zoj -1586 QS Network

http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=1586

简单题

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

#include <stdio.h>
#include <iostream>
#include <string.h>
#include <algorithm>
#include <math.h>
#include <stack>
#include <queue>

using namespace std;
#define INF 10000000

int n, m;
int a,b,c,d[1110];

int map[1110][1110], dis[1110], v[1110];

int prim(int n)
{
    int i, j, k, min, sum = 0;
    for (i = 1; i <= n; i++)
        dis[i] = map[1][i];

    memset(v, 0, sizeof(v));
    v[1] = 1;
    dis[1] = 0;

    for (i = 2; i <= n; i++)
    {
        k = 1;
        min = INF;
        for (j = 1; j <= n; j++)
            if (!v[j] && min>dis[j])
            {
                k = j;
                min = dis[j];
            }
        sum += min;
        v[k] = 1;
        for (j = 1; j <= n; j++)
            if (!v[j] && dis[j]>map[k][j])
                dis[j] = map[k][j];
    }
    return sum;
}

int main()
{
    int t;
    cin>>t;
    while (t--)
    {
        cin>>n;
        for (int i = 1; i <= n; i++)
            for (int j = 1; j <= n; j++)
            {
                if (i != j)
                    map[i][j] = INF;
                else
                    map[i][j]= 0;
            }
        for(int i=1;i<=n;i++)
            cin>>d[i];
        for (int i = 1; i <= n; i++)
            for (int j = 1; j <= n; j++)
        {
            cin>>a;
            if (map[i][j] > a)
            {
                map[i][j] = a + d[i] + d[j];
                map[j][i] = a + d[i] + d[j];
            }
            else
            {
                map[i][j] = map[i][j] + d[i] + d[j];
                map[j][i] = map[i][j] + d[i] + d[j];
            }
        }
        printf("%d\n",prim(n));
    }
    return 0;
}