N皇后问题java实现

    N皇后问题是一个典型的约束求解问题，利用递归机制，可以很快的得到结果。

    N皇后问题的描述：

在一个n*n的棋盘上，摆放n个皇后，要求每个皇后所在行、列、以及两个对角线上不能出现其他的皇后，否则这些皇后之间将会相互攻击。如下图所示。

      利用递归机制，可以很容易的求解n皇后问题。针对八皇后，总共有92种解。下面将给出N-皇后问题的一般求解代码，在这里代码是使用java编码的。

      总共设计了三个类，一个是皇后类（Queen），一个棋盘类（Board），一个是求解主程序类（NQueens）。具体代码如下：

  1: import java.util.ArrayList;

  2: import java.util.List;

  3: 

  4: public class NQueens {

  5: 

  6:   private int numSolutions;//求解结果数量

  7:   private int queenSize;//皇后的多少

  8:   private Board board;//棋盘

  9:   private List<Queen> queens = new ArrayList<Queen>();//皇后

 10:   //private List<Queen> nQueens = new ArrayList<Queen>();

 11:   

 12:   public NQueens(){

 13:     

 14:   }

 15:   

 16:   public NQueens(int size){

 17:     numSolutions = 0;

 18:     queenSize = size;

 19:     board = new Board(queenSize);

 20:     for (int i = 0; i < queenSize; i++) {

 21:       Queen queen = new Queen();

 22:       queens.add(queen);

 23:     }

 24:     

 25:   }

 26:   

 27:   public void solve(){

 28:     System.out.println("Start solve....");

 29:     putQueen(0);

 30:   }

 31:   

 32:   private void putQueen(int index){

 33:     

 34:     int row = index;

 35:     //如果此列可用

 36:     for (int col = 0; col < board.getQueenSize(); col++) {

 37:       if (board.getLayout()[row][col] == 0) {

 38:         //将皇后的位置置为此列位置

 39:         queens.get(row).setPosition(col);

 40:         //然后将相应的位置（此列的正下方以及两个对角线）加1（即使其不可用）

 41:         for (int i = row + 1; i < board.getQueenSize(); i++) {

 42:           board.getLayout()[i][col] ++;

 43:           if (row + col - i >= 0) {

 44:             board.getLayout()[i][row + col - i] ++;

 45:           }

 46:           if (i + col - row < board.getQueenSize()) {

 47:             board.getLayout()[i][i + col - row] ++;

 48:           }

 49:         }

 50:         

 51:         if (row == board.getQueenSize()-1) {

 52:           numSolutions++;

 53:           printSolution(numSolutions);

 54:         }else {

 55:           putQueen(row + 1);

 56:         }

 57:         //回溯，将相应的位置（此列的正下方以及两个对角线）减1

 58:         for (int i = row + 1; i < board.getQueenSize(); i++) {

 59:           board.getLayout()[i][col] --;

 60:           if (row + col - i >= 0) {

 61:             board.getLayout()[i][row + col - i] --;

 62:           }

 63:           if (i + col - row < board.getQueenSize()) {

 64:             board.getLayout()[i][i + col - row] --;

 65:           }

 66:         }

 67:         

 68:       }

 69:     }

 70:   }

 71:   //打印求解结果

 72:   private void printSolution(int i){

 73:     System.out.println("The "+i+ " solution is:");

 74:     for (int j = 0; j < board.getQueenSize(); j++) {

 75:       for (int k = 0; k < board.getQueenSize(); k++) {

 76:         System.out.print(queens.get(j).getPosition() == k ? " * ":" - ");

 77:       }

 78:       System.out.println();

 79:     }

 80:     System.out.println();

 81:   }

 82:   /**

 83:    * @param args

 84:    */

 85:   public static void main(String[] args) {

 86:     //可以改变参数

 87:     NQueens nQueens = new NQueens(8);

 88:     nQueens.solve();

 89: 

 90:   }

 91: 

 92:   

 93: 

 94: }

 95: import java.io.Serializable;

 96: 

 97: //皇后类

 98: public class Queen implements Serializable, Cloneable {

 99: 

100:   /**

101:    * 

102:    */

103:   private static final long serialVersionUID = 7354459222300557644L;

104:   //皇后的位置

105:   private int position;

106:   

107:   public Queen(){

108:     

109:   }

110: 

111:   public int getPosition() {

112:     return position;

113:   }

114: 

115:   public void setPosition(int position) {

116:     this.position = position;

117:   }

118:   

119:   public Object clone() throws CloneNotSupportedException {

120:         

121:         return super.clone();

122:     }

123: }

124: 

125: import java.io.Serializable;

126: 

127: //棋盘类

128: public class Board implements Serializable,Cloneable {

129: 

130:   /**

131:    * 

132:    */

133:   private static final long serialVersionUID = -2530321259544461828L;

134: 

135:   //棋盘的大小

136:   private int queenSize;

137:   

138:   //棋盘的布局

139:   private int[][] layout;

140:   

141:   public Board(int size){

142:     this.queenSize = size;

143:     this.layout = new int[queenSize][queenSize];

144:     //初始化，使棋盘所有位置都可用，即全部置为0

145:     for (int i = 0; i < queenSize; i++) {

146:       for (int j = 0; j < queenSize; j++) {

147:         layout[i][j] = 0;

148:         

149:       }

150:     }

151:   }

152:   

153:   public int getQueenSize() {

154:     return queenSize;

155:   }

156: 

157:   public void setQueenSize(int queenSize) {

158:     this.queenSize = queenSize;

159:   }

160: 

161:   public int[][] getLayout() {

162:     return layout;

163:   }

164: 

165:   public void setLayout(int[][] layout) {

166:     this.layout = layout;

167:   }

168:   

169:   public Object clone() throws CloneNotSupportedException {

170:         

171:         return super.clone();

172:     }

173: 

174: }

175: