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Unformatted text preview: COT 5405 Summer 2010 HW1 June 4, 2010 1.(10pts,1/2page per part) Prove or disprove (a) n 1 . 001 + n log n = n 1 . 001 (b) n 3 / log n = ( n 2 ) 2.(10pts,1page) Solve the given recurrence without using master theorem. T ( n ) = 2 T ( n/ 2) + n/logn 3.(10pts,1/2page) Use equivalence( ) and less than ( < ) to order the below functions according to asymptotic order. n ! n lgn ( lgn ) n (1 + 1 / 11) n lg * n ( lg ( n !)) 2 n log 10 n e n 4 1 gn 4 21 gn 1 n n/lgn n 1 / 10 4.(15pts,1page) Given a set of integers and another integer x, describe a (n lg n)-time algorithm to nd whether or not there are two integers in the set adds up to x. 5.(20pts,1page) Gvien a array of n elements, a majority element is any element appear in more than n/ 2 times position in A. Assume elements can only be compared for equality, they cannot be ordered or sorted. Design an e cient divide and conquer algorithm to nd a majority element in A (or determine that no majority element exists) and analyze its running...
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This note was uploaded on 01/15/2012 for the course COT 5405 taught by Professor Ungor during the Fall '08 term at University of Florida.
- Fall '08