linear-expected-time algorithm, Data Structure & Algorithms

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Implement a linear-expected-time algorithm for selecting the kth smallest element

Algorithm description

1. If |S| = 1, then k = 1 and return the element in S as the answer.

2. Pick a pivot element, v[S]. Partition S-{v} into S1 and S2, as done with quicksort

3. If k<=|S1|, then the kth smallest element must be in S1. In this case, return quickselect(S1,k).

4. If k=1+|S1|, the pivot is the kth smallest element and return it.

5. Otherwise, the kth smallest element lies in S2, and it is the (k-|

S1|-1)st smallest element in S2, and return quickselect(S2,k-| S1|-1).

Deliverables

1. Source code, i.e. *.java file

2. Time complexity analysis

 


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