poj2288之求有多少条哈密顿路

Islands and Bridges

Time Limit: 4000MS		Memory Limit: 65536K
Total Submissions: 8427		Accepted: 2174

Description

Given a map of islands and bridges that connect these islands, a Hamilton path, as we all know, is a path along the bridges such that it visits each island exactly once. On our map, there is also a positive integer value associated with each island. We call a Hamilton path the best triangular Hamilton path if it maximizes the value described below. 

Suppose there are n islands. The value of a Hamilton path C1C2...Cn is calculated as the sum of three parts. Let Vi be the value for the island Ci. As the first part, we sum over all the Vi values for each island in the path. For the second part, for each edge CiC _i+1 in the path, we add the product Vi*V _i+1. And for the third part, whenever three consecutive islands CiC _i+1C _i+2 in the path forms a triangle in the map, i.e. there is a bridge between Ci and C _i+2, we add the product Vi*V _i+1*V _i+2. 

Most likely but not necessarily, the best triangular Hamilton path you are going to find contains many triangles. It is quite possible that there might be more than one best triangular Hamilton paths; your second task is to find the number of such paths. 

Input

The input file starts with a number q (q<=20) on the first line, which is the number of test cases. Each test case starts with a line with two integers n and m, which are the number of islands and the number of bridges in the map, respectively. The next line contains n positive integers, the i-th number being the Vi value of island i. Each value is no more than 100. The following m lines are in the form x y, which indicates there is a (two way) bridge between island x and island y. Islands are numbered from 1 to n. You may assume there will be no more than 13 islands. 

Output

For each test case, output a line with two numbers, separated by a space. The first number is the maximum value of a best triangular Hamilton path; the second number should be the number of different best triangular Hamilton paths. If the test case does not contain a Hamilton path, the output must be `0 0'. 

Note: A path may be written down in the reversed order. We still think it is the same path.

Sample Input

2
3 3
2 2 2
1 2
2 3
3 1
4 6
1 2 3 4
1 2
1 3
1 4
2 3
2 4
3 4

Sample Output

22 3
69 1

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <string>
#include <queue>
#include <algorithm>
#include <map>
#include <cmath>
#include <iomanip>
#define INF 99999999
typedef long long LL;
using namespace std;

const int MAX=(1<<14)+10;
int n,m;
LL val[15],dp[MAX][15][15],num[MAX][15][15];
bool edge[15][15];

void DP(){
	int bit=1<<(n+1);
	for(int i=0;i<bit;++i){
		for(int j=0;j<=n;++j){
			for(int k=0;k<=n;++k)dp[i][j][k]=-1;
		}
	}
	//初始化0->i的状态,并且dp[s][i][0]也赋值是为了当n=1的时候也有0->1和1->0两种情况 
	for(int i=1;i<=n;++i)dp[1|(1<<i)][0][i]=dp[1|(1<<i)][i][0]=val[i],num[1|(1<<i)][0][i]=num[1|(1<<i)][i][0]=1;
	for(int i=0;i<bit;++i){
		for(int j=0;j<=n;++j){
			for(int k=1;k<=n;++k){//k必须从1开始,k如果从0开始会产生1->0>2这种1->2无边但是有结果的情况 
				if(dp[i][j][k] == -1)continue;//如果dp[i][j][k]这个状态没有出现过就不能由这个状态去推其他状态 
				for(int t=0;t<=n;++t){
					if(i&(1<<t))continue;//走过的点不能重复走 
					if(!edge[k][t])continue;//k->t有边才能从k->t 
					int w=dp[i][j][k]+val[t]+val[k]*val[t];
					if(edge[t][j])w+=val[k]*val[t]*val[j];
					if(w>dp[i|(1<<t)][k][t])dp[i|(1<<t)][k][t]=w,num[i|(1<<t)][k][t]=num[i][j][k];
					else if(w == dp[i|(1<<t)][k][t])num[i|(1<<t)][k][t]+=num[i][j][k];
				}
			}
		}
	}
	LL sum=0,ans=0;
	for(int i=0;i<=n;++i){
		for(int j=0;j<=n;++j){
			if(dp[bit-1][i][j]>sum)sum=dp[bit-1][i][j],ans=num[bit-1][i][j];
			else if(dp[bit-1][i][j] == sum)ans+=num[bit-1][i][j];
		}
	}
	printf("%lld %lld\n",sum,ans/2);
}

int main(){
	int t,u,v;
	scanf("%d",&t);
	while(t--){
		scanf("%d%d",&n,&m);
		for(int i=1;i<=n;++i)scanf("%lld",&val[i]);
		memset(edge,false,sizeof edge);
		for(int i=1;i<=n;++i)edge[0][i]=edge[i][0]=true;
		for(int i=0;i<m;++i){
			scanf("%d%d",&u,&v);
			edge[u][v]=edge[v][u]=true;
		}
		DP();
	}
	return 0;
}