POJ 1287 Networking 【最小生成树Kruskal】

Networking

Description

You are assigned to design network connections between certain points in a wide area. You are given a set of points in the area, and a set of possible routes for the cables that may connect pairs of points. For each possible route between two points, you are given the length of the cable that is needed to connect the points over that route. Note that there may exist many possible routes between two given points. It is assumed that the given possible routes connect (directly or indirectly) each two points in the area. 
Your task is to design the network for the area, so that there is a connection (direct or indirect) between every two points (i.e., all the points are interconnected, but not necessarily by a direct cable), and that the total length of the used cable is minimal.

Input

The input file consists of a number of data sets. Each data set defines one required network. The first line of the set contains two integers: the first defines the number P of the given points, and the second the number R of given routes between the points. The following R lines define the given routes between the points, each giving three integer numbers: the first two numbers identify the points, and the third gives the length of the route. The numbers are separated with white spaces. A data set giving only one number P=0 denotes the end of the input. The data sets are separated with an empty line. 
The maximal number of points is 50. The maximal length of a given route is 100. The number of possible routes is unlimited. The nodes are identified with integers between 1 and P (inclusive). The routes between two points i and j may be given as i j or as j i. 

Output

For each data set, print one number on a separate line that gives the total length of the cable used for the entire designed network.

Sample Input

1 0

2 3
1 2 37
2 1 17
1 2 68

3 7
1 2 19
2 3 11
3 1 7
1 3 5
2 3 89
3 1 91
1 2 32

5 7
1 2 5
2 3 7
2 4 8
4 5 11
3 5 10
1 5 6
4 2 12

0

Sample Output

0
17
16
26

题解

两点之间有很多条边  然而我们肯定选最小的   用Prim的话需要在输入的时候取最小的边 但用Kruskal就是一个模板的事、省力

代码

#include<iostream>
#include<cstdio>     //EOF,NULL
#include<cstring>    //memset
#include<cstdlib>    //rand,srand,system,itoa(int),atoi(char[]),atof(),malloc
#include<cmath>           //ceil,floor,exp,log(e),log10(10),hypot(sqrt(x^2+y^2)),cbrt(sqrt(x^2+y^2+z^2))
#include<algorithm>  //fill,reverse,next_permutation,__gcd,
#include<string>
#include<vector>
#include<queue>
#include<stack>
#include<utility>
#include<iterator>
#include<iomanip>             //setw(set_min_width),setfill(char),setprecision(n),fixed,
#include<functional>
#include<map>
#include<set>
#include<limits.h>     //INT_MAX
#include<bitset> // bitset<?> n
using namespace std;

typedef long long ll;
typedef pair<int,int> P;
#define all(x) x.begin(),x.end()

#define readc(x) scanf("%c",&x)
#define read(x) scanf("%d",&x)
#define read2(x,y) scanf("%d%d",&x,&y)
#define read3(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define print(x) printf("%d
",x)
#define mst(a,b) memset(a,b,sizeof(a))
#define lowbit(x) x&-x
#define lson(x) x<<1
#define rson(x) x<<1|1
#define pb push_back
#define mp make_pair
const int INF =0x3f3f3f3f;
const int inf =0x3f3f3f3f;
const int mod = 1e9+7;
const int MAXN = 105;
const int maxn = 10010;

int n,m;
int cnt ;
int ans;
int a,b,v;
int pre[MAXN];

struct node{
  int st,ed,v;
  bool operator < (node b) const{
     return v < b.v;
  }
}rod[MAXN];

void Init(){
  ans = 0;
  cnt = 0;
  for(int i = 0 ; i < MAXN ; i++){
    pre[i] = i;
  }
}
int find(int x){ return x == pre[x] ? x : pre[x] = find(pre[x]);}
bool join(int x,int y){
    if(find(x)!=find(y)){
        pre[find(y)] =find(x);
        return true;
    }
    return false;
}
void kruskal(){
    for(int i = 0; i < cnt ;i++){
        int mp1 = find(rod[i].st);
        int mp2 = find(rod[i].ed);
        if(join(mp1,mp2)) ans += rod[i].v;
    }
}
int main(){
    while(read(n) && n){
        read(m) ;
        if(n==1) {
            printf("0
");
            continue;
        }
        Init();
        while(m--){
            read3(a,b,v);
            rod[cnt].st = a;
            rod[cnt].ed = b;
            rod[cnt++].v = v;
         }
        sort(rod,rod + cnt);
        kruskal();
        print(ans);
    }
}