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

其實是理解錯題意了。。要求總費用最小，就不能還是找邊最小，然後加上邊左右的路由器費用，應該是每個邊上加上兩邊路由器的費用。。。。

#include<iostream>
#include<queue>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<map>
#include<cmath>
using namespace std;
typedef long long LL;
const int inf = 0x3f3f3f3f;
const double eps = 1e-8;
const double PI = acos(-1);
#define pb push_back
#define mp make_pair
#define fi first
#define se second
const int N = 1005;

int lowcost[N];
int mk[N][N];
bool vis[N];
int a[N];
int n,m;

int prim()
{
    memset(vis,false,sizeof(vis));
    for(int i = 1;i <= n;++i){
        lowcost[i] = mk[1][i];
    }
    lowcost[1] = 0;
    vis[1] = true;
    int ans = 0;
    for(int i = 0;i < n - 1;++i)
    {
        int MIN = inf;
        int k = 0;
        for(int j = 1;j <= n;++j){
            if(!vis[j] && MIN > lowcost[j]){
                MIN = lowcost[j];
                k = j;
            }
        }
        vis[k] = true;
        ans += MIN;
        for(int j = 1;j <= n;++j){
            if(!vis[j] && lowcost[j] > mk[k][j]){
                lowcost[j] = mk[k][j];
            }
        }
    }
    return ans;
}

int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        for(int i = 1;i <= n;++i){
            scanf("%d",&a[i]);
        }
        for(int i = 1;i <= n;++i){
            for(int j = 1;j <= n;++j){
                scanf("%d",&mk[i][j]);
                mk[i][j] += (a[i] + a[j]);
            }
        }
        int ans = prim();
        printf("%d\n",ans);
    }
    return 0;
}