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...