#include <iostream>    
#include <cmath>     
#include "RandomNumber.h"     
using namespace std;

class Queen
{
	friend bool nQueen(int);
private:
	bool Place(int k);//测试皇后k置于第x[k]列的合法性  
	bool Backtrack(int t);//解n后问题的回溯法  
	bool QueensLV(int stopVegas);//随机放置n个皇后拉斯维加斯算法  
	int n, *x, *y;
};

bool Queen::Place(int k)
{//测试皇后k置于第x[k]列的合法性  
	for (int j = 1; j<k; j++)
		if ((abs(k - j) == abs(x[j] - x[k])) || (x[j] == x[k]))
			return false;
	return true;
}

bool Queen::Backtrack(int t)
{//解n后问题的回溯法  
	if (t>n){
		for (int i = 1; i <= n; i++)
			y[i] = x[i];
		return true;
	}
	else
		for (int i = 1; i <= n; i++)
		{
			x[t] = i;
			if (Place(t) && Backtrack(t + 1))
				return true;
		}
	return false;
}

bool Queen::QueensLV(int stopVegas)
{//随机放置n个皇后拉斯维加斯算法  
	RandomNumber rnd;
	int k = 1;//随机数产生器  
	int count = 1;
	//1<=stopVegas<=n表示允许随机放置的皇后数  
	while ((k <= stopVegas) && (count>0))
	{
		count = 0;
		for (int i = 1; i <= n; i++)
		{
			x[k] = i;
			if (Place(k))
				y[count++] = i;
		}
		if (count>0)
			x[k++] = y[rnd.Random(count)];//随机位置  
	}
	return (count>0);//count>0表示放置成功  
}

bool nQueen(int n)
{
	//与回溯法相结合的解n后问题的拉斯维加斯算法  
	Queen X;
	//初始化X  
	X.n = n;
	int *p = new int[n + 1];
	int *q = new int[n + 1];
	for (int i = 0; i <= n; i++)
	{
		p[i] = 0;
		q[i] = 0;
	}
	X.y = p;
	X.x = q;
	int stop = 2;
	if (n>15)
		stop = n - 15;
	bool found = false;
	while (!X.QueensLV(stop));
	//算法的回溯搜索部分  
	if (X.Backtrack(stop + 1))
	{
		for (int i = 1; i <= n; i++)
			cout << p[i] << " ";
		found = true;
	}
	cout << endl;
	delete[]p;
	delete[]q;
	return found;
}

int main()
{
	if (!nQueen(8))
	{
		cout << "搜索不成功！！" << endl;
	}
	system("pause");
	return 0;
}

产生随机数的头文件

#include <ctime>  

//随机数类  
const unsigned long maxshort = 65536L;
const unsigned long multiplier = 1194211693L;
const unsigned long adder = 12345L;
class RandomNumber
{
private:
	//当前种子  
	unsigned long randSeed;
public:
	void RandonNumber(unsigned long s = 0);//构造函数，默认值0表示由系统自动产生种子  
	unsigned short Random(unsigned long n);//产生0：n-1之间的随机整数  
	double fRandom(void);//产生[0,1)之间的随机实数  
};

void RandomNumber::RandonNumber(unsigned long s)//产生种子  
{
	if (s == 0)
		randSeed = time(0);//用系统时间产生种子  
	else
		randSeed = s;//由用户提供种子  
}
unsigned short RandomNumber::Random(unsigned long n)//产生0：n-1之间的随机整数  
{
	randSeed = multiplier*randSeed + adder;
	return (unsigned short)((randSeed >> 16) % n);
}
double RandomNumber::fRandom(void)//产生[0,1)之间的随机实数  
{
	return Random(maxshort) / double(maxshort);
}