3.3 Fundamentals of data representation 3.1.4 Sorting algorithms 2 Lesson

Objectives Understand and explain how the merge sort algorithm works. Compare and contrast merge sort and bubble sort algorithms.

Introduction to the merge sort In the previous lesson, we looked at the idea of applying the bubble sort algorithm when ordering datasets. We concluded that the bubble sort was a simple but inefficient algorithm. Now we are going to look at a related but more sophisticated algorithm – the ‘merge sort’. youtube.com/watch?v=XaqR3G_NVoo&nohtml5=False Watch video from 0:20 minutes to 2:15 minutes. Note: there are an odd number of female dancers to sort.

How does a merge sort work? A merge sort is a method of arranging data by splitting a list into discrete elements and merging the elements together until an ordered list is obtained. Merge sorts are classed as as ‘divide-and-conquer’ algorithms. Divide (the problem into a small number of pieces), Conquer (solve each piece, by repeatedly applying divide-and-conquer to it), Combine (the pieces together into a solution).

Visual demonstration of a merge sort youtube.com/watch?v=HsZ-YRQM8sE&nohtml5=False Watch video from 0:40 minutes to 2:26 minutes.

Merge sorts We will stick to examples where an even number of elements are sorted. The merge sort starts off by repeatedly splitting the array in half until there are only individual elements left. Array 5 8 4 2 19 34 56 7 Split 5 8 4 2 19 34 56 7 Split 5 8 4 2 19 34 56 7 5 8 4 2 5 8 4 2

Merge sorts It is helpful to view the elements vertically for the next step. Merging occurs by making a ‘bottom up’ comparison and swapping values. 5 5 8 8 Now try Quiz 1 2 4 5 8 4 2 4 2 2 4 5 7 8 19 34 56 19 19 34 34 Note that for GCSE, it is not necessary to know how the more complex sorts are actioned. 7 19 34 56 56 7 56 7

Merge sorts Our example is a simple one – the array contained just eight elements and is easily split into pairs. The full algorithm must cope with the possibility of odd numbers of array elements, of much larger arrays and numbers which do not easily split into pairs. As with the searching algorithms, a more complex process requires fewer steps to complete than the simpler but more basic alternatives. The binary search involves bisecting a dataset until a match is made and a similar process occurs here in the merge sort.

Merge sorts We talk about the recursive operation of components of the underlying algorithm, i.e. it repeats itself where required. Recursive programming can consume a lot of memory and that is the price paid for having a more efficient algorithm.

Comparing sorting algorithms A quick review of the two sorting algorithms that we have seen in use so far. Bubble Merge What comparisons might be made of these two techniques?

Comparing sorting algorithms Bubble Advantages Mechanism easier to comprehend. Disadvantages Inefficient - uses ‘blunt’ approach’ to sorting with the number of iterations required rapidly expanding as the size of the data to be sorted grows. Merge Very quick in comparison to the bubble sort technique. More complex algorithm but relies on a recursive algorithm which can consume large amounts of memory.

To round things off… That brings us to the end of two separate topics – Searching Sorting Both of which have exhibited similar characteristics in that a clear trade-off between the efficiency and complexity of the underlying processes can be demonstrated. Now complete Quiz 1 in order to round off this final lesson.