The n-puzzle is a one-person game that

involves a square or rectangular frame that can contain exactly square tiles.

The game begins with n tiles numbered from 1 to n positioned randomly in the

frame. With one empty space in the frame, the objective is to slide the

tilesone at a time and either horizontally or verticallyuntil they appear in

numerical order, as shown in Figure 29-25a. This solved configuration is for a

15-puzzle using a 4-by-4 frame.

Figure 29-25

Not all initial configurations of an

n-puzzle can be solved. For example, if the initial configuration of a

15-

The n-puzzle is a one-person game that

involves a square or rectangular frame that can contain exactly square tiles.

The game begins with n tiles numbered from 1 to n positioned randomly in the

frame. With one empty space in the frame, the objective is to slide the

tilesone at a time and either horizontally or verticallyuntil they appear in

numerical order, as shown in Figure 29-25a. This solved configuration is for a

15-puzzle using a 4-by-4 frame.

Figure 29-25

Not all initial configurations of an

n-puzzle can be solved. For example, if the initial configuration of a

15-puzzle were as pictured in Figure 29-25b, with only the 14 and 15 tiles

interchanged, no solution would be possible. A solvable 15-puzzle can take up

to 80 moves to reach the solution; an 8-puzzle using a frame will take at most

31 moves to solve, if it has a solution. To reduce our effort even further, we

will consider 5-puzzles in frames. Figure 29-25 shows two such puzzles with

their solutions. Note that the empty space in a solution can be either before

the 1 or after the 5. Figure 24-23 in Chapter 24 showed a game tree for

tic-tac-toe. A game tree, which is a kind of graph, contains the possible moves

for a particular game. Because you cannot change a move made in tic-tac-toe,

the game tree is a directed graph. Such is not the case for the n-puzzle, as

you can change your mind about any move. Thus, an undirected graph can

represent all of the possible moves. Write Java code that creates an undirected

graph of the possible board configurations for the 5- puzzle. Using a

shortest-path search, find a solution to any given initial configuration.

Figure 29-26

The initial and final configurations of two

5-puzzles

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