Use a recursion tree to determine a good asymptotic upper bound on the recurrence . Use the substitution method to verify your answer.
Rate of increase in number of subproblems in each recursion = 1 Rate of decrease in subproblem size = 2
Hence in each level of the tree, there is only one node of cost at depth .
Hence, total cost of the tree is:
The last step comes from the fact that the sum is independent of , resulting in a constant factor.
Now we have to show that our guess holds using the substitution method.
The last step holds as long as , i.e. .