八皇后问题 --- 递归解法 --- java代码
八皇后问题是一个以国际象棋为背景的问题：如何能够在 8×8 的国际象棋棋盘上放置八个皇后，使得任何一个皇后都无法直接吃掉其他的皇后？为了达到此目的，任两个皇后都不能处于同一条横行、纵行或斜线上。八皇后问题可以推广为更一般的n皇后摆放问题：这时棋盘的大小变为n×n，而皇后个数也变成n。当且仅当 n = 1 或 n ≥ 4 时问题有解[1]。 以上内容摘自维基百科：http://zh.wikipedia.org/wiki/%E5%85%AB%E7%9A%87%E5%90%8E%E9%97%AE%E9%A2%98
代码如下：
public class Demo {
public static void main(String[] args) {
nextRowPlace(START_ROW);
}
private static final int ROW = 8, COL = 8, START_ROW = 0, START_COL = 0;
private static boolean[][] board = new boolean[8][8];
private static void nextRowPlace(final int row) {
if(row == ROW){
print();
return;
}
for(int j=START_COL; j!=COL; ++j)
if(checkPosValid(row, j)){
board[row][j] = true;
nextRowPlace(row+1);
board[row][j] = false;
}
return;
}
private static boolean checkPosValid(final int row, final int col) {
for(int i=START_ROW; i!=ROW; ++i)
if(board[i][col])
return false;
for(int i=row, j=col; i!=START_ROW-1 && j!=START_COL-1; --i, --j)
if(board[i][j])
return false;
for(int i=row, j=col; i!=START_ROW-1 && j!= COL; --i, ++j)
if(board[i][j])
return false;
return true;
}
private static int count = 0;
private static void print() {
System.out.println("--- --- --- --- --- " + ++count +" --- ---");
for(int i=START_ROW; i!=ROW; ++i){
for(int j=START_COL; j!=COL; ++j)
System.out.print(board[i][j] ? "O " : "X ");
System.out.println();
}
System.out.println();
return;
}
}
运行结果如下：
--- --- --- --- --- 1 --- --- O X X X X X X X X X X X O X X X X X X X X X X O X X X X X O X X X X O X X X X X X X X X X X O X X O X X X X X X X X X O X X X X --- --- --- --- --- 2 --- --- O X X X X X X X X X X X X O X X X X X X X X X O X X O X X X X X X X X X X X O X X X X O X X X X X O X X X X X X X X X X O X X X --- --- --- --- --- 3 --- --- O X X X X X X X X X X X X X O X X X X O X X X X X X X X X O X X X X X X X X X O X O X X X X X X X X X X O X X X X X O X X X X X --- --- --- --- --- 4 --- --- O X X X X X X X X X X X X X O X X X X X O X X X X X X X X X X O X O X X X X X X X X X O X X X X X X X X X O X X X X O X X X X X --- --- --- --- --- 5 --- --- X O X X X X X X X X X O X X X X X X X X X O X X X X X X X X X O X X O X X X X X O X X X X X X X X X X X X X O X X X X X O X X X --- --- --- --- --- 6 --- --- X O X X X X X X X X X X O X X X X X X X X X O X O X X X X X X X X X O X X X X X X X X X X X X O X X X X X O X X X X X O X X X X --- --- --- --- --- 7 --- --- X O X X X X X X X X X X O X X X X X X X X X O X X X X O X X X X O X X X X X X X X X X X X X X O X X X X X O X X X X O X X X X X --- --- --- --- --- 8 --- --- X O X X X X X X X X X X X O X X O X X X X X X X X X X X X X O X X X X O X X X X X X X X X X X O X X O X X X X X X X X X O X X X --- --- --- --- --- 9 --- --- X O X X X X X X X X X X X O X X X X X X X X X O X X O X X X X X O X X X X X X X X X X O X X X X X X X X X X O X X X X X O X X X --- --- --- --- --- 10 --- --- X O X X X X X X X X X X X X O X X X O X X X X X X X X X X O X X X X X X X X X O X X X X O X X X O X X X X X X X X X X O X X X X --- --- --- --- --- 11 --- --- X O X X X X X X X X X X X X O X X X X X O X X X X X X X X X X O O X X X X X X X X X X O X X X X X X X X X O X X X X O X X X X X --- --- --- --- --- 12 --- --- X O X X X X X X X X X X X X X O X X X X X O X X O X X X X X X X X X O X X X X X X X X X O X X X X X X X X X O X X X X O X X X X --- --- --- --- --- 13 --- --- X X O X X X X X O X X X X X X X X X X X X X O X X X X X O X X X X X X X X X X O X O X X X X X X X X X O X X X X X X X X X O X X --- --- --- --- --- 14 --- --- X X O X X X X X X X X X O X X X X O X X X X X X X X X X X X X O O X X X X X X X X X X X X X O X X X X O X X X X X X X X X O X X --- --- --- --- --- 15 --- --- X X O X X X X X X X X X O X X X X O X X X X X X X X X X X X X O X X X X X O X X X X X O X X X X X X X X X X O X O X X X X X X X --- --- --- --- --- 16 --- --- X X O X X X X X X X X X O X X X X X X X X X O X O X X X X X X X X X X O X X X X X O X X X X X X X X X X X X X O X X X X X O X X --- --- --- --- --- 17 --- --- X X O X X X X X X X X X O X X X X X X X X X X O X X X O X X X X O X X X X X X X X X X X X X O X X O X X X X X X X X X X X O X X --- --- --- --- --- 18 --- --- X X O X X X X X X X X X X O X X X O X X X X X X X X X X O X X X X X X X X X X O O X X X X X X X X X X X X X O X X X X O X X X X --- --- --- --- --- 19 --- --- X X O X X X X X X X X X X O X X X O X X X X X X X X X X X X O X O X X X X X X X X X X O X X X X X X X X X X X O X X X X O X X X --- --- --- --- --- 20 --- --- X X O X X X X X X X X X X O X X X O X X X X X X X X X X X X O X X X X X O X X X O X X X X X X X X X X X X X X O X X X O X X X X --- --- --- --- --- 21 --- --- X X O X X X X X X X X X X O X X X X X O X X X X O X X X X X X X X X X X X X X O X X X X O X X X X X X X X X O X X O X X X X X X --- --- --- --- --- 22 --- --- X X O X X X X X X X X X X O X X X X X O X X X X X O X X X X X X X X X X X X X O X X X X O X X X X X X X X X O X O X X X X X X X --- --- --- --- --- 23 --- --- X X O X X X X X X X X X X O X X X X X X X X X O O X X X X X X X X X X O X X X X X X X X X X O X X X X X O X X X X O X X X X X X --- --- --- --- --- 24 --- --- X X O X X X X X X X X X X O X X X X X X X X X O O X X X X X X X X X X X O X X X X X X X X X O X X O X X X X X X X X X O X X X X --- --- --- --- --- 25 --- --- X X O X X X X X X X X X X O X X X X X X X X X O X O X X X X X X X X X O X X X X O X X X X X X X X X X X X X O X X X X X O X X X --- --- --- --- --- 26 --- --- X X O X X X X X X X X X X X O X X O X X X X X X X X X X X X X O X X X X O X X X O X X X X X X X X X X O X X X X X X X X X O X X --- --- --- --- --- 27 --- --- X X O X X X X X X X X X X X O X X O X X X X X X X X X X X X X O X X X X X O X X X X X O X X X X O X X X X X X X X X X X O X X X --- --- --- --- --- 28 --- --- X X O X X X X X X X X X X X X O X X X O X X X X X X X X X X O X O X X X X X X X X X X X X O X X X O X X X X X X X X X X O X X X --- --- --- --- --- 29 --- --- X X X O X X X X O X X X X X X X X X X X O X X X X X X X X X X O X O X X X X X X X X X X X X O X X X O X X X X X X X X X X O X X --- --- --- --- --- 30 --- --- X X X O X X X X O X X X X X X X X X X X O X X X X X X X X X X O X X X X X O X X X X O X X X X X X X X X X X O X X O X X X X X X --- --- --- --- --- 31 --- --- X X X O X X X X X O X X X X X X X X X X O X X X X X X X X X X O X X X X X O X X O X X X X X X X X X O X X X X X X X X X X X O X --- --- --- --- --- 32 --- --- X X X O X X X X X O X X X X X X X X X X X X O X X X O X X X X X X X X X X O X X X X X X X X X O O X X X X X X X X X X X O X X X --- --- --- --- --- 33 --- --- X X X O X X X X X O X X X X X X X X X X X X O X X X O X X X X X X X X X X O X X X X X X X X X O X X X X O X X X O X X X X X X X --- --- --- --- --- 34 --- --- X X X O X X X X X O X X X X X X X X X X X X O X X X X X O X X X O X X X X X X X X X X X X X X O X X X X X O X X X X O X X X X X --- --- --- --- --- 35 --- --- X X X O X X X X X O X X X X X X X X X X X X X O X X X X O X X X X X X X X X O X O X X X X X X X X X O X X X X X X X X X X O X X --- --- --- --- --- 36 --- --- X X X O X X X X X O X X X X X X X X X X X X X O X X X X X O X X O X X X X X X X X X O X X X X X X X X X O X X X X X X X X X O X --- --- --- --- --- 37 --- --- X X X O X X X X X X X X X O X X O X X X X X X X X X X X O X X X X O X X X X X X X X X X X X X O X X O X X X X X X X X X X X O X --- --- --- --- --- 38 --- --- X X X O X X X X X X X X X O X X X X X X X X X O X O X X X X X X X X X X X X O X O X X X X X X X X X O X X X X X X X X X O X X X --- --- --- --- --- 39 --- --- X X X O X X X X X X X X X O X X X X X X X X X O X X O X X X X X O X X X X X X X X X X X X X O X X X X X O X X X X O X X X X X X --- --- --- --- --- 40 --- --- X X X O X X X X X X X X X X O X O X X X X X X X X X X X X X X O X X X X O X X X X O X X X X X X X X X X X O X X X X O X X X X X --- --- --- --- --- 41 --- --- X X X O X X X X X X X X X X O X X X O X X X X X X X X X X X X O X O X X X X X X X X X X O X X X O X X X X X X X X X X X X O X X --- --- --- --- --- 42 --- --- X X X O X X X X X X X X X X O X X X X X O X X X X O X X X X X X X X X X X O X X O X X X X X X X X X O X X X X X X X X X X X X O --- --- --- --- --- 43 --- --- X X X O X X X X X X X X X X O X X X X X O X X X X X O X X X X X O X X X X X X X X X X X X O X X X X X X X X X O X O X X X X X X --- --- --- --- --- 44 --- --- X X X O X X X X X X X X X X X O O X X X X X X X X X O X X X X X X X X X X O X X X O X X X X X X X X X X X X O X X X X X O X X X --- --- --- --- --- 45 --- --- X X X O X X X X X X X X X X X O O X X X X X X X X X X X O X X X X X X X X X O X X O X X X X X X X X X X X O X X X X O X X X X X --- --- --- --- --- 46 --- --- X X X O X X X X X X X X X X X O X X X X O X X X X X O X X X X X O X X X X X X X X X X X X X O X X O X X X X X X X X X X X O X X --- --- --- --- --- 47 --- --- X X X X O X X X O X X X X X X X X X X O X X X X X X X X X O X X X X X X X X X O X O X X X X X X X X X X X X O X X X O X X X X X --- --- --- --- --- 48 --- --- X X X X O X X X O X X X X X X X X X X X X X X O X X X O X X X X X O X X X X X X X X X X X X O X X X O X X X X X X X X X X O X X --- --- --- --- --- 49 --- --- X X X X O X X X O X X X X X X X X X X X X X X O X X X X X O X X X X O X X X X X X X X X X X O X X O X X X X X X X X X O X X X X --- --- --- --- --- 50 --- --- X X X X O X X X X O X X X X X X X X X O X X X X X X X X X O X X X X X X X X X O X X O X X X X X O X X X X X X X X X X X X X O X --- --- --- --- --- 51 --- --- X X X X O X X X X O X X X X X X X X X O X X X X X X X X X X O X X X O X X X X X X X X X X X X O X X X X X O X X O X X X X X X X --- --- --- --- --- 52 --- --- X X X X O X X X X O X X X X X X X X X X X O X X O X X X X X X X X X X X X X O X X X X O X X X X X X X X X X X O X X O X X X X X --- --- --- --- --- 53 --- --- X X X X O X X X X O X X X X X X X X X X X X X O O X X X X X X X X X X O X X X X X X X X X X O X X X O X X X X X X X X X X O X X --- --- --- --- --- 54 --- --- X X X X O X X X X X O X X X X X O X X X X X X X X X X X X O X X X X X X X X X O X O X X X X X X X X X O X X X X X X X X X X O X --- --- --- --- --- 55 --- --- X X X X O X X X X X O X X X X X O X X X X X X X X X X X X X O X X O X X X X X X X X X X X X X O X X X X X O X X X X X O X X X X --- --- --- --- --- 56 --- --- X X X X O X X X X X O X X X X X X X X X X X X O X X X O X X X X X X X X X X O X O X X X X X X X X X X X X O X X X O X X X X X X --- --- --- --- --- 57 --- --- X X X X O X X X X X X X X X O X O X X X X X X X X X O X X X X X X X X X X X X O X X X X X O X X X X X O X X X X X O X X X X X X --- --- --- --- --- 58 --- --- X X X X O X X X X X X X X X O X O X X X X X X X X X X O X X X X X O X X X X X X X X X X X X X O X X X X X O X X X X O X X X X X --- --- --- --- --- 59 --- --- X X X X O X X X X X X X X X O X X O X X X X X X X X X O X X X X X X X X X X X O O X X X X X X X X X O X X X X X X X X X X O X X --- --- --- --- --- 60 --- --- X X X X O X X X X X X X X X O X X O X X X X X X X X X X X O X X X X O X X X X X O X X X X X X X X X X O X X X X X X X X X X X O --- --- --- --- --- 61 --- --- X X X X O X X X X X X X X X O X X O X X X X X X X X X X X O X X X X O X X X X X O X X X X X X X X X X X X X X O X X X O X X X X --- --- --- --- --- 62 --- --- X X X X O X X X X X X X X X O X X X X O X X X X O X X X X X X X X X O X X X X X X X X X X X X O X X X X X O X X X O X X X X X X --- --- --- --- --- 63 --- --- X X X X O X X X X X X X X X X O X X X O X X X X O X X X X X X X X X O X X X X X X X X X X O X X X O X X X X X X X X X X X X O X --- --- --- --- --- 64 --- --- X X X X O X X X X X X X X X X O X X X O X X X X O X X X X X X X X X X X X X O X X O X X X X X X X X X X X O X X X X O X X X X X --- --- --- --- --- 65 --- --- X X X X X O X X O X X X X X X X X X X X O X X X X O X X X X X X X X X X X X X O X X O X X X X X X X X X X X O X X X X O X X X X --- --- --- --- --- 66 --- --- X X X X X O X X X O X X X X X X X X X X X X O X O X X X X X X X X X O X X X X X X X X X O X X X X X X X X X X O X X X O X X X X --- --- --- --- --- 67 --- --- X X X X X O X X X O X X X X X X X X X X X X O X O X X X X X X X X X X O X X X X X X X X X X X O X X X X O X X X X X O X X X X X --- --- --- --- --- 68 --- --- X X X X X O X X X X O X X X X X O X X X X X X X X X X X X X O X X X X X O X X X X X X X X X X O X O X X X X X X X X X O X X X X --- --- --- --- --- 69 --- --- X X X X X O X X X X O X X X X X O X X X X X X X X X X X X X X O X X X O X X X X X O X X X X X X X X X X X X O X X X X X O X X X --- --- --- --- --- 70 --- --- X X X X X O X X X X O X X X X X O X X X X X X X X X X X X X X O X X X X O X X X X O X X X X X X X X X O X X X X X X X X X X O X --- --- --- --- --- 71 --- --- X X X X X O X X X X O X X X X X X X X X O X X X X X X X X X O X O X X X X X X X X X X O X X X X X O X X X X X X X X X X X X X O --- --- --- --- --- 72 --- --- X X X X X O X X X X O X X X X X X X X X O X X X X X X X X X X O O X X X X X X X X X X O X X X X X O X X X X X X X X X X X X O X --- --- --- --- --- 73 --- --- X X X X X O X X X X O X X X X X X X X X X X O X X O X X X X X X X X X O X X X X X X X X X X X O O X X X X X X X X X X X O X X X --- --- --- --- --- 74 --- --- X X X X X O X X X X O X X X X X X X X X X X O X X O X X X X X X X X X X X X X O X X X X O X X X O X X X X X X X X X X O X X X X --- --- --- --- --- 75 --- --- X X X X X O X X X X O X X X X X X X X X X X O X X X X O X X X X O X X X X X X X X X X X X X X O X O X X X X X X X X X X O X X X --- --- --- --- --- 76 --- --- X X X X X O X X X X X O X X X X O X X X X X X X X X X X O X X X X X X X X X X O X O X X X X X X X X X X X X O X X X O X X X X X --- --- --- --- --- 77 --- --- X X X X X O X X X X X O X X X X X O X X X X X X X X X X X X X O X X X X O X X X X X X X X X O X O X X X X X X X X X O X X X X X --- --- --- --- --- 78 --- --- X X X X X O X X X X X O X X X X X X X X X X O X O X X X X X X X X X O X X X X X X X X X O X X X X O X X X X X X X X X X X X X O --- --- --- --- --- 79 --- --- X X X X X O X X X X X O X X X X X X X X X X O X O X X X X X X X X X X X X X X O X O X X X X X X X X X X O X X X X X O X X X X X --- --- --- --- --- 80 --- --- X X X X X O X X X X X X X X X O X O X X X X X X X X X O X X X X O X X X X X X X X X X X X X O X X X X X O X X X X X O X X X X X --- --- --- --- --- 81 --- --- X X X X X X O X O X X X X X X X X X O X X X X X X X X X X X X O X X X X X O X X X X X O X X X X X O X X X X X X X X X X O X X X --- --- --- --- --- 82 --- --- X X X X X X O X X O X X X X X X X X X O X X X X O X X X X X X X X X X X X X X O X X X X O X X X X X O X X X X X X X X X X O X X --- --- --- --- --- 83 --- --- X X X X X X O X X O X X X X X X X X X X X O X X X X O X X X X X O X X X X X X X X X X O X X X X X X X X X X X O X X X X O X X X --- --- --- --- --- 84 --- --- X X X X X X O X X X O X X X X X O X X X X X X X X X X X X O X X X X X X X X X O X X X X O X X X X O X X X X X X X X X O X X X X --- --- --- --- --- 85 --- --- X X X X X X O X X X O X X X X X X X X X X X X O X O X X X X X X X X X X O X X X O X X X X X X X X X X X X O X X X X X O X X X X --- --- --- --- --- 86 --- --- X X X X X X O X X X X O X X X X X O X X X X X X X X X X O X X X X X X X X X X O O X X X X X X X X X O X X X X X X X X X X O X X --- --- --- --- --- 87 --- --- X X X X X X O X X X X O X X X X X O X X X X X X X X X X X X X O X X X X X O X X O X X X X X X X X X O X X X X X X X X X O X X X --- --- --- --- --- 88 --- --- X X X X X X O X X X X X O X X X X X O X X X X X O X X X X X X X X X X X X O X X X X X X X X X O X O X X X X X X X X X O X X X X --- --- --- --- --- 89 --- --- X X X X X X X O X O X X X X X X X X X O X X X X O X X X X X X X X X X X X X O X X X X X O X X X X X O X X X X X X X X X X O X X --- --- --- --- --- 90 --- --- X X X X X X X O X O X X X X X X X X X X O X X X X X O X X X X X O X X X X X X X X X X X X X O X X X X O X X X X X X X X X O X X --- --- --- --- --- 91 --- --- X X X X X X X O X X O X X X X X O X X X X X X X X X X X X O X X X O X X X X X X X X X X O X X X X X X X X X O X X X X O X X X X --- --- --- --- --- 92 --- --- X X X X X X X O X X X O X X X X O X X X X X X X X X O X X X X X X X X X X O X X X O X X X X X X X X X X X X O X X X X X O X X X
2014-04-12
八皇后问题 --- 递归解法 --- java代码的更多相关文章
- 比赛组队问题 --- 递归解法 --- java代码 --- 八皇后问题
两队比赛,甲队为A.B.C3人,乙队为X.Y.Z3人.已知A不和X比,C不和X.Z比,请编程序找出3队赛手名单 采用了与八皇后问题相似的解法,代码如下: 如有疑问请链接八皇后问题的解法:http:// ...
- 骑士周游问题 --- 递归解法 --- java代码
骑士游历: 定义了向量的数组M,行数组X,列数组Y, 棋盘plane,计数器count,走动步数step 需要注意的是,递归函数的进入前的验证,原先的想法是传入来时的方向参数,可是这样的想法被实践否定 ...
- java实现八皇后问题(递归和循环两种方式)
循环方式: package EightQueens; public class EightQueensNotRecursive { private static final boolean AVA ...
- 八皇后问题 递归实现 C语言 超详细 思路 基础
八皇后问题 :假设 將八个皇后放到国际象棋盘上,使其两两之间无法相互攻击.共有几种摆法? 基础知识: 国际象棋里,棋盘为8X8格. 皇后每步可以沿直线.斜线 走任意格. 思路: 1.想把8个皇后放进去 ...
- 八皇后非递归（仅使用一个数组且可扩展为N皇后问题）
</pre><pre name="code" class="cpp">/* Theme:八皇后(非递归) Coder:秒针的声音 Tim ...
- [LeetCode系列]N皇后问题递归解法 -- 位操作方式
N皇后问题: 给定8*8棋盘, 放置n个皇后, 使其互相不能攻击(即2个皇后不能放在同一行/列/正反对角线上), 求解共有多少种放置方式? 这个问题的解答网上有不少, 但是位操作解法的我看到的不多. ...
- K皇后问题递归解法
#include<iostream> #include<cmath> #include<ctime> using namespace std; bool che ...
- java递归求八皇后问题解法
八皇后问题 八皇后问题,是一个古老而著名的问题,是回溯算法的典型案例.该问题是国际西洋棋棋手马克斯·贝瑟尔于1848年提出:在8×8格的国际象棋上摆放八个皇后,使其不能互相攻击,即任意两个皇后都不能处 ...
- 对八皇后的补充以及自己解决2n皇后问题代码
有了上次的八皇后的基础.这次准备解决2n皇后的问题,: //问题描述// 给定一个n*n的棋盘,棋盘中有一些位置不能放皇后.现在要向棋盘中放入n个黑皇后和n个白皇后,使任意的两个黑皇后都不在同一行./ ...
随机推荐
- Hadoop、Pig、Hive、Storm、NOSQL 学习资源收集
(一)hadoop 相关安装部署 1.hadoop在windows cygwin下的部署: http://lib.open-open.com/view/1333428291655 http://blo ...
- USACO Section 3.3: Riding the Fences
典型的找欧拉路径的题.先贴下USACO上找欧拉路径的法子: Pick a starting node and recurse on that node. At each step: If the no ...
- POJ 2689 Prime Distance （素数+两次筛选）
题目地址:http://poj.org/problem?id=2689 题意:给你一个不超过1000000的区间L-R,要你求出区间内相邻素数差的最大最小值,输出相邻素数. AC代码: #includ ...
- java实现给图片添加水印
package michael.io.image; import java.awt.AlphaComposite; import java.awt.Graphics2D; import java.aw ...
- hdu - 2102 A计划 (简单bfs)
http://acm.hdu.edu.cn/showproblem.php?pid=2102 题目还是不难,注意起点一定是(0,0,0),然后到达P点时间<=t都可以. 用一个3维字符数组存储图 ...
- [HZNUOJ1524]排队买票(DP)
题目链接:http://acm.hznu.edu.cn/JudgeOnline/problem.php?id=1524 简单分析后可以知道每一个手持两元的小朋友前面,售票员手里至少有一个一元. 假设d ...
- Webservce、WCF、WebApi的区别
Web Service It is based on SOAP and return data in XML form. It support only HTTP protocol. It is no ...
- 【转】对Android开发者有益的40条优化建议
下面是开始Android编程的好方法: 找一些与你想做事情类似的代码 调整它,尝试让它做你像做的事情 经历问题 使用StackOverflow解决问题 对每个你像添加的特征重复上述过程.这种方法能够激 ...
- HeadFirst Jsp 04 (请求和响应作为servlet)
servlet 的存在就是为了客服服务, servlet的任务是得到一个客户的请求, 再发回一个响应. 由上图可知, web 容器会在启动后就加载所有的servlet类, 并为之创建实例和初始化 注意 ...
- 【转载】正则表达式学习 & ASCII码表
文章原地址: http://www.jb51.net/tools/zhengze.html <正则表达式30分钟入门教程> 其中有几个地方可以有笔记: \s 匹配任意的空白符 \b 匹配单 ...