public void sort(int[] values) { int[] numbers = values; int[] auxillaryNumbers = new int[values.length]; mergesort(numbers, auxillaryNumbers, 0, values.length - 1); } private void mergesort(int [] numbers, int [] auxillaryNumbers, int low, int high) { // Check if low is smaller then high, if not then the array is sorted if (low < high) { // Get the index of the element which is in the middle int middle = low + (high - low) / 2; // Sort the left side of the array mergesort(numbers, auxillaryNumbers, low, middle); // Sort the right side of the array mergesort(numbers, auxillaryNumbers, middle + 1, high); // Combine them both // Alex: the first time we hit this when there is min difference between high and low. merge(numbers, auxillaryNumbers, low, middle, high); } } /** * Merges a[low .. middle] with a[middle..high]. * This method assumes a[low .. middle] and a[middle..high] are sorted. It returns * a[low..high] as an sorted array. */ private void merge(int [] a, int[] aux, int low, int middle, int high) { // Copy both parts into the aux array for (int k = low; k <= high; k++) { aux[k] = a[k]; } int i = low, j = middle + 1; for (int k = low; k <= high; k++) { if (i > middle) a[k] = aux[j++]; else if (j > high) a[k] = aux[i++]; else if (aux[j] < aux[i]) a[k] = aux[j++]; else a[k] = aux[i++]; } } public static void main(String args[]){ ... ms.sort(new int[] {5, 3, 1, 17, 2, 8, 19, 11}); ... } }Discussion...

- An auxillary array is used to achieve the sort. Elements to be sorted are copied into it and then once sorted copied back. It is important this array is only created once otherwise there can be a performance hit from extensive array created. The merge method does not have to create an auxiliary array however since it changes an object it means the merge method has side effects.
- Merge sort big(O) performance is N log N.

def mergeSort(xs: List[Int]): List[Int] = { val n = xs.length / 2 if (n == 0) xs else { def merge(xs: List[Int], ys: List[Int]): List[Int] = (xs, ys) match { case(Nil, ys) => ys case(xs, Nil) => xs case(x :: xs1, y :: ys1) => if (x < y) x::merge(xs1, ys) else y :: merge(xs, ys1) } val (left, right) = xs splitAt(n) merge(mergeSort(left), mergeSort(right)) } }Key discussion points:

- It is the same divide and conquer idea.
- The splitAt function is used to divide up the data up each time into a tuple. For every recursion this will new a new tuple.
- The local function merge is then used to perform the merging. Local functions are a useful feature as they help promote encapsulation and prevent code bloat.
- Neiher the mergeSort() or merge() functions have any side effects. They don't change any object. They create (and throw away) objects.
- Because the data is not been passed across iterations of the merging, there is no need to pass beginning and ending pointers which can get very buggy.
- This merge recursion uses pattern matching to great effect here. Not only is there matching for data lists but when a match happens the data lists are assigned to variables:
`x`

meaning the top element in the left list`xs1`

the rest of the left list`y`

meaning the top element in the right list`ys1`

meaning the rest of the data in the right list