Recursive Triangle Puzzle

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1 Recursive Triangle Puzzle Lecture 36 Section 14.7 Robb T. Koether Hampden-Sydney College Fri, Dec 7, 2012 Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

2 1 The Triangle Puzzle 2 Strategy 3 Coding the Solution 4 Assignment Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

3 Outline 1 The Triangle Puzzle 2 Strategy 3 Coding the Solution 4 Assignment Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

4 The Triangle Puzzle The triangle puzzle consists of a triangular board with 15 holes arranged as a triangle, 5 holes on a side. A peg is in every hole but one. A legal move: Three holes in a row. The hole at one end is empty. The other two holes have pegs in them. Remove the two pegs from those holes and place a peg in the empty hole (a jump ). The objective is to end up with only one peg left. Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

5 The Triangle Puzzle The Triangle Puzzle Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

6 Outline 1 The Triangle Puzzle 2 Strategy 3 Coding the Solution 4 Assignment Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

7 Strategy We will adopt a very simple strategy to solve the puzzle: Try every possible sequence of moves until we find one that works. This is somewhat like a sequential search, except that the possibilities are not arranged in sequence. If a move results in a dead end, then back up and try a different move. Apply that strategy recursively. Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

8 Strategy Number the holes Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

9 Strategy Create a list of every possible move. (0, 1, 3) (0, 2, 5) (1, 3, 6) (1, 4, 8) (2, 4, 7) (2, 5, 9) (3, 1, 0) (3, 4, 5) (3, 6, 10) (3, 7, 9) (4, 7, 11) (4, 8, 13) (5, 2, 0) (5, 4, 3) (5, 8, 12) (5, 9, 14) (6, 3, 1) (6, 7, 8) (7, 4, 2) (7, 8, 9) (8, 4, 1) (8, 7, 6) (9, 5, 2) (9, 8, 7) (10, 6, 3) (10, 11, 12) (11, 7, 4) (11, 12, 13) (12, 7, 3) (12, 8, 5) (12, 11, 10) (12, 13, 14) (13, 8, 4) (13, 12, 11) (14, 9, 5) (14, 13, 12) Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

10 Strategy Try the moves in the order in which they are listed. Skip any move in the list that is not legal, given the current board configuration. Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

11 Outline 1 The Triangle Puzzle 2 Strategy 3 Coding the Solution 4 Assignment Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

12 Coding the Solution Create a Move class. A Move object has 3 data members. int jumper The peg that jumps. int jumpee The peg that gets jumped. int newpeg The hole where jumper landed. Store the set of all possible moves in an array possmoves of Moves (size 36). Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

13 Coding the Solution Create an array soln of the sequence of moves so far, stored by their index (size 13). Create an array board of bools that represents the game board (size 15). true means there is a peg in the hole. false means the hole is empty. Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

14 Coding the Solution The sovlepuzzle() Function void solvepuzzle(bool board[], Move possmoves[], int soln[], int nummoves); Write a function solvepuzzle(). The function solvepuzzle() will scan the list of possible moves, looking for a legal move, given the current board configuration. The parameter currmove is the most recent move taken. Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

15 Coding the Solution The islegal() Function bool islegal(bool board[], Move move); We need a function islegal() that will determine whether a move is legal, given the current board configuration. This function will return true if move.jumper and move.jumpee are occupied, and move.newpeg is unoccupied. Otherwise, it returns false. Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

16 Outline 1 The Triangle Puzzle 2 Strategy 3 Coding the Solution 4 Assignment Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

17 Assignment Assignment Read Section Robb T. Koether (Hampden-Sydney College) Recursive Triangle Puzzle Fri, Dec 7, / 17

Pointers. The Rectangle Game. Robb T. Koether. Hampden-Sydney College. Mon, Jan 21, 2013

Pointers. The Rectangle Game. Robb T. Koether. Hampden-Sydney College. Mon, Jan 21, 2013 Pointers The Rectangle Game Robb T. Koether Hampden-Sydney College Mon, Jan 21, 2013 Robb T. Koether (Hampden-Sydney College) Pointers Mon, Jan 21, 2013 1 / 21 1 Introduction 2 The Game Board 3 The Move