### Prove by induction of recurrence relation has solution

Assignment Help Basic Computer Science
##### Reference no: EM1348084

Q1) Kim has a great idea. He ?gures that if his classmates don't like red-black trees, then they may be more interested in his own new creation: wimpy-red-black trees, or WRB-trees for short. Kim has de?ned them similarly to red-black trees except that instead of requiring that:

"Every red node has both children black."
he requires that:

"No red node may have a red sibling or a red child."

Kim ?rst analyzes the most number of nodes M(k) that an WRB-tree can have if every path from the root to a leaf has k black internal nodes. He discovers that M(k) is de?ned by the recurrence relation:

M(0) = 0
M(k) = 2 + 3M(k - 1) for k > 0.

a. Describe why Kim's recurrence relation is correct.

b. Prove by induction that Kim's recurrence relation has solution: M(k) = 3^(k - 1)

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