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.
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.
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.
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#define REP(i, s, n) for(int i = s; i <= n; i ++)
#define REP_(i, s, n) for(int i = n; i >= s; i --)
#define MAX_N 50 + 10
#define MAX_M 10000 + 10
using namespace std;
int n, m, u, v, w;
struct node{
int u, v, w;
}E[MAX_M];
int F[MAX_N];
int find(int x){
if(x == F[x]) return x;
return F[x] = find(F[x]);
}
void Union(int x,int y){
x = find(x); y = find(y);
if(x == y) return;
F[y] = x;
}
bool cmp(node a, node b){
return a.w < b.w;
}
int main(){
while(scanf("%d%d", &n, &m) != EOF){
if(n == 0) break;
if(n == 1 || m == 0) {printf("0\n"); continue;}
REP(i, 1, m) scanf("%d%d%d", &E[i].u, &E[i].v, &E[i].w);
sort(E + 1, E + m + 1, cmp);
REP(i, 1, n) F[i] = i;
int ans = 0;
REP(i, 1, m){
if(find(E[i].u) != find(E[i].v)){
Union(E[i].u, E[i].v);
ans += E[i].w;
}
}
printf("%d\n", ans);
}
return 0;
}
