Lex 7: Trees

1. Consider tree T1:
   

                     root: a
            children of a: q _
            children of q: p c
            children of c: b e
            children of b: _ d
           

   
   

   Show the contents of a one-array implementation of the tree. Start with element 0 of the array. Put exactly one space between array elements. If an array element is empty indicate it with an underscore, i.e., "_". All letters should be lowercase.
   

2. Consider tree T1 above
   

   Show the contents of a three-array implementation of the tree.
   

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3. Consider k-ary tree T2:
   

                     root: a
            children of a: b c  d
            children of b: e
            children of c: f g
            children of d: h i j k
            children of h: l m n  
           

   
   

   Convert the k-ary tree to a binary tree T3. Then answer the following questions about T3.
   

   What is the height of T3?
   

4. In T3, what is the depth of node k? Should be a non-negative int. Do not start with a space.
   

5. In T3, what is the height of node f? Should be a non-negative int. Do not start with a space.
   

6. How many leaves does T3 have?
   

7. How many interior nodes does T3 have?
   

8. How many T3 nodes have exactly one child? Should be a non-negative int. Do not start with a space.
   

9. In what sequence are T3 nodes visited in a preorder traversal of the tree?
   

10. In what sequence are T3 nodes visited in an inorder traversal of the tree? Do not start with a space. Put exactly one space between to letters. All letters should be lowercase.
    

11. In what sequence are T3 nodes visited in a postorder traversal of the tree?
    

12. Which nodes are the proper ancestors of T3 node n?
13. Which nodes are the descendants of T3 node f?

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