Data Structures and Algorithms with Object-Oriented Design Patterns in C++

## Example-Merge Sorting

Sorting algorithms and sorters are covered in detail in Chapter . In this section we consider a divide-and-conquer sorting algorithm--merge sort . Given an array of n items in arbitrary order, the objective is to rearrange the elements of the array so that they are ordered from the smallest element to the largest one.

The merge sort algorithm sorts a sequence of length n>1 by splitting it into to subsequences--one of length , the other of length . Each subsequence is sorted and then the two sorted sequences are merged into one.

Program  defines the function MergeSort which takes three arguments, array, i and n. The routine sorts the following n elements:

The MergeSort routine calls itself as well as the Merge routine. The purpose of the Merge routine is to merge two sorted sequences, one of length , the other of length , into a single sorted sequence of length n. This can easily be done in O(n) time. (See Program ).

Program: Divide-and-Conquer Example--Merge Sorting

The running time of the MergeSort routine depends on the number of items to be sorted, n. Although Program  works correctly for arbitrary values of n, it is much easier to determine the running time if we assume that n is a power of two. In this case, the running time is given by the recurrence

Equation  is easily solved using repeated substitution:

Setting gives .