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in Algorithms retagged by
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1 Answer

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As far as space complexity is concerned , first we consider those algo as having less space requirement which are inplace and hence no auxilliary space is required.

So bubble sort and selection both are simple are simple iterative sorting algos , so they will consume space mainly for the input array only.

So  1  = 2

Now coming to quicksort and mergesort ,

space required for input array = O(n)

for function call stack = O(logn)  [using tail recursion optmisation we can reduce the space complexity of function call for quicksort to O(logn) and for merge sort it is always O(logn) ]

The difference hence comes in the fact that mergesort requires auxilliary array for merge operation whereas quicksort does not require any auxilliary array as it is an inplace algorithm.

Hence space complexity of quicksort < mergesort

Therefore the correct order is : 1 = 2 < 4 < 3

Hence A) should be the correct option.

For reference on tail recursion optimisation , plz refer :

http://www.geeksforgeeks.org/quicksort-tail-call-optimization-reducing-worst-case-space-log-n/
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[using tail recursion optmisation we can reduce the space complexity of function call for quicksort to O(logn) and for merge sort it is always O(logn) ]

What does it mean...after optimisation what is the space complexity?
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For mergesort the recurrence is always :

T(n) = 2T(n/2) + O(n)

So the height of the recursion tree which decides the number of function instances in function call instances will remain O(logn) only.

And for tail recursion optimisation method for quicksort , plz refer :

http://www.geeksforgeeks.org/quicksort-tail-call-optimization-reducing-worst-case-space-log-n/

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okk..thank you
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