数据结构练习（42）八皇后问题

http://zhedahht.blog.163.com/blog/static/2541117420114331616329/

思路：

1. 生成一组初始数据：01234567

2. 对这组数据进行排列组合，然后找满足8皇后解法的排列即：任何两个皇后都不能在同一列或对角线上

3. permutation的时候要注意，交换数据要从自身交换起，终止的时候是index == length。

#include <iostream>
using namespace std;

void PrintQueens(int column[], int length)
{
    for (int i = 0; i < length; ++i)
        cout << column[i] << ' ';
    cout << endl;
}

bool CheckQueens(int column[], int length)
{
    for (int i = 0; i < length; ++i)
        for (int j = i+1; j < length; ++j)
            if (j - i == column[i] - column[j] || i - j == column[i] - column[j])
                return false;
    return true;
}

void SwapValue(int& a, int& b)
{
    int t = a;
    a = b, b = t;
}

void Permutation(int column[], int length, int index)
{
    if (index == length)
    {
        if (CheckQueens(column, length))
            PrintQueens(column, length);
    }
    else
    {
        for (int i = index; i < length; ++i)
        {
            SwapValue(column[index], column[i]);
            Permutation(column, length, index + 1);
            SwapValue(column[index], column[i]);
        }
    }
}

void EightQueen()
{
    const int queens = 8;
    int column[queens+1];

    for (int i = 0; i < queens; ++i)
        column[i] = i;

    Permutation(column, queens, 0);
}


int main()
{
    EightQueen();
    return 0;
}