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Triangular Peg Solitaire

Triangular Peg Solitaire. J. Wallace April 21, 2009. UML. 0. 1. 2. 3. 4. 0. 0. 1. 2. 3. 4. 0. 1. 1. 2. 3. 4. 1. 2. 2. 3. 4. 2. 3. 3. 4. 3. 4. 4. 4. Data Representation. Skewed coordinate system using jagged array. Constructor.

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Triangular Peg Solitaire

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  1. Triangular Peg Solitaire J. Wallace April 21, 2009

  2. UML

  3. 0 1 2 3 4 0 0 1 2 3 4 0 1 1 2 3 4 1 2 2 3 4 2 3 3 4 3 4 4 4 Data Representation • Skewed coordinate system using jagged array

  4. Constructor public Board(int magnitude, int empty_x, int empty_y) { board = new boolean[magnitude][]; int translated_x = empty_x; int translated_y = empty_y - empty_x; for(int i = 0; i < board.length; i++) { board[i] = new boolean[magnitude - i]; for(int j = 0; j < board[i].length; j++) { board[i][j] = (i != translated_x || j != translated_y); } } }

  5. getSlot() and setSlot() public boolean getSlot(int x, int y) { return board[x][y-x]; } public void setSlot(int x, int y, boolean filled) { board[x][y-x] = filled; }

  6. canJump() bool canMove(int src_x, int src_y, int dest_x, int dest_y) { bool horizontalMove = ... bool diagonalMove = ... // It must be either horinontal or diagonal if(!horizontalMove || !diagonalMove) return false // Make sure its not trying to jump to same slot if(horizontalMove && diagonalMove) return false // Find the distances for both x and y int xDist = ... int yDist = ... // If xDist or yDist is not 2 then you're trying to jump too short or far if(xDist != 2 || yDist != 2) return false

  7. canJump() continued // Find the middle slot int middle_x = ... int middle_y = ... // Check that the pegs are in the right slots if(!getSlot(src_x, src_y) || !getSlot(middle_x, middle_y) || getSlot(dest_x, dest_y)) return false return true }

  8. 3-, 6-, and trapezoid-purge Image credit: Bell, G. (2007)

  9. References • Berlekamp, E. R., Conway, J. H., & Guy, R. K. (1982). Winning Ways for Your Mathematical Plays, Vol. 2. London: Academic Press. • Brandeth, G. (1984). The Book of Solo Games. New York: Peter Bedrick Books. • Mohr, M. S. (1997). The New Games Treasury. New York: Mariner Books. • Bell, G.(2007) “Solving Triangular Peg Solitaire.”Paper presented at the annual meeting of the Mathematical Association of America, The Fairmont Hotel, San Jose, CA.2009-02-03from http://www.allacademic.com/meta/p206352_index.html.

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