heuristic search the location of the goal must be known prior to starting the search you must have heuristic that can be applied that will either under-estimate or provide an exact length of the path to the goal the better the heuristicthe better the hill climbing search algorithm hill climbing can perform well even in large search spaces hill climbing can handle infinite search branches if the heuristic can avoid them hill climbing may suffer from local maxima or peaks hill climbing may not find an optimal solution like breadth first search to implement hill climbing the alternative choices at each step are sorted according to the heuristic before they are placed on the stack otherwisethe code is exactly the same as that of depth first search closed knight' tour hill climbing can be used in solving the closed knight' tour problem solving this problem involves moving knight from the game of chess around chess board (or any size boardthe knight must be moved two squares followed by one square in the perpendicular directionforming an on the chessboard the closed knight tour problem is to find path that visits every location on the board through sequence of legal knight moves that starts and ends in the same location with no square being visited twice except the starting and ending location since we want to find path through the boardthe solution can be represented as path from start to finish each node in the path is move on the board move is valid if it is on the board and is not already in the path in this waythe board itself never has to be explicitly built generating possible moves for knight could be rather complex if you try to write code to deal with the edges of the board in generalwhen adjacent nodes have to be generated and special cases occur on boundariesit is far easier to generate set of possibly invalid moves along with the valid moves in the case of moving knight aroundthere are eight possible moves in the general case after generating all possible movesthe invalid moves are obvious and can be filtered out using this techniqueboundary conditions are handled in uniform manner once instead of with each separate possible move the code is much cleaner and the logic is much easier to understand figure provides solution to the closed knight' tour problem for board the tour starts in the lower left corner where two edges were not drawn so you can see where the tour began and ended while it was being computed the tour took few minutes to find using heuristic to sort the choices of next location least constrained heuristic was applied to sort the new choices before adding them to the stack the least constrained next choice was the choice that would have the most choices next sorting the next moves in this fashion avoids looking at paths that lead to dead ends by generally staying closer to the edges of the board where the next move has the most choices in other wordsit avoids moving to the middle this copy belongs to 'acha