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# CrowdedChess Class Reference [Scripts for problems]

Inherits Example.

## Detailed Description

Example: Crowded Chessboard

"You are given a chessboard together with 8 queens, 8 rooks, 14 bishops, and 21 knights. The puzzle is to arrange the 51 pieces on the chessboard so that no queen shall attack another queen, no rook attack another rook, no bishop attack another bishop, and no knight attack another knight. No notice is to be taken of the intervention of pieces of another type from that under consideration - that is, two queens will be considered to attack one another although there may be, say, a rook, a bishop, and a knight between them. It is not difficult to dispose of each type of piece separately; the difficulty comes in when you have to find room for all the arrangements on the board simultaneously." Dudeney, H.E., (1917), Amusements in Mathematics, Thomas Nelson and Sons.

This puzzle can be generalized to chess-boards of size , where the number of pieces to place are:

• queens
• rooks
• bishops
• knights where k is a number to maximize.

The maximum k for some different values of are presented below (from Jesper Hansen and Joachim Schimpf, ECLiPSe solution
 n k 8 21 9 29 10 37 11 47 12 57 13 69 14 81 15 94 16 109

A solution for n = 8 is:
 Q B K . K B K R . K . K Q K R B B . K R K . K Q B K R K . Q . B B R Q . K . K B R K . K . K Q B B Q K . K R K . B K B Q R K B B

Definition at line 183 of file crowded-chess.cc.

## Public Types

enum  { PROP_TUPLE_SET, PROP_DECOMPOSE }

## Public Member Functions

CrowdedChess (const SizeOptions &opt)
The model of the problem.
CrowdedChess (bool share, CrowdedChess &e)
Constructor for cloning e.
virtual Spacecopy (bool share)
Copy during cloning.
virtual void print (std::ostream &os)
Print solution.

enum  {
Q, R, B, K,
E, PMAX
}

## Protected Member Functions

bool valid_pos (int i, int j)
void knight_constraints (void)
Post knight-constraints.

## Protected Attributes

const int n
Board-size.
IntVarArray s
The board.
IntVarArray queens
Row of queen in column x.
IntVarArray rooks
Row of rook in column x.
BoolVarArray knights
True iff the corresponding place has a knight.
enum CrowdedChess:: { ... }  piece

## Related Functions

(Note that these are not member functions.)

TupleSet bishops
Set of valid positions for the bishops.
void init_bishops (int size)
Initialize bishops.

## Member Enumeration Documentation

 anonymous enum` [protected]`

Symbolic names of pieces. The order determines which piece will be placed first.

Enumerator:
 Q Queen. R Rook. B Bishop. K Knight. E Empty square. PMAX Number of pieces (including empty squares).

Definition at line 194 of file crowded-chess.cc.

 anonymous enum

Enumerator:
 PROP_TUPLE_SET Propagate bishops placement extensionally. PROP_DECOMPOSE Propagate bishops placement with decomposition.

Definition at line 228 of file crowded-chess.cc.

## Constructor & Destructor Documentation

 CrowdedChess::CrowdedChess ( const SizeOptions & opt ) ` [inline]`

The model of the problem.

Definition at line 234 of file crowded-chess.cc.

 CrowdedChess::CrowdedChess ( bool share, CrowdedChess & e ) ` [inline]`

Constructor for cloning e.

Definition at line 344 of file crowded-chess.cc.

## Member Function Documentation

 bool CrowdedChess::valid_pos ( int i, int j ) ` [inline, protected]`

Definition at line 204 of file crowded-chess.cc.

 void CrowdedChess::knight_constraints ( void ) ` [inline, protected]`

Post knight-constraints.

Definition at line 210 of file crowded-chess.cc.

 virtual Space* CrowdedChess::copy ( bool share ) ` [inline, virtual]`

Copy during cloning.

Implements Gecode::Space.

Definition at line 354 of file crowded-chess.cc.

 virtual void CrowdedChess::print ( std::ostream & os ) ` [inline, virtual]`

Print solution.

Reimplemented from Example.

Definition at line 360 of file crowded-chess.cc.

## Friends And Related Function Documentation

 TupleSet bishops` [related]`

Set of valid positions for the bishops.

Definition at line 58 of file crowded-chess.cc.

 void init_bishops ( int size ) ` [related]`

Initialize bishops.

Definition at line 104 of file crowded-chess.cc.

## Member Data Documentation

 const int CrowdedChess::n` [protected]`

Board-size.

Definition at line 185 of file crowded-chess.cc.

 IntVarArray CrowdedChess::s` [protected]`

The board.

Definition at line 186 of file crowded-chess.cc.

 IntVarArray CrowdedChess::queens` [protected]`

Row of queen in column x.

Definition at line 187 of file crowded-chess.cc.

 IntVarArray CrowdedChess::rooks` [protected]`

Row of rook in column x.

Definition at line 187 of file crowded-chess.cc.

 BoolVarArray CrowdedChess::knights` [protected]`

True iff the corresponding place has a knight.

Definition at line 189 of file crowded-chess.cc.

 enum { ... } CrowdedChess::piece` [protected]`

Symbolic names of pieces. The order determines which piece will be placed first.

The documentation for this class was generated from the following file: