Building an 8-puzzle solver

8-puzzle is a variant of the 15-puzzle. You can check it out at  https://en.wikipedia.org/wiki/15_puzzle. You will be presented with a randomized grid and your goal is to get it back to the original ordered configuration. You can play the game to get familiar with it at  http://mypuzzle.org/sliding .

We will use an A* algorithm to solve this problem. It is an algorithm that's used to find paths to the solution in a graph. This algorithm is a combination of Dijkstra's algorithm and a greedy best-first search. Instead of blindly guessing where to go next, the A* algorithm picks the one that looks the most promising. At each node, we generate the list of all possibilities and then pick the one with the minimal cost required to reach the goal.

Let's see how to define the cost function. At each node, we need to compute the cost. This cost is basically the sum of two costs - the first cost is the cost of getting to the current node and the second cost is the cost of reaching...