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POJ – 2377 Bad Cowtractors(图论/最大生成树)

编程语言 karry_zzj 13℃ 0评论
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问题描述

Bessie has been hired to build a cheap internet network among Farmer John’s N (2 <= N <= 1,000) barns that are conveniently numbered 1..N. FJ has already done some surveying, and found M (1 <= M <= 20,000) possible connection routes between pairs of barns. Each possible connection route has an associated cost C (1 <= C <= 100,000). Farmer John wants to spend the least amount on connecting the network; he doesn’t even want to pay Bessie.

Realizing Farmer John will not pay her, Bessie decides to do the worst job possible. She must decide on a set of connections to install so that (i) the total cost of these connections is as large as possible, (ii) all the barns are connected together (so that it is possible to reach any barn from any other barn via a path of installed connections), and (iii) so that there are no cycles among the connections (which Farmer John would easily be able to detect). Conditions (ii) and (iii) ensure that the final set of connections will look like a “tree”.

Input


* Line 1: Two space-separated integers: N and M


* Lines 2..M+1: Each line contains three space-separated integers A, B, and C that describe a connection route between barns A and B of cost C.

Output


* Line 1: A single integer, containing the price of the most expensive tree connecting all the barns. If it is not possible to connect all the barns, output -1.

Sample Input

5 8
1 2 3
1 3 7
2 3 10
2 4 4
2 5 8
3 4 6
3 5 2
4 5 17

Sample Output

42

1.分析:

代码如下:

#include
#include
using namespace std;
const int maxn = 1000+10;
const int maxe = 20000+10;
struct edge{
    int u, v, cost;
}es[maxe];

int cmp(const edge &a, const edge &b)
{
    return a.cost > b.cost;
}
int N,M;
int par[maxn];
/*初始化*/
void Init()
{
    for(int i=1; i<=N; i++)
    {
        par[i] = i;
    }
}
/*找爹*/
int find(int x)
{
    int r = x;
    while(r!=par[r])
    r = par[r];

    int i = x;
    int j;  
    while(i != r)
    {
        j = par[i];
        par[i] = r;
        i = j;
    }
    return r;
}
/*是不是同个爹*/
bool same(int x, int y)
{
    return find(x)==find(y);
}
/*合并爹*/
void unite(int x, int y)
{
    par[find(x)] = find(y);
}
/*最小生成树算法*/
int kruskal()
{
    sort(es, es+M, cmp);
    Init();
    int res = 0;
    for(int i=0; iif(!same(e.u, e.v))
        {
            res += e.cost;
            unite(e.u, e.v);
        }
    }
    return res;
}
int main()
{
    scanf("%d%d",&N,&M);
    for(int i=0; iscanf("%d%d%d",&es[i].u,&es[i].v,&es[i].cost);
    }
    int k = 0;
    kruskal();
    for(int i=1; i<=N; i++)
    {
        if(par[i] == i)
        k++;
    }
    if(k>1) printf("-1\n");
    else
    printf("%d\n", kruskal());
    return 0;
}

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