Unformatted text preview: →Ν #L.0 #L(d, ∅ , ∅ )=l. #L.1 #L(d,t1,t2)= #L(t1)+ #L(t2)) The number of internal nodes of a binary tree, #I:: t →Ν #I.0 #I(d, ∅ , ∅ )=0. #I.1 #I(d,t1,t2)= #I(t1)+ #I(t2) +1 DEFINITIONS Let f and g be functions from N to R. Then f is asymptotically dominated by g (we say that f is O(g)) iff ( ∃ C,k: ( ∀ x x>k: f(x) ≤ Cg(x))) Let f and g be functions from N to R. Then f asymptotically dominates g (we say that f is Ω (g)) iff ( ∃ C,k: ( ∀ x x>k: f(x) ≥ Cg(x))) Let f and g be functions from N to R. If f is O(g)) and f is Ω (g)) then f is of order of g and we say f is Θ (g). ( Σ i 1 ≤ i ≤ n:i) = n(n+1)/2 ( Σ i 0 ≤ i ≤ n:a i ) = (a n+11)/(a1)...
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This note was uploaded on 11/30/2010 for the course CS 336 taught by Professor Myers during the Fall '08 term at University of Texas.
 Fall '08
 Myers

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