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Solved: Big-O, big-Theta, And big-Omega notation can be
Chapter 2, Problem 55E(choose chapter or problem)
Show that \(\lfloor x y\rfloor\) is \(O(x y)\).
Equation Transcription:
Text Transcription:
⎣xy⎦
O(xy)
Questions & Answers
QUESTION:
Show that \(\lfloor x y\rfloor\) is \(O(x y)\).
Equation Transcription:
Text Transcription:
⎣xy⎦
O(xy)
ANSWER:
Solution:
Step 1:
In this problem we need to show that
Note:
Let us consider f and g are functions from the set of integers to the set of real numbers.
The estimate value can be said that f(x) is O(g(x)) if there are constants C and k such that
, where C > 0 and x> k.The constants C and k are called the witnesses to the relationship.
The definition of f(x) is O(g(x)) says that f(x) grows slower than some fixed multiple of g(x) as x grows without bound.