Discrete Mathematics with Graph Theory (3rd Edition) 246

# Discrete Mathematics with Graph Theory (3rd Edition) 246 -...

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244 Solutions to Review Exercises cross outs. So the number of basic operations is at most (l+i) + ... + (1+ ;) = (M -1) + n( 1 + ~ + ! + it) = M -1 + nO(logM) = y'n + nO(~ logn) = O(nlogn). 10. Since n = 11 -=I- 1, we set m = L 121 J = 5. Since 5 = x = a5 = 1 and x < are both false, we replace n by 11 - 5 = 6 and change our list to 2,4,5,8,9, 12. Since 6 = n -=I- 1, we set m = L~J = 3. Since 5 = x output "true" and stop. This search required three comparisons of 5 with an element in the list; a linear search would have used two comparisons. 11. -1,3,7,10,12,15 3,7,10,12,15 -3, -1, 2 -1,2 2 -4 -4,-3 -4, -3,-1 -4, -3, -1,-1 -4, -3, -1, -3, -1, -1,2,3,7,10,12,15 The algorithm required five comparisons. 12. (a) Here's the bubble sort: k = 6: 9, -3, 1,0, -4,5,3 --t -3,9,1,0, -4, 5, 3 -3,1,9,0, -4, 5, 3 -3,1,0, 9, -4, 5, 3 -3, f,O, -4,~, 3 -3,1, 0, -4, 5, 9, 3 k = 5: -3,1,0, -4, 5, 3, 9 -3,1,0, -4,5,3,9 -3,0,1, -4,5,3,9 -3,0, -4,~, 3, 9 -3, 0, -4, 1, 5, 3, 9 -- k = 4 -3,0, -4, 1, 3, 5, 9 -4, 1, 3, 5, 9 -3, -4, 0,1,3,5,9 -3, O,~, 5, 9 k = 3: -4, 0,1,3,5,9 -4, -3,0,1,3,5,9 -3,~, 3, 5, 9 k = 2: k = 1: -4, -3,0, 1, 3, 5, 9
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## This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.

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