![]() The rules also varied somewhat from region to region. The rules continued to be slightly modified until the early 19th century, when they reached essentially their current form. While the exact origins of chess are unclear, modern rules first took form during the Middle Ages. A game can end in various ways besides checkmate: a player can resign, and there are several ways a game can end in a draw. The object of the game is to checkmate the opponent's king checkmate occurs when a king is threatened with capture and has no escape. Each type of piece moves in a distinct way. Each player controls sixteen pieces of six types on a chessboard. Chess is a two-player abstract strategy board game. The rules of chess (also known as the laws of chess) govern the play of the game of chess. Left to right: king, rook, queen, pawn, knight, bishop If we have backtracked to the starting square and tried all possible moves without finding a solution, there is no solution to the problem.Staunton style chess pieces. ![]() If all moves have been tried from the current square and we have not found a solution, backtrack to the previous square and try a different move from there.Otherwise, undo the last move and try a different move. If all squares on the chessboard have been visited, we have found a solution.For each valid move from the current square, make the move and recursively repeat the process for the new square.Choose a starting square for the knight on the chessboard.Here's the basic outline of the backtracking algorithm to solve the Knight's tour problem: The backtracking algorithm works by exploring all possible moves for the knight, starting from a given square, and backtracking to try different moves if it reaches a dead end. Suppose we have a graph with five vertices and the following edges: Let's take an example of the Hamiltonian path problem. ![]() The Hamiltonian path problem is a well-known problem in graph theory that asks whether a given graph contains a path that visits every vertex exactly once.Ī path that visits every vertex exactly once is called a Hamiltonian path, and a graph that contains a Hamiltonian path is called a Hamiltonian graph. There is also a backtracking approach.īut first moving to all that, let's take a quick understanding of the Hamiltonian path problem. ![]() One popular solution to solve the Knight's tour problem is Warnsdorff's rule, which involves choosing the next move that leads to a square with the fewest available moves. The simple solution will be to find every conceivable configuration and selecting the best one is one technique to solve this problem. This problem has fascinated many mathematicians for centuries, but the solutions they found were very difficult. It is a type of Hamiltonian path problem in graph theory, where the squares represent the vertices and the knight's moves represent the edges of the graph. The Knight's Tour problem is about finding a sequence of moves for the knight on a chessboard such that it visits every square on the board exactly one time. This means it will first move two squares in one direction and then one square in a perpendicular direction. Just for a reminder, the knight is a piece in chess that usually looks like a horse and moves in an L-shaped pattern. So, let's get started! What is Knight's Tour Problem? Ever wondered how a computer playing as a chess player improves its algorithm to defeat you in the game? In this article, we will learn about the Knight's Tour Problem, the various ways to solve it along with their time and space complexities.
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