CSC165H1 Lecture Notes - Inside Out Music, Natural Number, Precondition

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29 Oct 2012

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Fall 2011: write a detailed, structured proof that. Assume f : n r+ and g : n r+. Then c r+, b n, n n, n (cid:62) b g(n) (cid:54) c f (n). Let c0 r+ and b0 n be such that n n, n (cid:62) b0 g(n) (cid:54) c0 f (n). # show that g2 o(f 2): then c1 r+. Then b1 n. # because b0 n. Assume n n and n (cid:62) b1 = b0. Then g(n) (cid:54) c0 f (n) (because n (cid:62) b0), so g2(n) = g(n) g(n) (cid:54) (c0 f (n)) (c0 f (n)) = c2. Hence, n n, n (cid:62) b1 g2(n) (cid:54) c1 f 2(n). Then c r+, b n, n n, n (cid:62) b g2(n) (cid:54) c f 2(n). Therefore, g o(f ) g2 o(f 2). 0 f (n) f (n) = c1 f 2(n): prove that tbft(n) (n2), where bft is the algorithm below.

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CSC165H1 Lecture Notes - Inside Out Music, Natural Number, Precondition

CSC165H1 Full Course Notes

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