Exer2 - CSE 5311 Design and Analysis of Algorithms FALL...

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CSE 5311 Design and Analysis of Algorithms FALL 2007 Department of Computer Science The University of Texas at Arlington Exercise Set 2 1) Answer questions 1a to 1c pertaining to the STOOGE_SORT Algorithm given below. STOOGE_SORT(A, i , j ) 1 if A [ i ] > A [ j ] 2 then exchange A [ i ] A [ j ] 3 if i +1 j 4 then return 5 k (j-i+1)/3 6 STOOGE_SORT(A, i , j-k ) 7 STOOGE_SORT(A, i+k , j ) 8 STOOGE_SORT(A, i , j-k ) a. Argue that STOOGE_SORT ( A ,1,length[ A ]) correctly sorts the input array A [1 . . n ], where n = length[ A ]. b. Give a recurrence for the worst-case running time of STOOGE_SORT and a tight asymptotic bound on the worst-case running time. c. Compare the worst-case running time of STOOGE_SORT with that of insertion sort, merge sort, heapsort, and quicksort. 2) Given an array of integers A [1. . n ], such that, for all i , 1 i < n , we have A [ i ]- A [ i +1] 1. Let A [1] = x and A [ n ] = y , such that x < y . Design an efficient search algorithm to find j such that
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Exer2 - CSE 5311 Design and Analysis of Algorithms FALL...

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