Question

1. If T is a tree with 999 vertices, then T has_edges (5 pts) 2. There are 3. The best comparison-based sorting algorithms for a list of n items have complexity ). (5 pts) 4. If T is a binary tree with 100 vertices, its minimum height is 5. If T is a full binary tree with 101 vertices, its maximum height is 6. If T is a full binary tree with 50 leaves, its minimum height is 7. Every full binary tree with 61 vertices has 8. Every full binary tree with 50 leaves has full binary trees with six vertices (10 pts) (5 pts) (5 pts) (5 pts) leaves (5 pts) vertices (5 pts)

Answer 1

ans 1 .

Total number of vertices = total edge + 1;

so T has 998 edge.

Ans 2.

zero full binary tree .

Internal nodes is I = (N – 1)/2

you cant take 2.5 internal node

Ans 3.

O(n log(n))

Ans 4.

6.

?log₂n?

or

?log₂n+1??1

Ans 5.

The number of node n the complete binary tree in between2^h (min) and 2^(h+1)-1 max

Ans 6.

5

leaf node in full binary tree is 2^h.

Ans 7.

The number of leaf nodes in a full binary tree with n nodes is equal to (n+1)/2.

31

Ans 8.

50 leaves so internal is 50-1

total 99;