ZOJ1586 QS Network 2017-04-13 11:46 39人阅读 评论(0) 收藏

QS Network

---

Time Limit: 2 Seconds      Memory Limit: 65536 KB

---

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

---

题目的意思是给出n个点，每个点有点权，现在要将所有点连通，连接两个点的花费是2个点的点权加这条边的边权，问最小花费

思路：奖点权并到相应的边上，然后做最小生成树

#include <iostream>
#include<queue>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<set>
using namespace std;
#define LL long long

struct node
{
    int u,v,w;
} p[1000005];
int n,cnt,pre[1005];
 int mp[1005][1005],a[1005];
bool cmp(node a,node b)
{
    return a.w<b.w;
}
void init()
{
    for(int i=0; i<1005; i++)
        pre[i]=i;
}

int fin(int x)
{
    return pre[x]==x?x:pre[x]=fin(pre[x]);
}

void kruskal()
{
    sort(p,p+cnt,cmp);
    init();
   int cost=0;
    int ans=0;
    for(int i=0; i<cnt; i++)
    {
        int a=fin(p[i].u);
        int b=fin(p[i].v);
        if(a!=b)
        {
            pre[a]=b;
            cost+=p[i].w;
            ans++;
        }
        if(ans==n-1)
        {
            break;
        }
    }
    printf("%d\n",cost);
}

int main()
{
    int T;
scanf("%d",&T);
    while(T--)
    {
        scanf("%d",&n);
        for(int i=0;i<n;i++)
            scanf("%d",&a[i]);
        for(int i=0; i<n; i++)
            for(int j=0; j<n; j++)
                scanf("%d",&mp[i][j]);
                cnt=0;
        for(int i=0; i<n; i++)
            for(int j=i+1; j<n; j++)
            {
                p[cnt].u=i,p[cnt].v=j;
                p[cnt++].w=mp[i][j]+a[i]+a[j];
            }
        kruskal();
    }
    return 0;
}