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cs161-02 - Analyzing Insertion Sort as a Recursive...

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1 19 Analyzing Insertion Sort as a Recursive Algorithm Recursive Algorithm l Basic idea: divide and conquer » Divide into 2 (or more) subproblems. » Solve each subproblem recursively. » Combine the results. l Insertion sort is just a bad divide & conquer ! » Subproblems: (a) last element (b) all the rest » Combine: find where to put the last element Lecture 2, April 5, 2001 20 Recursion for Insertion Sort Recursion for Insertion Sort l We get a recursion for the running time T(n): l Formal proof: by induction. l Another way of looking: split into n subproblems, merge one by one. 1 2 ( 1) for 1 ( ) 1 for 1 ( ) ( 1) ( 2) ( 1) ( 3) ( 2) ( 1) ... ( ) n i T n n n T n n T n T n n T n n n T n n n n i n = - + = = = - + = - + - + = - + - + - + = = ∑
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