specification and complexity - algorithm
TRANSCRIPT
Algorithm Specification and Complexity
Algorithm Criteria Every Algorithm must have satisfied following
Criteria:
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Algorithm Specification
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Algorithm Specification (Cont.)
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Algorithm Specification (Cont.)
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Algorithm Specification (Cont.)
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Algorithm Time ComplexityAsymptotic Notations
, O,
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(Theta) (Average Case)
(Big-oh) (Worst Case)(Upper Bound)
(Omega) (Best case)(Lower Bound)
Algorithm Time Complexity (Cont.)
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Example: f(n) = 3n2 + 17
(1), (n), (n2) lower bounds
O(n2), O(n3), ... upper bounds
(n2) exact bound
Algorithm Time Complexity (Cont.)
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Examples (For Practices):
3n+2=O(n) /* 3n+24n for n2 */
3n+3=O(n) /* 3n+34n for n3 */
100n+6=O(n) /* 100n+6101n for n10 */
10n2+4n+2=O(n2) /* 10n2+4n+211n2 for n5 */
6*2n+n2=O(2n) /* 6*2n+n2 7*2n for n4 */
Algorithm Time Complexity (Cont.)
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Relations Between , , O:
Theorem : For any two functions g(n) and f(n), f(n) = (g(n)) if
f(n) = O(g(n)) and f(n) = (g(n)).
I.e., (g(n)) = O(g(n)) (g(n))
In practice, asymptotically tight bounds are obtained from asymptotic upper and lower bounds.
Algorithm Space Complexity S(P)=C+SP(I)
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Fixed Space Requirements (C)Independent of the characteristics of the inputs and outputs instruction space space for simple variables, fixed-size structured variable,
constants Variable Space Requirements (SP(I))
depend on the instance characteristic I number, size, values of inputs and outputs associated with
I recursive stack space, formal parameters, local variables,
return address
Any Questions?????
Thanks To Everybody
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