a. State space diagram: The state space of start state number 1 and the successor function for state ‘k’ returns two states, numbers 2k and 2k+1. So, if the start state is 1, then it will have two states 2(1)=2 and 2(1)+1=3. For each state, till 15 the corresponding states are obtained from the functions 2k and 2k+1...

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Answer 1

Expert Solution & Answer

Chapter 3, Problem 15E

Explanation of Solution

a.

State space diagram:

The state space of start state number 1 and the successor function for state ‘k’ returns two states, numbers 2k and 2k+1.

So, if the start state is 1, then it will have two states 2(1)=2 and 2(1)+1=3.

For each state, till 15 the corresponding states are obtained from the functions 2k and 2k+1...

Explanation of Solution

b.

Breadth first search:

The breadth first search begins from the root node, then examines the neighbouring nodes and travels to the next level neighbours.

Until the solution is found, the breadth first search creates one tree at a time.

Using the FIFO queue data form, the breadth first search algorithm can be applied. This approach provides the shortest path of the solution.

It expands the shallowest nodes first if the goal state is 11, the order in which the nodes will be visited for breadth first search is

1 →2→3→4→5→6→7→8→9→10→11

Depth limit search:

To prevent the infinite loop in depth first search, it is conducted with a fixed depth limit in depth dependent search technique.

The depth limit search checks for the solution up to a specified depth...

Explanation of Solution

c.

bidirectional search for the problem:

The idea of a bidirectional search is to reduce the search time by simultaneously searching forward from the beginning and back from the goal.

For the given problem, the bidirectional search would work because, the only successor for “n” in the reverse direction floor of (n/2).

Branching factor:

Consider that the breadth first search is done in both forward direction and backward direction, the search node will be as follows,

Consider the visited node as 1, then the forward fringe will be node {2,3}...

Explanation of Solution

“yes”, the reformulation is the branching factor for moving forward is 2. And moving backward is 2...

Explanation of Solution

Explanation of algorithm for the problem and its solution:

The solution for the target number can be read off the binary number.

Write the binary target number.

Since the user can enter only positive integer numbers, these binary expansion being have a 1...

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Students have asked these similar questions

For problem 1, you should provide a list of numbers of states for each of the search methods. Problem 1 In the state space shown below ( refer to image ), write the order in which states are expanded if the initial state is 4 and there are two goal states: 5 and 8. For example, for breadth first search the answer would be: 4 2 7 1 3 6 8 using depth-first search using iterative deepening.

Consider a state space where the start state is number 1 and each state k has two successors: numbers 2k and 2k+1. 1. Draw the portion of the state space for states 1 to 15. 2. Suppose the goal state is 11. List the order in which nodes will be visited for breadth-first search, depth-limited search with limit 3, and iterative deepening search. 3. How well would bidirectional search work on this problem? What is the branching factor in each direction of the bidirectional search? 4. Does the answer to (c) suggest a reformulation of the problem that would allow you to solve the problem of getting from state 1 to a given goal state with almost no search? 5. Call the action going from k to 2k Left, and the action going to 2k+1 Right. Can you find an algorithm that outputs the solution to this problem without any search at all?

The diagram below shows a search space in which the initial state is List the states in the order in which they would be explored in a depth-first search Given that the goal state is H, show the current state, and open and closed lists, at each iteration of a breadth-first search to locate the goal state. State the main advantage of breadth-first search and give the reason for this advantage. List the states in the order in which they would be explored in a iterative deepening search.

Answer 2

Expert Solution & Answer

Chapter 3, Problem 15E

Explanation of Solution

a.

State space diagram:

The state space of start state number 1 and the successor function for state ‘k’ returns two states, numbers 2k and 2k+1.

So, if the start state is 1, then it will have two states 2(1)=2 and 2(1)+1=3.

For each state, till 15 the corresponding states are obtained from the functions 2k and 2k+1...

Explanation of Solution

b.

Breadth first search:

The breadth first search begins from the root node, then examines the neighbouring nodes and travels to the next level neighbours.

Until the solution is found, the breadth first search creates one tree at a time.

Using the FIFO queue data form, the breadth first search algorithm can be applied. This approach provides the shortest path of the solution.

It expands the shallowest nodes first if the goal state is 11, the order in which the nodes will be visited for breadth first search is

1 →2→3→4→5→6→7→8→9→10→11

Depth limit search:

To prevent the infinite loop in depth first search, it is conducted with a fixed depth limit in depth dependent search technique.

The depth limit search checks for the solution up to a specified depth...

Explanation of Solution

c.

bidirectional search for the problem:

The idea of a bidirectional search is to reduce the search time by simultaneously searching forward from the beginning and back from the goal.

For the given problem, the bidirectional search would work because, the only successor for “n” in the reverse direction floor of (n/2).

Branching factor:

Consider that the breadth first search is done in both forward direction and backward direction, the search node will be as follows,

Consider the visited node as 1, then the forward fringe will be node {2,3}...

Explanation of Solution

“yes”, the reformulation is the branching factor for moving forward is 2. And moving backward is 2...

Explanation of Solution

Explanation of algorithm for the problem and its solution:

The solution for the target number can be read off the binary number.

Write the binary target number.

Since the user can enter only positive integer numbers, these binary expansion being have a 1...

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Expert Solution & Answer

Chapter 3, Problem 15E

Explanation of Solution

a.

State space diagram:

The state space of start state number 1 and the successor function for state ‘k’ returns two states, numbers 2k and 2k+1.

So, if the start state is 1, then it will have two states 2(1)=2 and 2(1)+1=3.

For each state, till 15 the corresponding states are obtained from the functions 2k and 2k+1...

Explanation of Solution

b.

Breadth first search:

The breadth first search begins from the root node, then examines the neighbouring nodes and travels to the next level neighbours.

Until the solution is found, the breadth first search creates one tree at a time.

Using the FIFO queue data form, the breadth first search algorithm can be applied. This approach provides the shortest path of the solution.

It expands the shallowest nodes first if the goal state is 11, the order in which the nodes will be visited for breadth first search is

1 →2→3→4→5→6→7→8→9→10→11

Depth limit search:

To prevent the infinite loop in depth first search, it is conducted with a fixed depth limit in depth dependent search technique.

The depth limit search checks for the solution up to a specified depth...

Explanation of Solution

c.

bidirectional search for the problem:

The idea of a bidirectional search is to reduce the search time by simultaneously searching forward from the beginning and back from the goal.

For the given problem, the bidirectional search would work because, the only successor for “n” in the reverse direction floor of (n/2).

Branching factor:

Consider that the breadth first search is done in both forward direction and backward direction, the search node will be as follows,

Consider the visited node as 1, then the forward fringe will be node {2,3}...

Explanation of Solution

“yes”, the reformulation is the branching factor for moving forward is 2. And moving backward is 2...

Explanation of Solution

Explanation of algorithm for the problem and its solution:

The solution for the target number can be read off the binary number.

Write the binary target number.

Since the user can enter only positive integer numbers, these binary expansion being have a 1...

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Expert Solution & Answer

Chapter 3, Problem 15E

Explanation of Solution

a.

State space diagram:

The state space of start state number 1 and the successor function for state ‘k’ returns two states, numbers 2k and 2k+1.

So, if the start state is 1, then it will have two states 2(1)=2 and 2(1)+1=3.

For each state, till 15 the corresponding states are obtained from the functions 2k and 2k+1...

Explanation of Solution

b.

Breadth first search:

The breadth first search begins from the root node, then examines the neighbouring nodes and travels to the next level neighbours.

Until the solution is found, the breadth first search creates one tree at a time.

Using the FIFO queue data form, the breadth first search algorithm can be applied. This approach provides the shortest path of the solution.

It expands the shallowest nodes first if the goal state is 11, the order in which the nodes will be visited for breadth first search is

1 →2→3→4→5→6→7→8→9→10→11

Depth limit search:

To prevent the infinite loop in depth first search, it is conducted with a fixed depth limit in depth dependent search technique.

The depth limit search checks for the solution up to a specified depth...

Explanation of Solution

c.

bidirectional search for the problem:

The idea of a bidirectional search is to reduce the search time by simultaneously searching forward from the beginning and back from the goal.

For the given problem, the bidirectional search would work because, the only successor for “n” in the reverse direction floor of (n/2).

Branching factor:

Consider that the breadth first search is done in both forward direction and backward direction, the search node will be as follows,

Consider the visited node as 1, then the forward fringe will be node {2,3}...

Explanation of Solution

“yes”, the reformulation is the branching factor for moving forward is 2. And moving backward is 2...

Explanation of Solution

Explanation of algorithm for the problem and its solution:

The solution for the target number can be read off the binary number.

Write the binary target number.

Since the user can enter only positive integer numbers, these binary expansion being have a 1...

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Expert Solution & Answer

Answer 6

Expert Solution & Answer

Answer 7

Chapter 3, Problem 15E

Explanation of Solution

a.

State space diagram:

The state space of start state number 1 and the successor function for state ‘k’ returns two states, numbers 2k and 2k+1.

So, if the start state is 1, then it will have two states 2(1)=2 and 2(1)+1=3.

For each state, till 15 the corresponding states are obtained from the functions 2k and 2k+1...

Explanation of Solution

b.

Breadth first search:

The breadth first search begins from the root node, then examines the neighbouring nodes and travels to the next level neighbours.

Until the solution is found, the breadth first search creates one tree at a time.

Using the FIFO queue data form, the breadth first search algorithm can be applied. This approach provides the shortest path of the solution.

It expands the shallowest nodes first if the goal state is 11, the order in which the nodes will be visited for breadth first search is

1 →2→3→4→5→6→7→8→9→10→11

Depth limit search:

To prevent the infinite loop in depth first search, it is conducted with a fixed depth limit in depth dependent search technique.

The depth limit search checks for the solution up to a specified depth...

Explanation of Solution

c.

bidirectional search for the problem:

The idea of a bidirectional search is to reduce the search time by simultaneously searching forward from the beginning and back from the goal.

For the given problem, the bidirectional search would work because, the only successor for “n” in the reverse direction floor of (n/2).

Branching factor:

Consider that the breadth first search is done in both forward direction and backward direction, the search node will be as follows,

Consider the visited node as 1, then the forward fringe will be node {2,3}...

Explanation of Solution

“yes”, the reformulation is the branching factor for moving forward is 2. And moving backward is 2...

Explanation of Solution

Explanation of algorithm for the problem and its solution:

The solution for the target number can be read off the binary number.

Write the binary target number.

Since the user can enter only positive integer numbers, these binary expansion being have a 1...

Answer 8

Chapter 3, Problem 15E

Explanation of Solution

a.

State space diagram:

The state space of start state number 1 and the successor function for state ‘k’ returns two states, numbers 2k and 2k+1.

So, if the start state is 1, then it will have two states 2(1)=2 and 2(1)+1=3.

For each state, till 15 the corresponding states are obtained from the functions 2k and 2k+1...

Answer 9

Chapter 3, Problem 15E

Explanation of Solution

a.

State space diagram:

The state space of start state number 1 and the successor function for state ‘k’ returns two states, numbers 2k and 2k+1.

So, if the start state is 1, then it will have two states 2(1)=2 and 2(1)+1=3.

For each state, till 15 the corresponding states are obtained from the functions 2k and 2k+1...

Answer 10

Explanation of Solution

b.

Breadth first search:

The breadth first search begins from the root node, then examines the neighbouring nodes and travels to the next level neighbours.

Until the solution is found, the breadth first search creates one tree at a time.

Using the FIFO queue data form, the breadth first search algorithm can be applied. This approach provides the shortest path of the solution.

It expands the shallowest nodes first if the goal state is 11, the order in which the nodes will be visited for breadth first search is

1 →2→3→4→5→6→7→8→9→10→11

Depth limit search:

To prevent the infinite loop in depth first search, it is conducted with a fixed depth limit in depth dependent search technique.

The depth limit search checks for the solution up to a specified depth...

Answer 11

Explanation of Solution

b.

Breadth first search:

The breadth first search begins from the root node, then examines the neighbouring nodes and travels to the next level neighbours.

Until the solution is found, the breadth first search creates one tree at a time.

Using the FIFO queue data form, the breadth first search algorithm can be applied. This approach provides the shortest path of the solution.

It expands the shallowest nodes first if the goal state is 11, the order in which the nodes will be visited for breadth first search is

1 →2→3→4→5→6→7→8→9→10→11

Depth limit search:

To prevent the infinite loop in depth first search, it is conducted with a fixed depth limit in depth dependent search technique.

The depth limit search checks for the solution up to a specified depth...

Answer 12

Explanation of Solution

c.

bidirectional search for the problem:

The idea of a bidirectional search is to reduce the search time by simultaneously searching forward from the beginning and back from the goal.

For the given problem, the bidirectional search would work because, the only successor for “n” in the reverse direction floor of (n/2).

Branching factor:

Consider that the breadth first search is done in both forward direction and backward direction, the search node will be as follows,

Consider the visited node as 1, then the forward fringe will be node {2,3}...

Answer 13

Explanation of Solution

c.

bidirectional search for the problem:

The idea of a bidirectional search is to reduce the search time by simultaneously searching forward from the beginning and back from the goal.

For the given problem, the bidirectional search would work because, the only successor for “n” in the reverse direction floor of (n/2).

Branching factor:

Consider that the breadth first search is done in both forward direction and backward direction, the search node will be as follows,

Consider the visited node as 1, then the forward fringe will be node {2,3}...

Answer 14

Explanation of Solution

“yes”, the reformulation is the branching factor for moving forward is 2. And moving backward is 2...

Answer 15

Explanation of Solution

“yes”, the reformulation is the branching factor for moving forward is 2. And moving backward is 2...

Answer 16

Explanation of Solution

Explanation of algorithm for the problem and its solution:

The solution for the target number can be read off the binary number.

Write the binary target number.

Since the user can enter only positive integer numbers, these binary expansion being have a 1...

Answer 17

Explanation of Solution

Explanation of algorithm for the problem and its solution:

The solution for the target number can be read off the binary number.

Write the binary target number.

Since the user can enter only positive integer numbers, these binary expansion being have a 1...

Answer 18

Expert Solution & Answer

Answer 19

Expert Solution & Answer

Answer 20

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Check out a sample textbook solution

See solution

Answer 21

Ch. 3 - Explain why problem formulation must follow goal...Ch. 3 - Prob. 2E Ch. 3 - Prob. 3E Ch. 3 - Prob. 4E Ch. 3 - Prob. 5E Ch. 3 - Prob. 6E Ch. 3 - Prob. 8E Ch. 3 - Prob. 9E Ch. 3 - Prob. 10E Ch. 3 - Prob. 11E

Explanation of Solution

Explanation of Solution

Explanation of Solution

Explanation of Solution

“yes”, the reformulation is the branching factor for moving forward is 2. And moving backward is 2...

Explanation of Solution

Explanation of algorithm for the problem and its solution: The solution for the target number can be read off the binary number. Write the binary target number. Since the user can enter only positive integer numbers, these binary expansion being have a 1...

Want to see the full answer?

Chapter 3 Solutions

Explanation of algorithm for the problem and its solution:

The solution for the target number can be read off the binary number.

Write the binary target number.

Since the user can enter only positive integer numbers, these binary expansion being have a 1...