Recursion Tree Method1. Recursion Tree Method is a pictorial representation of an iteration method which is in the form of a tree where at each level nodes are expanded. 2. In general, we consider the second term in recurrence as root. 3. It is useful when the divide & Conquer algorithm is used. 4. It is sometimes difficult to come up with a good guess. In Recursion tree, each root and child represents the cost of a single subproblem. 5. We sum the costs within each of the levels of the tree to obtain a set of prelevel costs and then sum all prelevel costs to determine the total cost of all levels of the recursion. 6. A Recursion Tree is best used to generate a good guess, which can be verified by the Substitution Method. Example 1 Consider T (n) = 2T + n^{2} We have to obtain the asymptotic bound using recursion tree method. Solution: The Recursion tree for the above recurrence is Example 2: Consider the following recurrence T (n) = 4T +n Obtain the asymptotic bound using recursion tree method. Solution: The recursion trees for the above recurrence Example 3: Consider the following recurrence Obtain the asymptotic bound using recursion tree method. Solution: The given Recurrence has the following recursion tree When we add the values across the levels of the recursion trees, we get a value of n for every level. The longest path from the root to leaf is
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