Non-recursive merge sort with two nested loops - how?

Question

First question here, and yes this is a homework question. We are tasked with performing merge sort on an array (which I am familiar with), but in a way I am unsure of how to do.

Answer 1

Here is C# version of bottom-up-mergesort (for some more details you may refer to my blog @ http://dream-e-r.blogspot.com/2014/07/mergesort-arrays-and-lists.html)

void BottomUpMergesort(int[] a)
        {
            int[] temp = new int[a.Length];
            for (int runWidth = 1; runWidth < a.Length; runWidth = 2 * runWidth)
            {
                for (int eachRunStart = 0; eachRunStart < a.Length; 
                    eachRunStart = eachRunStart + 2 * runWidth)
                {
                    int start = eachRunStart;
                    int mid = eachRunStart + (runWidth - 1);
                    if(mid >= a.Length)
                    {
                        mid = a.Length - 1;
                    }
                    int end = eachRunStart + ((2 * runWidth) - 1);
                    if(end >= a.Length)
                    {
                        end = a.Length - 1;
                    }

                    this.Merge(a, start, mid, end, temp);
                }
                for (int i = 0; i < a.Length; i++)
                {
                    a[i] = temp[i];
                }
            }

And merge is defined as:

void Merge(int[] a, int start, int mid, int end, int[] temp)
        {
            int i = start, j = mid+1, k = start;
            while((i<=mid) && (j<=end))
            {
                if(a[i] <= a[j])
                {
                    temp[k] = a[i];
                    i++;
                }
                else
                {
                    temp[k] = a[j];
                    j++;
                }
                k++;
            }
            while(i<=mid)
            {
                temp[k] = a[i];
                i++;
                k++;
            }
            while (j <= end)
            {
                temp[k] = a[j];
                j++;
                k++;
            }
            Assert.IsTrue(k == end+1);
            Assert.IsTrue(i == mid+1);
            Assert.IsTrue(j == end+1);
        }

        }

Just for reference here is the TopDownMergesort:

void TopDownMergesort(int[] a, int[] temp, int start, int end)
        {
            if(start==end)
            {
                //run size of '1'
                return;
            }
            int mid = (start + end) / 2;
            this.TopDownMergesort(a, temp, start, mid);
            this.TopDownMergesort(a, temp, mid + 1, end);
            this.Merge(a, start, mid, end, temp);
            for(int i = start;i<=end;i++)
            {
                a[i] = temp[i];
            }
        }

UnitTests

[TestMethod]
        public void BottomUpMergesortTests()
        {
            int[] a = { 13, 4, 1, 3, 8, 11, 9, 10 };
            this.BottomUpMergesort(a);
            int[] b = { 1, 3, 4, 8, 9, 10, 11, 13 };
            Assert.IsTrue(a.Length == b.Length);
            for (int i = 0; i < a.Length; i++)
            {
                Assert.IsTrue(a[i] == b[i]);
            }
            List l = new List();
            for (int i = 10; i >= 1; i--)
            {
                l.Add(i);
            }
            var la = l.ToArray();
            this.BottomUpMergesort(la);
            for (int i = 1; i <= 10; i++)
            {
                Assert.IsTrue(la[i - 1] == i);
            }
            l.Clear();
            for (int i = 16; i >= 1; i--)
            {
                l.Add(i);
            }
            la = l.ToArray();
            this.BottomUpMergesort(la);
            for (int i = 1; i <= l.Count; i++)
            {
                Assert.IsTrue(la[i - 1] == i);
            }
        }