Question 1

Form a binary search tree from the words of the sentence This test is not so diﬃcult, using alphabetical order, inserting words in the order they appear in the sentence.

Accepted Answer

The follow...

Question 2

Find a minimum spanning tree in the following weighted graph using Prim's algorithm.

Accepted Answer

Prim's algorithm adds the edges {d, e} o...

Question 3

Perform a preorder, inorder, and postorder traversal of the rooted tree below.

Accepted Answer

The preorder traversal is a, b, e, f, j, k, c, d, g, h, i; the inorder traversal is $e , b , j , f , k , a , c , g , d , h , i$ and the postorder traversal is e, j, k, f, b, c, g, h, i, d, a.

Question 4

Is the code $\mathrm { A } : 11 , \mathrm {~B} : 10 , \mathrm { C } : 0$a prefix code?

Accepted Answer

This is a preﬁx code since the code for ...

Question 5

(a) Suppose that a full 3-ary tree has 100 internal vertices. How many leaves does it have? (b) Suppose that a full 4-ary tree has 100 leaves. How many internal vertices does it have?

Accepted Answer

(a) A full 3-ary tree with 100 internal vertices has l = (3 − 1) · 100 + 1 = 201 leaves. (b) A full 4-ary tree with 100 leaves has i = (100 − 1)/(4 − 1) = 33 internal vertices.

Question 6

Use a depth-ﬁrst search to ﬁnd a spanning tree of the following graph. Start at the vertex a, and use alphabetical order.

Accepted Answer

The edges produced b...

Question 7

Use backtracking to ﬁnd a sum of integers in the set {18, 19, 23, 25, 31} that equals 44.

Accepted Answer

We build the followi...

Question 8

Construct an expression tree for $( 3 + x ) - 5 \cdot y$ and write this expression is preﬁx form and postﬁx form.

Accepted Answer

The following tree represents the expres...

Question 9

Use Prim's algorithm to ﬁnd a minimum spanning tree for the following weighted graph. Use alphabetical

Accepted Answer

Prim's algorithm adds the edge...

Question 10

A tree has 99 edges. How many vertices does it have?

Accepted Answer

If a tree has e edge...

Question 11

Which of the following graphs are trees ? Explain your answers.
a)

b)

C)

Accepted Answer

The graph in part (a) is not connected, ...

Question 12

Is the code A: 111, B: 101, C: 011, D: 010, E: 10, F: 1101 a preﬁx code?

Accepted Answer

This is not a preﬁx ...

Question 13

How many nonisomorphic trees are there with four vertices? Draw them.

Accepted Answer

There are two nonisomorphic unrooted trees with four vertices, as shown.

Exam 11: Trees

Form a binary search tree from the words of the sentence This test is not so diﬃcult, using alphabetical order, inserting words in the order they appear in the sentence.

Correct Answer
verified
The follow...
View Answer

Find a minimum spanning tree in the following weighted graph using Prim's algorithm.

Correct Answer
verified
Prim's algorithm adds the edges {d, e} o...
View Answer

Perform a preorder, inorder, and postorder traversal of the rooted tree below.

Correct Answer
verified
The preorder traversal is a, b, e, f, j, k, c, d, g, h, i; the inorder traversal is \(e , b , j , f , k , a , c , g , d , h , i\) and the postorder traversal is e, j, k, f, b, c, g, h, i, d, a.

Is the code $\mathrm { A } : 11 , \mathrm {~B} : 10 , \mathrm { C } : 0$ a prefix code?

Correct Answer
verified
This is a preﬁx code since the code for ...
View Answer

(a) Suppose that a full 3-ary tree has 100 internal vertices. How many leaves does it have? (b) Suppose that a full 4-ary tree has 100 leaves. How many internal vertices does it have?

Correct Answer
verified
(a) A full 3-ary tree with 100 internal vertices has l = (3 − 1) · 100 + 1 = 201 leaves. (b) A full 4-ary tree with 100 leaves has i = (100 − 1)/(4 − 1) = 33 internal vertices.

Use a depth-ﬁrst search to ﬁnd a spanning tree of the following graph. Start at the vertex a, and use alphabetical order.

Correct Answer
verified
The edges produced b...
View Answer

Use backtracking to ﬁnd a sum of integers in the set {18, 19, 23, 25, 31} that equals 44.

Correct Answer
verified
We build the followi...
View Answer

Construct an expression tree for $( 3 + x ) - 5 \cdot y$ and write this expression is preﬁx form and postﬁx form.

Correct Answer
verified
The following tree represents the expres...
View Answer

Use Prim's algorithm to ﬁnd a minimum spanning tree for the following weighted graph. Use alphabetical

Correct Answer
verified
Prim's algorithm adds the edge...
View Answer

A tree has 99 edges. How many vertices does it have?

Correct Answer
verified
If a tree has e edge...
View Answer

Which of the following graphs are trees ? Explain your answers. a) b) C)

Correct Answer
verified
The graph in part (a) is not connected, ...
View Answer

Is the code A: 111, B: 101, C: 011, D: 010, E: 10, F: 1101 a preﬁx code?

Correct Answer
verified
This is not a preﬁx ...
View Answer

How many nonisomorphic trees are there with four vertices? Draw them.

Correct Answer
verified
There are two nonisomorphic unrooted trees with four vertices, as shown. 11eb49e0_d240_3ffb_b736_391c25b5bb9e_TB6843_00

Exam 11: Trees

Form a binary search tree from the words of the sentence This test is not so diﬃcult, using alphabetical order, inserting words in the order they appear in the sentence.

Correct AnswerverifiedThe follow...View AnswerShow Answer

Find a minimum spanning tree in the following weighted graph using Prim's algorithm.

Correct AnswerverifiedPrim's algorithm adds the edges {d, e} o...View AnswerShow Answer

Perform a preorder, inorder, and postorder traversal of the rooted tree below.

Correct AnswerverifiedThe preorder traversal is a, b, e, f, j, k, c, d, g, h, i; the inorder traversal is \(e , b , j , f , k , a , c , g , d , h , i\) and the postorder traversal is e, j, k, f, b, c, g, h, i, d, a.

Is the code A:11, B:10,C:0\mathrm { A } : 11 , \mathrm {~B} : 10 , \mathrm { C } : 0A:11, B:10,C:0 a prefix code?

Correct AnswerverifiedThis is a preﬁx code since the code for ...View AnswerShow Answer

(a) Suppose that a full 3-ary tree has 100 internal vertices. How many leaves does it have? (b) Suppose that a full 4-ary tree has 100 leaves. How many internal vertices does it have?

Correct Answerverified(a) A full 3-ary tree with 100 internal vertices has l = (3 − 1) · 100 + 1 = 201 leaves. (b) A full 4-ary tree with 100 leaves has i = (100 − 1)/(4 − 1) = 33 internal vertices.

Use a depth-ﬁrst search to ﬁnd a spanning tree of the following graph. Start at the vertex a, and use alphabetical order.

Correct AnswerverifiedThe edges produced b...View AnswerShow Answer

Use backtracking to ﬁnd a sum of integers in the set {18, 19, 23, 25, 31} that equals 44.

Correct AnswerverifiedWe build the followi...View AnswerShow Answer

Construct an expression tree for (3+x)−5⋅y( 3 + x ) - 5 \cdot y(3+x)−5⋅y and write this expression is preﬁx form and postﬁx form.

Correct AnswerverifiedThe following tree represents the expres...View AnswerShow Answer

Use Prim's algorithm to ﬁnd a minimum spanning tree for the following weighted graph. Use alphabetical

Correct AnswerverifiedPrim's algorithm adds the edge...View AnswerShow Answer

A tree has 99 edges. How many vertices does it have?

Correct AnswerverifiedIf a tree has e edge...View AnswerShow Answer

Which of the following graphs are trees ? Explain your answers. a) b) C)

Correct AnswerverifiedThe graph in part (a) is not connected, ...View AnswerShow Answer

Is the code A: 111, B: 101, C: 011, D: 010, E: 10, F: 1101 a preﬁx code?

Correct AnswerverifiedThis is not a preﬁx ...View AnswerShow Answer

How many nonisomorphic trees are there with four vertices? Draw them.

Correct AnswerverifiedThere are two nonisomorphic unrooted trees with four vertices, as shown. 11eb49e0_d240_3ffb_b736_391c25b5bb9e_TB6843_00

Correct Answer
verified
The follow...
View Answer

Correct Answer
verified
Prim's algorithm adds the edges {d, e} o...
View Answer

Correct Answer
verified
The preorder traversal is a, b, e, f, j, k, c, d, g, h, i; the inorder traversal is \(e , b , j , f , k , a , c , g , d , h , i\) and the postorder traversal is e, j, k, f, b, c, g, h, i, d, a.

Is the code $\mathrm { A } : 11 , \mathrm {~B} : 10 , \mathrm { C } : 0$ a prefix code?

Correct Answer
verified
This is a preﬁx code since the code for ...
View Answer

Correct Answer
verified
(a) A full 3-ary tree with 100 internal vertices has l = (3 − 1) · 100 + 1 = 201 leaves. (b) A full 4-ary tree with 100 leaves has i = (100 − 1)/(4 − 1) = 33 internal vertices.

Correct Answer
verified
The edges produced b...
View Answer

Correct Answer
verified
We build the followi...
View Answer

Construct an expression tree for $( 3 + x ) - 5 \cdot y$ and write this expression is preﬁx form and postﬁx form.

Correct Answer
verified
The following tree represents the expres...
View Answer

Correct Answer
verified
Prim's algorithm adds the edge...
View Answer

Correct Answer
verified
If a tree has e edge...
View Answer

Correct Answer
verified
The graph in part (a) is not connected, ...
View Answer

Correct Answer
verified
This is not a preﬁx ...
View Answer

Correct Answer
verified
There are two nonisomorphic unrooted trees with four vertices, as shown. 11eb49e0_d240_3ffb_b736_391c25b5bb9e_TB6843_00