ProjectAthena

A compilation of simple chess algorithms :)

Algorithmic solutions for different chess problems link

• Knight’s Tour Problem link

  A knight is placed on the first block of an empty board and, moving according to the rules of chess, must visit each square exactly once.

  • Some of the algorithms tried here are as mentioned below
    • Naive Algorithm link
      • For every possible position of the knight on the chess board, the sequence for the tour is pre-fed to the program.
      • Based on the user input the corresponding tour is chosen and traversed.
      • To view : link
    • Backtracking Algorithm link
      • Add one of the next moves to solution vector and recursively check if this move leads to a solution.
        • If the move chosen in the above step doesn’t lead to a solution then remove this move from the solution vector and try other alternative moves.
        • If none of the alternatives work then no solution exists.
      • To view : link
    • Warnsdorff’s Algorithm link
      • There are 2 rules according to this algorithm
        • The knight is moved so that it always proceeds to the square from which the knight will have the fewest onward moves.
        • When calculating the number of onward moves for each candidate square, we do not count moves that revisit any square already visited.
      • To view : link
    • Divide and Conquer Algorithm link
      • Divide the board into 4 quadrants with 4 diamonds.
        • When the knight is placed in the board finish the diamond containing the square and all the same diamonds in the other quadrants.
        • When one set of diamonds are done move to the next set of diamonds and finish traveling the squares.
      • To view : link
• N Queens Problem link

  To find out how many queens can be placed on a chess board such that no two queens attack each other.

  • Some of the algorithms tried here are as mentioned below
    • Naive Algorithm link
      • Generate all possible configurations of queens on board and print a configuration that satisfies the given constraints.
      • To view : link
    • Backtracking Algorithm link
      • Start from the leftmost column
      • Fill up the next column such that none of the existing queens clash
        • If the queens clash then move to the next row
        • If moving the current queen is not feasible the move the previous queen and repeat the process.
      • To view : link
    • New constraint link
      • Have to think about it :)
• N Knights Problem link

  To find out how many knights can be placed on a chess board such that no two knights attack each other given some of the cells are blocked by non attacking pawns. Since placing knights simply on the board is a little too easy to have algorithms -.- link.

  • Some of the algorithms tried here are as mentioned below
    • Odd/Even Position Algorithm
      • Find the no of pawns placed on a dark square and a light square.
        • If more light square pawns are present then print knights on every alternate dark square except for those dark squares with pawns.
        • Else print knights on every alternate light square except for those light squares with pawns.
      • To view : link
• Queens and Knights Problem link

  To be able to place an equal number of knights and queens on a chessboard such that no piece attacks any other piece.

  • Some of the algorithms tried here are as mentioned below
    • Naive Algorithm
      • Generate all possible configurations of knights and queens on board and print a configuration that has the highest no of knights and queens that satisfies the given conditions.
      • To view : link

Assets

• Chess emoji - link
• Problem statement - Have linked where it was appropriate
• Algorithms - Same here :)

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