Let f (n) and g(n) be asymptotically nonnegative functions. Using the basic definition of _-notation, prove that max( f (n), g(n)) = Θ( f (n) + g(n)).
`Hey,
Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.
We can write
f(n)+g(n)=<max(f(n),g(n))
Also, we can write
max(f(n),g(n))<=2*(f(n)+g(n))
So, combining
f(n)+g(n)=<max(f(n),g(n))<=2*(f(n)+g(n))
So, we found c1=1 and c2=2
So,
by definition of big theta
max(f,g)=theta(f(n)+g(n))
Kindly revert for any queries
Thanks.
Let f (n) and g(n) be asymptotically nonnegative functions. Using the basic definition of _-notation, prove...
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