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Discrete Mathematics with Graph Theory (3rd Edition) 240

# Discrete Mathematics with Graph Theory (3rd Edition) 240 -...

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238 Solutions to Exercises (c) t Penn{t} j m S 17 341 2 3 2 {3,4,2Y = {I} 7f17f27f37f4 18 342 1 1 4 {4}C = {1,2,3} 7f17f27f37f4 19 4 1 2 3 3 3 {4, 1, 3}C = {2} 7f17f27f37f4 20 4 1 3 2 2 2 {4, 2Y = {I, 3} 7f17f27f37f4 21 4 2 1 3 3 3 {4,2,3}C = {I} 7f17f27f37f4 22 423 1 2 3 {4,3}C = {I, 2} 7f17f27f37f4 23 4 3 1 2 3 2 {4,3,2}C = {I} 7f17f27f37f4 24 432 1 2. (a) 12345 12354 12435 12453 12534 (b) [BB] 42531,43125,43152,43215,43251 3. 12543 13245 13254 13425 13452 (c) 41532,42135,42153,42315,42351 13524 13542 14235 14253 14325 14352 14523 14532 15234 15243 (a) [BB] We consider each part of Step 2. Finding the largest j such that 7f j < 7f i+ 1 requires at most n comparisons. At most another n comparisons are needed to find the minimum of {7fi I i < j, 7fi > 7fj}. To find the complement of a subset A of {I, 2, ... , n} requires searching A for each of the elements 1,2, ... , n and noting those which are not in A. Using the efficient binary search, each search is 0 (log2 n), adding another n 10g2
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