ZOJ

QS Network

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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Sunny Cup 2003 - Preliminary Round

April 20th, 12:00 - 17:00

Problem E: QS Network

In the planet w-503 of galaxy cgb, there is a kind of intelligent creature named QS. QScommunicate with each other via networks. If two QS want to get connected, they need to buy two network adapters (one for each QS) and a segment of network cable. Please be advised that ONE NETWORK ADAPTER CAN ONLY BE USED IN A SINGLE CONNECTION.(ie. if a QS want to setup four connections, it needs to buy four adapters). In the procedure of communication, a QS broadcasts its message to all the QS it is connected with, the group of QS who receive the message broadcast the message to all the QS they connected with, the procedure repeats until all the QS's have received the message.

A sample is shown below:

A sample QS network, and QS A want to send a message.

Step 1. QS A sends message to QS B and QS C;

Step 2. QS B sends message to QS A ; QS C sends message to QS A and QS D;

Step 3. the procedure terminates because all the QS received the message.

Each QS has its favorate brand of network adapters and always buys the brand in all of its connections. Also the distance between QS vary. Given the price of each QS's favorate brand of network adapters and the price of cable between each pair of QS, your task is to write a program to determine the minimum cost to setup a QS network.

Input

The 1st line of the input contains an integer t which indicates the number of data sets.

From the second line there are t data sets.

In a single data set,the 1st line contains an interger n which indicates the number of QS.

The 2nd line contains n integers, indicating the price of each QS's favorate network adapter.

In the 3rd line to the n+2th line contain a matrix indicating the price of cable between ecah pair of QS.

Constrains:

all the integers in the input are non-negative and not more than 1000.

Output

for each data set,output the minimum cost in a line. NO extra empty lines needed.

Sample Input

1
3
10 20 30
0 100 200
100 0 300
200 300 0

Sample Output

370

题意：在一个叫做QS的星系，他们使用一些特殊的通讯方式，两个人之间通讯需要使用一个网络适配器，但是一个网络适配器只能跟一个人联系，所有它连接几个人就需要及格适配器，而且每个人都有一些不同的偏好，喜欢的适配器的牌子也是不同的，现在让你求出来让QS人之间相互通讯最少需要多少代价？

输入第一行是测试数据组数，下面是一个N，代表N个人，下一样有N个数表示每个人喜欢的适配器的价格，接着一个矩阵，表示两点间通讯的价格。

思路：只要在每条边的权值上加上两个适配器的价格就可以了。

#include <iostream>#include <cstdio>#include <queue>#define max_ 1010using namespace std;int n;int mp[max_][max_],cost[max_],pre[max_];struct edge{int u,v,w;bool operator < (const edge &a)const{return a.w<w;}}e;priority_queue<edge>q;int find(int x){return pre[x]==x?x:pre[x]=find(pre[x]);}int kruskal(){int cnt=0,s=0;while(q.size()){e=q.top();q.pop();int tx=find(e.u);int ty=find(e.v);if(tx!=ty){pre[tx]=ty;cnt++;s+=e.w;}if(cnt==n-1)return s;}return 0;}int main(){int t,i,j;scanf("%d",&t);while(t--){scanf("%d",&n);for(i=1;i<=n;i++)pre[i]=i;while(q.size())q.pop();for(i=1;i<=n;i++)scanf("%d",&cost[i]);for(i=1;i<=n;i++){for(j=1;j<=n;j++){int c;scanf("%d",&c);if(i==j)mp[i][j]=c;else if(i<j){mp[i][j]=c+cost[i]+cost[j];e.u=i;e.v=j;e.w=mp[i][j];q.push(e);}elsemp[i][j]=c+cost[i]+cost[j];}}printf("%d\n",kruskal());}}