求教（有没有人能做的出来的--最好能用多种方法）

[CycloneFox]

9个数字从1~9分别放在3*3的格子里使横,竖,斜相加所得的数均等于同一个数.
用C++编写.
扩展为25,49,81个数.
那位大虾肯帮小弟这个忙呀?

[Kavent]

幻方问题嘛~

[nealzane]

扔块砖头：

#include <iostream>
using namespace std;

bool used[12] = { false };

int board[4][4];

bool check(void) {
return (board[1][1] + board[2][1] + board[3][1] == 15 &&
board[1][2] + board[2][2] + board[3][2] == 15 &&
board[1][3] + board[2][3] + board[3][3] == 15 &&
board[1][1] + board[2][2] + board[3][3] == 15 &&
board[1][3] + board[2][2] + board[3][1] == 15);
}

void rowAt(int row) {
if (row == 0) {
if (check()) {
for (int i = 1; i <= 3; i ++, cout << endl)
for (int j = 1; j <= 3; j ++)
cout << board[i][j] << ' ';
cout << endl;
}
}
else {
for (int i = 1; i <= 9; i ++) {
if (!used[i]) {
used[i] = true;
board[row][1] = i;
for (int j = 1; j <= 9; j ++) {
if (!used[j]) {
used[j] = true;
board[row][2] = j;
int k = 15 - i - j;
if (k > 0 && !used[k]) {
used[k] = true;
board[row][3] = k;
rowAt(row - 1);
used[k] = false;
}
used[j] = false;
}
}
used[i] = false;
}
}
}
}

int main(void) {
rowAt(3);
}

------------------------------------------------------------

输出：

4 3 8
9 5 1
2 7 6

6 1 8
7 5 3
2 9 4

2 7 6
9 5 1
4 3 8

8 1 6
3 5 7
4 9 2

2 9 4
7 5 3
6 1 8

8 3 4
1 5 9
6 7 2

4 9 2
3 5 7
8 1 6

6 7 2
1 5 9
8 3 4

[nealzane]

修正了小小的漏洞（不过也是洞啊 =_=b）：

#include <iostream>
using namespace std;

bool used[12] = { false };

int board[4][4];

bool check(void) {
return (board[1][1] + board[2][1] + board[3][1] == 15 &&
board[1][2] + board[2][2] + board[3][2] == 15 &&
board[1][3] + board[2][3] + board[3][3] == 15 &&
board[1][1] + board[2][2] + board[3][3] == 15 &&
board[1][3] + board[2][2] + board[3][1] == 15);
}

void rowAt(int row) {
if (row == 0) {
if (check()) {
for (int i = 1; i <= 3; i ++, cout << endl)
for (int j = 1; j <= 3; j ++)
cout << board[i][j] << ' ';
cout << endl;
}
}
else {
for (int i = 1; i <= 9; i ++) {
if (!used[i]) {
used[i] = true;
board[row][1] = i;
for (int j = 1; j <= 9; j ++) {
if (!used[j]) {
used[j] = true;
board[row][2] = j;
int k = 15 - i - j;
if (k > 0 && k < 10 && !used[k]) {
used[k] = true;
board[row][3] = k;
rowAt(row - 1);
used[k] = false;
}
used[j] = false;
}
}
used[i] = false;
}
}
}
}

int main(void) {
rowAt(3);
}

------------------------------------------------------------

输出：

4 3 8
9 5 1
2 7 6

6 1 8
7 5 3
2 9 4

2 7 6
9 5 1
4 3 8

8 1 6
3 5 7
4 9 2

2 9 4
7 5 3
6 1 8

8 3 4
1 5 9
6 7 2

4 9 2
3 5 7
8 1 6

6 7 2
1 5 9
8 3 4

[BlueSky2008]

FAQ->组合数学算法->n阶幻方解法。

[CycloneFox]

谢谢了真是太好了.
哈哈.

[CycloneFox]

楼上的师兄，谢谢了。