Question 1

If T is a binary tree with 100 vertices, its minimum height is .

Accepted Answer

The answer of If T is a binary tree with...

Question 2

(a) Set up a binary tree for the following list, in the given order, using alphabetical ordering: SHE, SELLS, SEA, SHELLS, BY, THE, SEASHORE.
(b) How many comparisons with words in the tree are needed to determine if the word SHARK is in the tree?
(c) How many comparisons with words in the tree are needed to determine if the word SEAWEED is in the tree?
(d) How many comparisons with words in the tree are needed to determine if the word SHELLS is in the tree?

Accepted Answer

(a) 11ec7c2d_2824_68

Question 3

Suppose that the universal address set address of a vertex v in an ordered rooted tree is 3.2.5.1.5. Find
(a) the level of v. (b) the minimum number of siblings of v.
(c) the address of the parent of v. (d) the minimum number of vertices in the tree.

Accepted Answer

The answer of Suppose that the universal address set address...

Question 4

If T is a tree, then its vertex-chromatic number is and its region-chromatic number is .

Accepted Answer

The answer of If T is a tree, then its...

Question 5

Prove that if T is a full m-ary tree with v vertices, then T has ((m − 1)v + 1)/m leaves.

Accepted Answer

The answer of Prove that if T is a full...

Question 6

If T is a full binary tree with 50 internal vertices, then T has vertices.

Accepted Answer

The answer of If T is a full binary tree...

Question 7

Find the preorder traversal of the parsing tree for $$( 8 x - y ) ^ { 5 } - 7 \sqrt { 4 z - 3 }$$

Accepted Answer

The answer of Find the preorder traversal of the parsing...

Question 8

Suppose you have 50 coins, one of which is counterfeit (either heavier or lighter than the others). You use a
pan balance scale to ﬁnd the bad coin. Prove that 4 weighings are not enough to guarantee that you ﬁnd the
bad coin and determine whether it is heavier or lighter than the other coins.

Accepted Answer

Four weighings yield a 3-ary t

Question 9

Write $3 n - ( k + 5 )$ in prefix notation:

Accepted Answer

The answer of Write \(3 n - ( k +...

Question 10

refer to this graph.  
-Using the ordering C, D, E, F, G, H, I, J, A, B, C, ﬁnd a spanning tree for this graph by using a depth-ﬁrst
search.

Accepted Answer

The answer of refer to this graph.  
-Using the...

Question 11

Find the postorder traversal of the parsing tree for $$( 8 x - y ) ^ { 5 } - 7 \sqrt { 4 z - 3 }$$

Accepted Answer

The answer of Find the postorder traversal of the parsing...

Question 12

mark the statement TRUE or FALSE.
-There is a tree with degrees 3, 2, 2, 2, 1, 1, 1, 1, 1.

Accepted Answer

A) True 
 B)False

Question 13

Write the compound proposition $$( \neg p ) \rightarrow ( q \vee ( r \wedge \neg s ) ) \text { in postfix notation. }$$

Accepted Answer

The answer of Write the compound proposition \[( \neg p...

Question 14

mark the statement TRUE or FALSE.
-Every tree is bipartite.

Accepted Answer

A) True 
 B)False

Question 15

mark the statement TRUE or FALSE.
-If T is a tree with 50 vertices, the largest degree that any vertex can have is 49.

Accepted Answer

A) True 
 B)False

Question 16

refer to this graph.  
-Using the ordering B, G, J, A, C, I, F, H, D, E, ﬁnd a spanning tree for this graph by using a depth-ﬁrst
search.

Accepted Answer

The answer of refer to this graph.  
-Using the...

Question 17

Find a spanning tree of minimum cost for this graph.

Accepted Answer

The answer of Find a spanning tree of minimum cost...

Question 18

mark the statement TRUE or FALSE.
-There is a tree with degrees 3, 3, 2, 2, 1, 1, 1, 1.

Accepted Answer

A) True 
 B)False

Question 19

Use the bubble sort to sort the list  5,2,3,1,4  in increasing order.

Accepted Answer

The answer of Use the bubble sort to sort the...

Question 20

There are non-isomorphic trees with four vertices.

Accepted Answer

The answer of There are non-isomorphic trees with four vertices....

If T is a binary tree with 100 vertices, its minimum height is .

Suppose that the universal address set address of a vertex v in an ordered rooted tree is 3.2.5.1.5. Find (a) the level of v. (b) the minimum number of siblings of v. (c) the address of the parent of v. (d) the minimum number of vertices in the tree.

If T is a tree, then its vertex-chromatic number is and its region-chromatic number is .

Prove that if T is a full m-ary tree with v vertices, then T has ((m − 1)v + 1)/m leaves.

If T is a full binary tree with 50 internal vertices, then T has vertices.

Find the preorder traversal of the parsing tree for $( 8 x - y ) ^ { 5 } - 7 \sqrt { 4 z - 3 }$

Suppose you have 50 coins, one of which is counterfeit (either heavier or lighter than the others). You use a pan balance scale to ﬁnd the bad coin. Prove that 4 weighings are not enough to guarantee that you ﬁnd the bad coin and determine whether it is heavier or lighter than the other coins.

Write $3 n - ( k + 5 )$ in prefix notation:

refer to this graph. -Using the ordering C, D, E, F, G, H, I, J, A, B, C, ﬁnd a spanning tree for this graph by using a depth-ﬁrst search.

Find the postorder traversal of the parsing tree for $( 8 x - y ) ^ { 5 } - 7 \sqrt { 4 z - 3 }$

mark the statement TRUE or FALSE. -There is a tree with degrees 3, 2, 2, 2, 1, 1, 1, 1, 1.

Write the compound proposition $( \neg p ) \rightarrow ( q \vee ( r \wedge \neg s ) ) \text { in postfix notation. }$

mark the statement TRUE or FALSE. -Every tree is bipartite.

mark the statement TRUE or FALSE. -If T is a tree with 50 vertices, the largest degree that any vertex can have is 49.

refer to this graph. -Using the ordering B, G, J, A, C, I, F, H, D, E, ﬁnd a spanning tree for this graph by using a depth-ﬁrst search.

Find a spanning tree of minimum cost for this graph.

mark the statement TRUE or FALSE. -There is a tree with degrees 3, 3, 2, 2, 1, 1, 1, 1.

Use the bubble sort to sort the list 5,2,3,1,4 in increasing order.

There are non-isomorphic trees with four vertices.

The Foundations: Logic and Proofs

Basic Structures: Sets, Functions, Sequences, Sums, Matrices

Algorithms

Number Theory and Cryptography

Induction and Recursion

Counting

Discrete Probability

Advanced Counting Techniques

Relations

Graphs

Boolean Algebra

Modeling Computation

Filters

Exam 11: Trees

If T is a binary tree with 100 vertices, its minimum height is .

Suppose that the universal address set address of a vertex v in an ordered rooted tree is 3.2.5.1.5. Find (a) the level of v. (b) the minimum number of siblings of v. (c) the address of the parent of v. (d) the minimum number of vertices in the tree.

If T is a tree, then its vertex-chromatic number is and its region-chromatic number is .

Prove that if T is a full m-ary tree with v vertices, then T has ((m − 1)v + 1)/m leaves.

If T is a full binary tree with 50 internal vertices, then T has vertices.

Find the preorder traversal of the parsing tree for (8x−y)5−74z−3( 8 x - y ) ^ { 5 } - 7 \sqrt { 4 z - 3 }(8x−y)5−74z−3​

Suppose you have 50 coins, one of which is counterfeit (either heavier or lighter than the others). You use a pan balance scale to ﬁnd the bad coin. Prove that 4 weighings are not enough to guarantee that you ﬁnd the bad coin and determine whether it is heavier or lighter than the other coins.

Write 3n−(k+5)3 n - ( k + 5 )3n−(k+5) in prefix notation:

refer to this graph. -Using the ordering C, D, E, F, G, H, I, J, A, B, C, ﬁnd a spanning tree for this graph by using a depth-ﬁrst search.

Find the postorder traversal of the parsing tree for (8x−y)5−74z−3( 8 x - y ) ^ { 5 } - 7 \sqrt { 4 z - 3 }(8x−y)5−74z−3​

mark the statement TRUE or FALSE. -There is a tree with degrees 3, 2, 2, 2, 1, 1, 1, 1, 1.

Write the compound proposition (¬p)→(q∨(r∧¬s)) in postfix notation. ( \neg p ) \rightarrow ( q \vee ( r \wedge \neg s ) ) \text { in postfix notation. }(¬p)→(q∨(r∧¬s)) in postfix notation.

mark the statement TRUE or FALSE. -Every tree is bipartite.

mark the statement TRUE or FALSE. -If T is a tree with 50 vertices, the largest degree that any vertex can have is 49.

refer to this graph. -Using the ordering B, G, J, A, C, I, F, H, D, E, ﬁnd a spanning tree for this graph by using a depth-ﬁrst search.

Find a spanning tree of minimum cost for this graph.

mark the statement TRUE or FALSE. -There is a tree with degrees 3, 3, 2, 2, 1, 1, 1, 1.

Use the bubble sort to sort the list 5,2,3,1,4 in increasing order.

There are non-isomorphic trees with four vertices.

The Foundations: Logic and Proofs

Basic Structures: Sets, Functions, Sequences, Sums, Matrices

Algorithms

Number Theory and Cryptography

Induction and Recursion

Counting

Discrete Probability

Advanced Counting Techniques

Relations

Graphs

Boolean Algebra

Modeling Computation

Filters

Find the preorder traversal of the parsing tree for $( 8 x - y ) ^ { 5 } - 7 \sqrt { 4 z - 3 }$

Write $3 n - ( k + 5 )$ in prefix notation:

Find the postorder traversal of the parsing tree for $( 8 x - y ) ^ { 5 } - 7 \sqrt { 4 z - 3 }$

Write the compound proposition $( \neg p ) \rightarrow ( q \vee ( r \wedge \neg s ) ) \text { in postfix notation. }$