Use a recursion tree to determine a good asymptotic upper bound on the recurrence T(n) = 4T(n/2 + 2) + n. Use the substitution method to verify your answer.

Follows are the solution to this question:

Explanation:

The scale of the subproblem for a node is  at depth.  

The tree then has lg n + 1 and leaves.  

Complete costs for all depth I nodes for I = 0. 1 , 2, ......, lg n-1 is:

verfify the value:

Where there is the last stage for  .

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