解法二

用数字i代表集合,比如i=15，表示成二进制位1111，代表a1，a2,a3,a4均在集合中

(x&i）==x则x为i子集

因为若x&i==x 则x与i的二进制表示中x为1的位i必为1，x为0的位，i可为0或1，又x<i所以x为0的位i不可能全为1，所以x为i的真子集

代码参考了

http://blog.csdn.net/suwei19870312/article/details/5830373

#include<iostream>
#include<string>
#include<math.h>
#include<vector>
using namespace std;
const int CardsNumber = 4;  
const double ResultValue=24;
const int PowCardsNumber = (1 << CardsNumber);  
const double Threshold=1E-6;
class node;
vector<node> s[16];
int number[CardsNumber];

class node{
public:
	node(){}
	node(double v,string s):value(v),exp(s){}
	double value;
	string exp;

};

void fork(int i){
	node a,b;
	//若已有值，则直接返回
	if(!s[i].empty())return;
	for(int x=1;x<i;x++){
		//&运算，若相等，说明x是i的子集
		if((x&i)==x){
			fork(x);
			fork(i-x);
			vector<node>::iterator itera,iterb;
			for(itera=s[x].begin();itera!=s[x].end();itera++){
				for(iterb=s[i-x].begin();iterb!=s[i-x].end();iterb++){
					a=*itera;
					b=*iterb;
					s[i].push_back(node(a.value+b.value,'('+a.exp+'+'+
						b.exp+')'));
					s[i].push_back(node(a.value-b.value,'('+a.exp+'-'+
						b.exp+')'));
					s[i].push_back(node(b.value-a.value,'('+b.exp+'+'+
						a.exp+')'));
					s[i].push_back(node(a.value*b.value,'('+a.exp+'*'+
						b.exp+')'));

					if(b.value!=0)
						s[i].push_back(node(a.value/b.value,'('+a.exp+'/'+
						b.exp+')'));

					if(a.value!=0)
						s[i].push_back(node(b.value/a.value,'('+b.exp+'/'+
						a.exp+')'));

				}
			}
		}


	}


}
void Game(){
	node a;
	for(int i=1;i<PowCardsNumber;i++)
		s[i].clear();
	char buf[10];
	//初始化集合中只有一张牌的情形
	//可能的四则混合运算值为该卡片的值本身
	for(int i=0;i<CardsNumber;i++){
		sprintf(buf, "%d", number[i]);
		string str = buf;
		s[1<<i].push_back(node(number[i],str));
	}
	fork(15);
	vector<node>::iterator iter;
	for(iter=s[PowCardsNumber-1].begin();
		iter!=s[PowCardsNumber-1].end();iter++){
			a=*iter;
			if(fabs(a.value-ResultValue)<Threshold){
				cout<<a.exp<<endl;
			}
	}
	cout<<"can not find a case for 24 Game"<<endl;

}
int main(){
	while(true){
		cout<<"please enter 4 numbers for 24 point game"<<endl;
		for(int i=0;i<CardsNumber;i++)
			cin>>number[i];
		Game();
	}
	return 0;

}