Zoj QS 1586 Network (prim algorithm)

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 are a kind of intelligent creature named QS. Qscommunicate with all other via networks. If the QS want to get connected, the they need to buy the network adapters (one for each QS) and a segment of the network cable. Please be advised that one NETWORK ADAPTER CAN is only used in A and 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 their message to all the QS it was connected with, the group of QS Eive the message broadcast the message to all the "Qs they connected with," the procedure repeats until all the QS ' s has a re ceived 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 have its Favorate brand's 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's 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 the data sets.

From the second line there is 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.

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 is non-negative and not more than 1000.

Output

For each data set,output, the minimum cost of 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

The minimum spanning tree, which adds the vertex value to the two endpoints of each edge.

#include "stdio.h" #include "string.h" #include "iostream" #include "queue" #include "algorithm" using namespace std;#     Define n 1005const int inf=0x3fffffff;int g[n][n],a[n],dis[n];bool mark[n];void prim (int s,int N) {int i,j,u,min,sum=0;    memset (Mark,0,sizeof (Mark));    Mark[s]=1;    for (i=0;i<n;i++) {dis[i]=g[s][i];        } for (j=1;j<n;j++) {min=inf;        U=s;                for (i=0;i<n;i++) {if (!mark[i]&&dis[i]<min) {min=dis[i];            U=i;        }} mark[u]=1;        Sum+=min;            for (i=0;i<n;i++) {if (Dis[i]>g[u][i]) {dis[i]=g[u][i]; }}} printf ("%d\n", sum);}    int main () {int t,n,i,j;    scanf ("%d", &t);        while (t--) {scanf ("%d", &n);        for (i=0;i<n;i++) {scanf ("%d", &a[i]);      } for (i=0;i<n;i++) {for (j=0;j<n;j++)      {scanf ("%d", &g[i][j]);            if (i!=j) g[i][j]+= (A[i]+a[j]);    }} prim (0,n); } return 0;}