big o - solving recurrence T(n) = T(n/2) + T(n/2 - 1) + n/2 + 2 -
need on solving runtime recurrence, using big-oh:
t(n) = t(n/2) + t(n/2 - 1) + n/2 + 2
i don't quite how use master theorem here
for n big enough can assume t(n/2 - 1) == t(n/2)
, can change
t(n) = t(n/2) + t(n/2 - 1) + n/2 + 2
into
t(n) = 2*t(n/2) + n/2 + 2
and use master theorem (http://en.wikipedia.org/wiki/master_theorem) for
t(n) = a*t(n/b) + f(n) = 2 b = 2 f(n) = n/2 + 2 c = 1 k = 0 log(a, b) = 1 = c
and have (case 2, since log(a, b) = c
)
t(n) = o(n**c * log(n)**(k + 1)) t(n) = o(n * log(n))
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