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Recursive and Iterative Merge Sort Implementations

03.07.2012
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Curator's Note: In response to Stoimen Popov's Algorithm of the Week Post: Merge Sort, Chaker Nakhli pointed out that Stoimen only presented a recursive version of the merge sort algorithm. In this post, Chaker presents an iterative approach written in C#, but it can be easily converted to Java or any other language...


I find merge sort elegant and easy to implement and to understand for both iterative and recursive approaches. In this post I’ll share a quick (and probably dirty) iterative and recursive implementations of merge sort. Both versions share exactly the same merge operation. The implementation takes less than 30 lines of C#.

Recursive Merge Sort

public static T[] Recursive(T[] array, IComparer<T> comparer)
 {
     Recursive(array, 0, array.Length, comparer);
     return array;
 }
 
 private static void Recursive(T[] array, int start, int end, IComparer<T> comparer)
 {
     if (end - start <= 1) return;
     int middle = start + (end - start) / 2;
 
     Recursive(array, start, middle, comparer);
     Recursive(array, middle, end, comparer);
     Merge(array, start, middle, end, comparer);
 }

Iterative Merge Sort

public static T[] Iterative(T[] array, IComparer<T> comparer)
{
    for (int i = 1; i <= array.Length / 2 + 1; i *= 2)
    {
        for (int j = i; j < array.Length; j += 2 * i)
        {
            Merge(array, j - i, j, Math.Min(j + i, array.Length), comparer);
        }
    }
 
    return array;
}

Merge Function

The merge method below is used for both methods: recursive and iterative. It merges the two provided sub-arrays T[start, middle) and T[middle, end). The result of the merge cannot stored in the input array, it needs to be stored in a separate temporary array. This takes (end-start) memory space and will have a worst case space complexity O(n) where n is the size of the input array.

private static void Merge(T[] array, int start, int middle, int end, IComparer<T> comparer)
{
    T[] merge = new T[end-start];
    int l = 0, r = 0, i = 0;
    while (l < middle – start && r < end – middle)
    {
        merge[i++] = comparer.Compare(array[start + l], array[middle + r]) < 0
            ? array[start + l++]
            : array[middle + r++];
    }
 
    while (r < end – middle) merge[i++] = array[middle + r++];
 
    while (l < middle – start) merge[i++] = array[start + l++];
 
    Array.Copy(merge, 0, array, start, merge.Length);
}


Conclusion

As opposed to other in-place sorting algorithms, merge sort needs O(n) space to perform the merging step. On the other hand, it is a stable sort and it can be easily modified to implement external sorting for big data sets that do not fit in RAM.

Published at DZone with permission of its author, Chaker Nakhli. (source)

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Comments

Goel Yatendra replied on Thu, 2012/03/15 - 1:44pm

Merge sort can be implemented in-place and stable, even thought it is a bit complicated. An implementation is included in the C++ STL.

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