Lecture 16: Midterm Test Review

October 31, 2016

data structures |

Problem 1: Induction Proof

Base case:

Is one node a perfect binary tree? Yes. 1 node. Is it odd? Yes.

Assume this holds true for values k = 1 to N.

You need to add a full row of nodes at the bottom. So we need to add twice the number of elements, an even number.

So you’d have an odd number plus an even number; an

Problem 2

a. Binary search, searching a well balanced binary tree b. … c. Popping from a stack, assigning to head in LinkedList d. Towers of Hanoi and Fibonnaci recursively

Problem 3

Stack. Straightforward.

Problem 4

Given postorder traversal or tree and inorder traversal, uniquely reconstruct the tree.

  • Root has to be the A
  • Locate that node in the inorder traversal and realize that all nodes to the left are on the left side of the tree. Same for those on the right.
  • Look at the postorder for those on the left and you can find the root
  • Do the same for the right

Problem 5

Pretty much 100% correct. Didn’t really need to check if both left and right are null, can leave that out.

Problem 6

Problem 7

Alex Scott If you're a nerd, I'm a nerd.
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