直接上15ms代码，还没想好记忆化怎么弄  应该还能更快一点

AC代码如下：

#include<iostream>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;

char s[2000],sr[2000];
int res,book[20],n,flag;

int cmp(char a,char b)
{
	return a>b;
}

void dfs(int k,int sum,int q)
{
	if(k==6)
	{
		if(res==sum)
		{
			flag=1;
			sr[k-1]=0;
			return ;
		}
		return ;
	}
	int i,z;
	for(i=0;i<n;i++)
	{
		if(!book[i])
		{
			z=s[i]-'A'+1;
			book[i]=1;
			sr[k-1]=s[i];
			dfs(k+1,sum+q*pow(z,k),-q);
			if(flag) return ;
			sr[k-1]=0;
			book[i]=0;
		}
	}
	return ;
}

int main()
{
	while(cin>>res>>s && (res||strcmp(s,"END")))
	{
		n=strlen(s);
		flag=0;
		memset(book,0,sizeof(book));
		sort(s,s+n,cmp);
		//先把结果不能达到的筛掉
		if(pow(s[0]-'A'+1,5)+pow(s[1]-'A'+1,4)+pow(s[2]-'A'+1,3)-pow(s[n-1]-'A'+1,2)-pow(s[n-2]-'A'+1,1)<res ||
		pow(s[n-1]-'A'+1,5)+pow(s[n-2]-'A'+1,4)+pow(s[n-3]-'A'+1,3)-pow(s[0]-'A'+1,2)-pow(s[1]-'A'+1,1)>res)
		{
			cout<<"no solution"<<endl;
			continue;
		}
		dfs(1,0,1);
		if(flag)
			cout<<sr<<endl;
		else
			cout<<"no solution"<<endl;
	}
	return 0;
}