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Growth of Functions: Asymptotic Notations Direct Address Tables Hashing

Growth of Functions: Asymptotic Notations Direct Address Tables Hashing. מושגים O   (Asymptotic Notation). הגדרה : T(n)=O(g(n)) אם קיים n 0 וקבוע C>0 כך שלכל n  n 0 מתקיים T(n) Cg(n) דוגמא : 4 n 100+ =O(n) 4n+100  Cn C4+100/n n 0 =100 , C=5.

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Growth of Functions: Asymptotic Notations Direct Address Tables Hashing

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  1. Growth of Functions: Asymptotic Notations • Direct Address Tables • Hashing

  2. מושגים O(Asymptotic Notation) הגדרה: T(n)=O(g(n))אם קיים n0 וקבוע C>0 כך שלכל n  n0מתקיים T(n)Cg(n) דוגמא: 4n100+=O(n) 4n+100  Cn C4+100/n n0=100 , C=5

  3. מושגים Oמהו הנכון? 3n+1 = O(n2) (n+1)2=O(n2) (n+1)2=O(n) 8=O(1) log(n)=O(n) nlog(n)=O(n)

  4. מושגים O(Asymptotic Notation) הגדרה: T(n)=  (g(n))אם קיים n0 וקבוע C>0 כך שלכל n  n0מתקיים T(n)Cg(n) דוגמא: 4n100+= (n) 4n+100 Cn C  4+100/n n0=1 , C=4

  5. מושגים Oמהו הנכון? 3n+1 = (n2) (n+1)2= (n2) (n+1)2= (n) 8= (1) log(n)= (n) nlog(n)= (n)

  6. מושגים O(Asymptotic Notation) הגדרה: T(n)= (g(n))אם קיים n0 וקבועים C1,C2>0 כך שלכל n  n0מתקיים C1g(n)  T(n)C2g(n) דוגמא: 4n100+= (n) C1 n  4n+100 C2n C24+100/n C1 4+100/n n0=100 , C2=5, C1=4

  7. מושגים Oמהו הנכון? 3n+1 =  (n2) (n+1)2=  (n2) (n+1)2=  (n) 8=  (1) log(n)=  (n) nlog(n)=  (n)

  8. תכונות של O A={O} 1) Transitivity: if f(n)=A(g(n)) and g(n)=A(h(n)) then f(n)=A(h(n)) 2) Reflexivity: f(n)=A(f(n)) 3) Symmetry: if f(n)= (g(n)) then g(n)= (f(n)) 3’) Transpose symmetry: if f(n)= O(g(n)) then g(n)=  (h(n))

  9. דוגמא:

  10. דוגמא:

  11. דוגמא: פעולות על רשימה. זמני ריצהL={x1,x2,…, xn} ListSearch(value):Ptr Ptr x  Head() While (not Outside(x)) and Key(x) <> value x  Next(x) (worst case:) If Outside(x)  (n) Return nil Else Return x

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