¶

A natural approach to problem solving is divide and conquer. To use divide and conquer when sorting, we might consider breaking the list to be sorted into pieces, process the pieces, and then put them back together somehow. A simple way to do this would be to split the list in half, sort the halves, and then merge the sorted halves together. This is the idea behind Mergesort.

Mergesort is one of the simplest sorting algorithms conceptually, and has good performance both in the asymptotic sense and in empirical running time. Unfortunately, even though it is based on a simple concept, it is relatively difficult to implement in practice. Here is a pseudocode sketch of Mergesort:

List mergesort(List inlist) {
  if (inlist.length() <= 1) return inlist;;
  List L1 = half of the items from inlist;
  List L2 = other half of the items from inlist;
  return merge(mergesort(L1), mergesort(L2));
}

Here is a visualization that illustrates how Mergesort works.

The hardest step to understand about Mergesort is the merge function. The merge function starts by examining the first record of each sublist and picks the smaller value as the smallest record overall. This smaller value is removed from its sublist and placed into the output list. Merging continues in this way, comparing the front records of the sublists and continually appending the smaller to the output list until no more input records remain.

Here is pseudocode for merge on lists:

List merge(List L1, List L2) {
  List answer = new List();
  while (L1 != NULL || L2 != NULL) {
    if (L1 == NULL) { // Done L1
      answer.append(L2);
      L2 = NULL;
    }
    else if (L2 == NULL) { // Done L2
      answer.append(L1);
      L1 = NULL;
    }
    else if (L1.value() <= L2.value()) {
      answer.append(L1.value());
      L1 = L1.next();
    }
    else {
      answer.append(L2.value());
      L2 = L2.next();
    }
  }
  return answer;
}