algorithm - Solving the recurrence T(n) = T(n / 2) + O(1) using the Master Theorem? -


i'm trying solve recurrence relation find out complexity of algorithm using master theorem , recurrences concepts, how can prove that:

t(n) = t(n/2)+o(1)

is

t(n) = o(log(n)) ?

any explanation apprecciated!!

your recurrence is

t(n) = t(n / 2) + o(1)

since master theorem works recurrences of form

t(n) = at(n / b) + nc

in case have

  • a = 1
  • b = 2
  • c = 0

since c = logba (since 0 = log2 1), in case two of master theorem, solves θ(nc log n) = θ(n0 log n) = θ(log n).

hope helps!


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