~<#67844#><#42926#>Warning<#42926#>: This exercise is complex and requires serious work. At Rice, we assign it as a project after eight weeks of work and give students two weeks to think about it. Then they turn in a design for solitaire (based on generative recursion template, plus backtracking) and headers plus purpose statements for all help functions mentioned in the design. For the final product, ask that they specify for each function whether it is a function based on structural processing (including which argument's structure is used), generative recursion, or domain knowledge. Also, if a function uses an accumulator, request a comment on what the accumulator invariant is and how it is maintained during evaluation.<#67844#>
Peg Solitaire is a board game for individuals. The board comes in various
shapes. Here is the simplest one:
The circle with a black dot represents an unoccupied hole, the others holes with little pegs. The goal of the game is to eliminate the pegs one by one, until only one peg is left. A player can eliminate a peg if one of the neighboring holes is unoccupied and if there is a peg in the hole in the opposite direction. In that case, the second peg can jump over the first one and the first one is eliminated. Consider the following configuration:
Here the pegs labeled~1 and~2 could jump. If the player decides to move the
peg labeled~2, the next configuration is
Some configurations are dead-ends. For a simple example, consider the first
board configuration. Its hole is in the middle of the board, Hence, not one
peg can jump, because there are no two pegs in a row, column, or diagonal
such that one can jump over the other into the hole. A player who discovers
a dead-end configuration must stop or backtrack by undoing moves and trying
alternatives.
<#42973#>Exercise 32.3.1<#42973#>
Solution<#67865#><#67865#>
<#42981#>Exercise 32.3.2<#42981#>
Solution<#67866#><#67866#>
<#42989#>Exercise 32.3.3<#42989#>
Solution<#67869#><#67869#>