标签：style class blog code java ext
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了，
从理论上看，一个棋子走向哪里是不受它的过去制约的，最近的过去也不例外，
详情请见：http://en.wikipedia.org/wiki/Knights_tour
代码如下：
/**
* Created by kodoyang on 2014/5/3.
*/
public class KnightTour {
private static final int[][] M= {
{2, 1}, {1, 2}, {-1, 2}, {-2, 1}, {-2, -1}, {-1, -2}, {1, -2}, {2, -1}
};
private static final int[] X = {0, 1, 2, 3, 4, 5, 6, 7}, Y = {0, 1, 2, 3, 4, 5, 6, 7};
private static final int[][] plane = new int[X.length][Y.length];
public final static void main(String[] args){
int[] O = {0, 0};
next(X[0], Y[0], 1);
}
private static int count = 0;
private final static void next(final int x, final int y, final int step){
plane[x][y] = step;
if(step == 64)
print( ++count );
else {
for(int i = 0; i < M.length; i++){
int[] v = M[i];
int _x = x + v[0], _y = y + v[1];
if (valid(_x, _y))
next(_x, _y, step + 1);
}
}
plane[x][y] = 0;
}
private static final boolean valid(final int x, final int y){
boolean result = false;
if(x >= X[0] && x <= X[7] && y >= Y[0] && y <= Y[7]){
result = plane[x][y] == 0;
}
return result;
}
private static final void print(int step){
System.out.println("---------------------------------- " + step + " ------");
for(int i = X[0]; i <= X[7]; ++i) {
for (int j = Y[0]; j <= Y[7]; ++j) {
System.out.print("\t" + plane[i][j]);
}
System.out.println();
}
System.out.println("---------------------------------------------------");
}
}
这里一共有26,534,728,821,064种结果，程序被我提前停掉了，运行结果如下：
---------------------------------- 1 ------ 1 60 39 34 31 18 9 64 38 35 32 61 10 63 30 17 59 2 37 40 33 28 19 8 36 49 42 27 62 11 16 29 43 58 3 50 41 24 7 20 48 51 46 55 26 21 12 15 57 44 53 4 23 14 25 6 52 47 56 45 54 5 22 13 --------------------------------------------------- ---------------------------------- 2 ------ 1 50 45 62 31 18 9 64 46 61 32 49 10 63 30 17 51 2 47 44 33 28 19 8 60 35 42 27 48 11 16 29 41 52 3 34 43 24 7 20 36 59 38 55 26 21 12 15 53 40 57 4 23 14 25 6 58 37 54 39 56 5 22 13 --------------------------------------------------- ---------------------------------- 3 ------ 1 60 45 48 31 18 9 64 46 49 32 61 10 63 30 17 59 2 47 44 33 28 19 8 50 35 42 27 62 11 16 29 41 58 3 34 43 24 7 20 36 51 38 55 26 21 12 15 57 40 53 4 23 14 25 6 52 37 56 39 54 5 22 13 --------------------------------------------------- ---------------------------------- 4 ------ 1 60 57 44 31 18 9 64 58 43 32 61 10 63 30 17 33 2 59 56 45 28 19 8 42 47 54 27 62 11 16 29 53 34 3 46 55 24 7 20 48 41 50 37 26 21 12 15 35 52 39 4 23 14 25 6 40 49 36 51 38 5 22 13 --------------------------------------------------- ---------------------------------- 5 ------ 1 60 43 48 31 18 9 64 44 49 32 61 10 63 30 17 59 2 45 42 47 28 19 8 50 33 40 27 62 11 16 29 39 58 3 46 41 24 7 20 34 51 36 55 26 21 12 15 57 38 53 4 23 14 25 6 52 35 56 37 54 5 22 13 --------------------------------------------------- ---------------------------------- 6 ------ 1 60 43 48 31 18 9 64 44 47 32 61 10 63 30 17 59 2 45 42 49 28 19 8 46 33 40 27 62 11 16 29 39 58 3 50 41 24 7 20 34 51 36 55 26 21 12 15 57 38 53 4 23 14 25 6 52 35 56 37 54 5 22 13 --------------------------------------------------- ---------------------------------- 7 ------ 1 60 35 30 37 18 9 64 34 31 28 61 10 63 38 17 59 2 33 36 29 40 19 8 32 49 42 27 62 11 16 39 43 58 3 50 41 24 7 20 48 51 46 55 26 21 12 15 57 44 53 4 23 14 25 6 52 47 56 45 54 5 22 13 --------------------------------------------------- ---------------------------------- 8 ------ 1 50 45 62 43 18 9 64 46 61 28 49 10 63 42 17 51 2 47 44 29 40 19 8 60 31 38 27 48 11 16 41 37 52 3 30 39 24 7 20 32 59 34 55 26 21 12 15 53 36 57 4 23 14 25 6 58 33 54 35 56 5 22 13 --------------------------------------------------- ---------------------------------- 9 ------ 1 60 45 48 43 18 9 64 46 49 28 61 10 63 42 17 59 2 47 44 29 40 19 8 50 31 38 27 62 11 16 41 37 58 3 30 39 24 7 20 32 51 34 55 26 21 12 15 57 36 53 4 23 14 25 6 52 33 56 35 54 5 22 13 --------------------------------------------------- ---------------------------------- 10 ------ 1 60 39 34 29 18 9 64 38 35 28 61 10 63 32 17 59 2 37 40 33 30 19 8 36 49 42 27 62 11 16 31 43 58 3 50 41 24 7 20 48 51 46 55 26 21 12 15 57 44 53 4 23 14 25 6 52 47 56 45 54 5 22 13 --------------------------------------------------- ---------------------------------- 11 ------ 1 50 45 62 29 18 9 64 46 61 28 49 10 63 32 17 51 2 47 44 33 30 19 8 60 35 42 27 48 11 16 31 41 52 3 34 43 24 7 20 36 59 38 55 26 21 12 15 53 40 57 4 23 14 25 6 58 37 54 39 56 5 22 13 --------------------------------------------------- ---------------------------------- 12 ------ 1 60 45 48 29 18 9 64 46 49 28 61 10 63 32 17 59 2 47 44 33 30 19 8 50 35 42 27 62 11 16 31 41 58 3 34 43 24 7 20 36 51 38 55 26 21 12 15 57 40 53 4 23 14 25 6 52 37 56 39 54 5 22 13 --------------------------------------------------- ---------------------------------- 13 ------ 1 34 59 46 29 18 9 64 60 45 28 33 10 63 30 17 35 2 61 58 47 32 19 8 44 49 56 27 62 11 16 31 55 36 3 48 57 24 7 20 50 43 52 39 26 21 12 15 37 54 41 4 23 14 25 6 42 51 38 53 40 5 22 13 --------------------------------------------------- ---------------------------------- 14 ------ 1 60 35 46 29 18 9 64 36 47 28 61 10 63 30 17 59 2 49 34 45 32 19 8 48 37 44 27 62 11 16 31 43 58 3 50 33 24 7 20 38 51 40 55 26 21 12 15 57 42 53 4 23 14 25 6 52 39 56 41 54 5 22 13 --------------------------------------------------- ---------------------------------- 15 ------ 1 50 35 62 29 18 9 64 36 61 28 49 10 63 30 17 51 2 47 34 45 32 19 8 60 37 44 27 48 11 16 31 43 52 3 46 33 24 7 20 38 59 40 55 26 21 12 15 53 42 57 4 23 14 25 6 58 39 54 41 56 5 22 13 --------------------------------------------------- ---------------------------------- 16 ------ 1 60 35 48 29 18 9 64 36 49 28 61 10 63 30 17 59 2 47 34 45 32 19 8 50 37 44 27 62 11 16 31 43 58 3 46 33 24 7 20 38 51 40 55 26 21 12 15 57 42 53 4 23 14 25 6 52 39 56 41 54 5 22 13 --------------------------------------------------- ---------------------------------- 17 ------ 1 56 35 62 29 18 9 64 36 61 28 57 10 63 30 17 55 2 59 34 45 32 19 8 60 37 44 27 58 11 16 31 43 54 3 46 33 24 7 20 38 47 40 51 26 21 12 15 53 42 49 4 23 14 25 6 48 39 52 41 50 5 22 13 --------------------------------------------------- ---------------------------------- 18 ------ 1 46 35 58 29 18 9 64 36 59 28 45 10 63 30 17 47 2 61 34 57 32 19 8 60 37 44 27 62 11 16 31 43 48 3 56 33 24 7 20 38 55 40 51 26 21 12 15 49 42 53 4 23 14 25 6 54 39 50 41 52 5 22 13 --------------------------------------------------- ---------------------------------- 19 ------ 1 46 35 58 29 18 9 64 36 57 28 45 10 63 30 17 47 2 61 34 59 32 19 8 56 37 44 27 62 11 16 31 43 48 3 60 33 24 7 20 38 55 40 51 26 21 12 15 49 42 53 4 23 14 25 6 54 39 50 41 52 5 22 13 --------------------------------------------------- ---------------------------------- 20 ------ 1 60 35 46 29 18 9 64 36 45 28 61 10 63 30 17 59 2 49 34 47 32 19 8 50 37 44 27 62 11 16 31 43 58 3 48 33 24 7 20 38 51 40 55 26 21 12 15 57 42 53 4 23 14 25 6 52 39 56 41 54 5 22 13 --------------------------------------------------- ---------------------------------- 21 ------ 1 56 35 62 29 18 9 64 36 45 28 57 10 63 30 17 55 2 59 34 61 32 19 8 46 37 44 27 58 11 16 31 43 54 3 60 33 24 7 20 38 47 40 51 26 21 12 15 53 42 49 4 23 14 25 6 48 39 52 41 50 5 22 13 --------------------------------------------------- ---------------------------------- 22 ------ 1 50 35 62 29 18 9 64 36 45 28 49 10 63 30 17 51 2 47 34 61 32 19 8 46 37 44 27 48 11 16 31 43 52 3 60 33 24 7 20 38 59 40 55 26 21 12 15 53 42 57 4 23 14 25 6 58 39 54 41 56 5 22 13 --------------------------------------------------- ---------------------------------- 23 ------ 1 60 35 48 29 18 9 64 36 45 28 61 10 63 30 17 59 2 47 34 49 32 19 8 46 37 44 27 62 11 16 31 43 58 3 50 33 24 7 20 38 51 40 55 26 21 12 15 57 42 53 4 23 14 25 6 52 39 56 41 54 5 22 13 --------------------------------------------------- ---------------------------------- 24 ------ 1 60 35 56 29 18 9 64 36 57 28 61 10 63 30 17 45 2 59 34 55 32 19 8 58 37 44 27 62 11 16 31 43 46 3 54 33 24 7 20 38 53 40 49 26 21 12 15 47 42 51 4 23 14 25 6 52 39 48 41 50 5 22 13 --------------------------------------------------- ---------------------------------- 25 ------ 1 60 35 56 29 18 9 64 36 55 28 61 10 63 30 17 45 2 59 34 57 32 19 8 54 37 44 27 62 11 16 31 43 46 3 58 33 24 7 20 38 53 40 49 26 21 12 15 47 42 51 4 23 14 25 6 52 39 48 41 50 5 22 13 --------------------------------------------------- ---------------------------------- 26 ------ 1 60 35 48 29 18 9 64 36 49 28 61 10 63 30 17 59 2 37 34 47 32 19 8 50 39 46 27 62 11 16 31 45 58 3 38 33 24 7 20 40 51 42 55 26 21 12 15 57 44 53 4 23 14 25 6 52 41 56 43 54 5 22 13 --------------------------------------------------- ---------------------------------- 27 ------ 1 40 35 62 29 18 9 64 36 51 28 39 10 63 30 17 41 2 37 34 61 32 19 8 50 59 52 27 38 11 16 31 53 42 3 60 33 24 7 20 58 49 56 45 26 21 12 15 43 54 47 4 23 14 25 6 48 57 44 55 46 5 22 13 --------------------------------------------------- ---------------------------------- 28 ------ 1 60 35 38 29 18 9 64 36 49 28 61 10 63 30 17 59 2 37 34 39 32 19 8 50 41 48 27 62 11 16 31 47 58 3 40 33 24 7 20 42 51 44 55 26 21 12 15 57 46 53 4 23 14 25 6 52 43 56 45 54 5 22 13 --------------------------------------------------- ---------------------------------- 29 ------ 1 38 35 50 29 18 9 64 36 49 28 61 10 63 30 17 39 2 37 34 51 32 19 8 48 53 60 27 62 11 16 31 59 40 3 52 33 24 7 20 54 47 56 43 26 21 12 15 41 58 45 4 23 14 25 6 46 55 42 57 44 5 22 13 --------------------------------------------------- ---------------------------------- 30 ------ 1 60 35 40 29 18 9 64 36 39 28 61 10 63 30 17 59 2 37 34 41 32 19 8 38 49 42 27 62 11 16 31 43 58 3 50 33 24 7 20 48 51 46 55 26 21 12 15 57 44 53 4 23 14 25 6 52 47 56 45 54 5 22 13 --------------------------------------------------- ---------------------------------- 31 ------ 1 60 35 40 29 18 9 64 36 39 28 61 10 63 30 17 59 2 37 34 41 32 19 8 38 43 50 27 62 11 16 31 49 58 3 42 33 24 7 20 44 55 46 51 26 21 12 15 57 48 53 4 23 14 25 6 54 45 56 47 52 5 22 13 --------------------------------------------------- ---------------------------------- 32 ------ 1 52 35 40 29 18 9 64 36 39 28 51 10 63 30 17 53 2 37 34 41 32 19 8 38 43 50 27 62 11 16 31 49 54 3 42 33 24 7 20 44 57 46 61 26 21 12 15 55 48 59 4 23 14 25 6 58 45 56 47 60 5 22 13 --------------------------------------------------- ---------------------------------- 33 ------ 1 60 35 40 29 18 9 64 36 39 28 61 10 63 30 17 59 2 37 34 41 32 19 8 38 43 50 27 62 11 16 31 49 58 3 42 33 24 7 20 44 51 46 55 26 21 12 15 57 48 53 4 23 14 25 6 52 45 56 47 54 5 22 13 --------------------------------------------------- ---------------------------------- 34 ------ 1 60 35 48 29 18 9 64 36 47 28 61 10 63 30 17 59 2 37 34 49 32 19 8 46 51 58 27 62 11 16 31 57 38 3 50 33 24 7 20 52 45 54 41 26 21 12 15 39 56 43 4 23 14 25 6 44 53 40 55 42 5 22 13 --------------------------------------------------- Process finished with exit code -1
骑士周游问题 --- 递归解法 --- java代码,布布扣,bubuko.com
标签：style class blog code java ext
原文地址：http://www.cnblogs.com/kodoyang/p/Algorithm_Recursive_KnightTour.html
