CSCI3136: Principles of Programming Languages - IT Assignment Help

Assignment Task

Rush Hour 

Rush Hour is an entertaining puzzle game. You are given a 6 × 6 grid with cars (horizontal or vertical 3 × 1 or 2 × 1 rectangles) placed on it. From here on, I call this grid the board because the original Rush Hour game was a board game. The board is enclosed by walls, but there is an opening on the right side of the third row: 

Horizontal cars are allowed to move left and right but only as far as they can go without hitting other cars or the wall. (“Hit” means “occupy the same grid cell as”.) Vertical cars are allowed to move up and down subject to the same rules. By moving cars out of the way, you create new possible moves for other cars. The third row has a single horizontal 2 × 1 car on it. In the example above, this car is red. Your goal is to find the shortest sequence of moves that allows the red car to move through the gap on the right of the third row. A single move moves a single horizontal car left or right or a single vertical car up or down. Whether you move this car by 1, 2, 3 or 4 positions is unimportant; it still counts as only one move as long as the move is legal (does not hit the wall or other cars). Since the board is a 6 × 6 grid and every car is at least 2 cells long, no car can legally move by more than 4 positions. 

To simplify the computational modelling of the problem, we will consider the red car to be free if it is in the 5th and 6th columns, that is, its right end is right next to the opening in the wall. Clearly, if we can move the red car to this position, we can also move it through the opening without any additional moves. The following is a possible solution state reachable from the state above.

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