# A* Solution to the Traffic Jam Game

### About A*

The A* search algorithm is a search algorithm that uses a heuristic to estimate the cost of taking a given path in the solution tree to the goal state. The cost is calculated by adding the g + h values. The g value is the cost in steps to get to the current state and the h value is the estimated distance from the solution. For the algorithm to work correctly the heuristic must be at best an underestimate of the actual distance from a solution.

### How the Code Works

The actual A* search is only a few lines of code. It first takes a board node from the top of the priority queue, if the node is a goal node the algorithm quits, if not it expands all of the board conconfigurations that are reachable from the current board node and adds then to the queue(after checking to make sure that the board node has not been explored). The process is repeated until the queue is emptied or a solution is found. In the event that the queue is emptied it signals that there is no solution.

The implementation used generates board configurations and then adds then to board nodes. Each board has the ability to calculate its heuristic, generate all moves that can be made, generate a hash, and determine if the board is at a goal state. To determine if a board is at a goal state the method isGoal checks to make sure there are spaces before the car trying to exit and the exit. The heuristic is determined by adding the number of spaces that are blocked in front of the car trying to exit.

The driver program can take an integer command line argument from 1-10 that will use a stored board to solve. The boards range in complexity, with numbers closer to 10 being harder to solve. All of the boards are solvable though.

### Source Code

The source code for the program can be downloaded here: Rush Hour Code