Question

use this forum to discuss homework and material related to recursion and recurrence relations. some prompts for discussion: for those of you who have taken programming classes, how have you used recursion to solve problems? how can an understanding of recursion help make one a better programmer? you need to do initial posting before you can see responses from your peers. see the rubric below.

Answer 1

Recurrence relations can be resolved using the Recursion Tree Method. Recursive trees are created using this method from a recurrence relation.

Each node reflects the expense incurred at different recursive levels. The overall cost is calculated by adding the costs from each level.

20 nodes at level 0 are equal to one.

21 + 2 Equals number of nodes at level 1.

Number of nodes at level 2log10/9(n), which is equal to nlog10/9 (2)

nlog10/9(2) x T(1) = nlog10/9(2) x 1 = nlog10/9 Cost of subproblems at level log2(n) (last level) (2)

Step 4: Add up all of the levels' costs in the recursive tree.

T(n) = n times (number of levels - 1) plus the cost of the last level.

= log10/9(n) times + (nlog10/9(2)) = n + n + n + —-

= (nlog10/9(2)) + nlog10/9(n)

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