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
1310 20 300 100 200100 0 300200 300 0
Sample Output
370
题意：
首先给一个t，，代表t个测试样例，再给一个n，表示有n个QS装置，接下来一行是n个QS装置的成本。接下来是n*n的矩阵，表示每两个QS 装置之间链接需要的费用。求在全联通的情况下求最少费用。
思路：
直接kruskal，注意在记录两个装置之间的权值时直接加上两个装置的成本就好了。不要最后求和再加！
代码：
//12004 KB210 ms#include<iostream>#include<cstdio>#include<algorithm>using namespace std;const int inf=0xfffffff;typedef struct node{int l,r;int w;bool operator < (const node &a) const{return w<a.w;}}node;node p[1000010];int pre[1010],dis[1010],qs[1010];int num,n;int Find(int x){return pre[x]==x?pre[x]:Find(pre[x]);}int Union(int a,int b){int f1=Find(a),f2=Find(b);if(f1!=f2){pre[f1]=f2;return 1;}return 0;}void kruskal(){int sum=0;for(int i=0;i<num;i++){if(!Union(p[i].l,p[i].r))continue;sum=sum+p[i].w;}printf("%d\n",sum);}int main(){int t;scanf("%d",&t);while(t–){num=0;scanf("%d",&n);for(int i=0;i<=n;i++)pre[i]=i;for(int i=1;i<=n;i++)scanf("%d",&qs[i]);int val;for(int i=1;i<=n;i++){for(int j=1;j<=n;j++){p[num].l=i;p[num].r=j;scanf("%d",&val);p[num++].w=val+qs[i]+qs[j];}}sort(p,p+num);kruskal();}return 0;}
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