Strand Sort

Strand sort is a recursive sorting algorithm that sorts items of a list into increasing order. It has O(n²) worst time complexity which occurs when the input list is reverse sorted. It has a best case time complexity of O(n) which occurs when the input is a list that is already sorted.

Given a list of items, sort them in increasing order. 

Examples:

Input: ip[] = {10, 5, 30, 40, 2, 4, 9}
Output: op[] = {2, 4, 5, 9, 10, 30, 40}

Input: ip[] = {1, 10, 7}
Output: op[] = {1, 7, 10}

Illustrations:

Let, input[] = {10, 5, 30, 40, 2, 4, 9}

Initialize:output[] = {}, sublist[] = {}

Move first item of input to sublist.
sublist[] = {10}

Traverse remaining items of input and if current element is greater than last item of sublist, move this item from input to sublist. 
Now, sublist[] = {10, 30, 40}, input[] = {5, 2, 4, 9}

Merge sublist into output.
op = {10, 30, 40}

Next recursive call: Move first item of input to sublist. sublist[] = {5}

Traverse remaining items of input and move elements greater than last inserted.
input[] = {2, 4}
sublist[] = {5, 9}

Merge sublist into op.
output = {5, 9, 10, 30, 40}

Last Recursive Call:

{2, 4} are first moved to sublist and then merged into output.
output = {2, 4, 5, 9, 10, 30, 40}

Below are simple steps used in the algorithm:

• Let ip[] be input list and op[] be output list.
• Create an empty sublist and move first item of ip[] to it.
• Traverse remaining items of ip. For every item x, check if x is greater than last inserted item to sublist. If yes, remove x from ip and add at the end of sublist. If no, ignore x (Keep it in ip)
• Merge sublist into op (output list)
• Recur for remaining items in ip and current items in op.

Below is the implementation of above algorithm in C++ and Javascript. The C++ implementation uses list in C++ STL. 

2 4 5 9 10 30 40

Time complexity: O(N²)
Auxiliary Space: O(N)

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Practice Problems on Sorting