So, we can move Right or Down.Īgain we find the states obtained from (1).
We won't move Left as we were previously in that state. The next possible moves can be Left, Right or Down. We chose the state with minimum cost which is state (1). So states obtained after moving those moves are: 1 _ 3 4 1 3Īgain the total cost function is computed for these states using the method described above and it turns out to be 6 and 7 respectively. Now, the possible states that can be reached from initial state are found and it happens that we can either move _ to right or downwards. Total cost function f(n) is equal to 8 + 0 = 8. So total value for h(n) is 1 + 1 + 1 + 1 + 2 + 2 = 8. _ is 2 horizontal distance away and 2 vertical distance away. The above value is obtained, as 1 in the current state is 1 horizontal distance away than the 1 in final state. The cost function, g(n) = 0, as we are in the initial state h(n) = 8 So the total cost function f(n) is given by, f(n) = g(n) + h(n), where g(n) is the cost required to reach the current state from given initial stateįirst we find the heuristic value required to reach the final state from initial state. P and q are cell co-ordinates in the final state Where x and y are cell co-ordinates in the current state Let us consider the Manhattan distance between the current and final state as the heuristic for this problem statement. Given an initial state of 8-puzzle game and a final state of to be reached, find the most cost-effective path to reach the final state from initial state. The object is to move to squares around into different positions and having the numbers displayed in the "goal state".
polynomial-time bounded algorithm for Minimum Vertex CoverĪn 8 puzzle is a simple game consisting of a 3 x 3 grid (containing 9 squares).Lowest common ancestor of a Binary Tree.Algo:- Print a m*n matrix in square wise.Solving 8-puzzle problem using A* algorithm.A* Pathfinding through a maze with no obstacles.
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