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hw2-s10-rec1a-soln

# hw2-s10-rec1a-soln - Problem Rec1a We can find the order...

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Problem Rec1a: We can find the order class of through substitution. At i = 2, . At i = 3, T n ( ) = 2 T n 8 Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ + lg n 4 Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ + lg n 2 + lg n = T n 8 Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ + lg n 4 + lg n 2 + lg n . In general, then, T n ( ) = T n 2 i Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ + lg n 2 k Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ k = 0 i 1 = T 1 ( ) + lg n lg2 k ( ) k = 0 i 1 = T 1 ( ) + lg n k ( ) k = 0 i 1 = T n 2 i Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ + i lg n k k = 0 i 1 = T 1 ( ) + i lg n i i 1 ( ) 2 Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ . Since our base case is T (1) = 1, we stop substituting when

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hw2-s10-rec1a-soln - Problem Rec1a We can find the order...

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