POJ-3164 Command Network

After a long lasting war on words, a war on arms finally breaks out between littleken’s and KnuthOcean’s kingdoms. A sudden and violent assault by KnuthOcean’s force has rendered a total failure of littleken’s command network. A provisional network must be built immediately. littleken orders snoopy to take charge of the project.

With the situation studied to every detail, snoopy believes that the most urgent point is to enable littenken’s commands to reach every disconnected node in the destroyed network and decides on a plan to build a unidirectional communication network. The nodes are distributed on a plane. If littleken’s commands are to be able to be delivered directly from a node A to another node B, a wire will have to be built along the straight line segment connecting the two nodes. Since it’s in wartime, not between all pairs of nodes can wires be built. snoopy wants the plan to require the shortest total length of wires so that the construction can be done very soon.

Input

The input contains several test cases. Each test case starts with a line containing two integer N (N ≤ 100), the number of nodes in the destroyed network, and M (M ≤ 10⁴), the number of pairs of nodes between which a wire can be built. The next Nlines each contain an ordered pair x_i and y_i, giving the Cartesian coordinates of the nodes. Then follow M lines each containing two integers i and j between 1 and N(inclusive) meaning a wire can be built between node i and node j for unidirectional command delivery from the former to the latter. littleken’s headquarter is always located at node 1. Process to end of file.

Output

For each test case, output exactly one line containing the shortest total length of wires to two digits past the decimal point. In the cases that such a network does not exist, just output ‘poor snoopy’.

Sample Input

4 6
0 6
4 6
0 0
7 20
1 2
1 3
2 3
3 4
3 1
3 2
4 3
0 0
1 0
0 1
1 2
1 3
4 1
2 3

Sample Output

31.19
poor snoopy

传说中的最小树形图。。Orz，慢慢再研究一下。

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>

#define MAX 1010
#define INF 0x3fffffff

using namespace std;

typedef struct {
    int from;
    int to;
    double cost;
} Edge;

typedef struct {
    double x;
    double y;
} Point;

Point p[MAX];
Edge edges[MAX * MAX];
int pre[MAX];
int id[MAX];
int visit[MAX];
double in[MAX];

double dis( Point a, Point b ) {
    return sqrt( ( a.x - b.x ) * ( a.x - b.x ) + ( a.y - b.y ) * ( a.y - b.y ) );
}

// root 根节点，n点个数，m边条数
double Directed_MST( int root, int n, int m ) {
    double ans = 0.0;
    while( 1 ) {
        for( int i = 0; i < n; i++ ) in[i] = INF;
        for( int i = 0; i < m; i++ ) {
            if( edges[i].from != edges[i].to && edges[i].cost < in[edges[i].to] ) {
                pre[edges[i].to] = edges[i].from;
                in[edges[i].to] = edges[i].cost;
            }
        }

        for( int i = 0; i < n; i++ ) {
            if( i != root && in[i] == INF ) return -1;  // 不存在最小树形图
        }

        int cnt = 0;
        memset( id, -1, sizeof( id ) );
        memset( visit, -1, sizeof( visit ) );
        in[root] = 0;
        // 标记环
        for( int i = 0; i < n; i++ ) {
            ans = ans + in[i];
            int v = i;
            while( visit[v] != i && id[v] == -1 && v != root ) {
                visit[v] = i;
                v = pre[v];
            }
            // 缩点
            if( v != root && id[v] == -1 ) {
                for( int u = pre[v]; u != v; u = pre[u] ) id[u] = cnt;
                id[v] = cnt++;
            }
        }
        if( cnt == 0 ) break;   // 没有有向环
        for( int i = 0; i < n; i++ ) {
            if( id[i] == -1 ) id[i] = cnt++;
        }
        // 建立新图
        for( int i = 0; i < m; i++ ) {
            int v = edges[i].to;
            edges[i].from = id[edges[i].from];
            edges[i].to = id[edges[i].to];
            if( edges[i].from != edges[i].to ) edges[i].cost -= in[v];
            // else swap( edges[i], edges[--m] );
        }
        n = cnt;
        root = id[root];
    }

    return ans;
}

int main() {
    int n, m;
    while( scanf( "%d%d", &n, &m ) != EOF ) {
        for( int i = 0; i < n; i++ ) {
            scanf( "%lf%lf", &p[i].x, &p[i].y );
        }
        for( int i = 0; i < m; i++ ) {
            scanf( "%d%d", &edges[i].from, &edges[i].to );
            edges[i].from--;
            edges[i].to--;
            if( edges[i].from != edges[i].to ) {
                edges[i].cost = dis( p[edges[i].from], p[edges[i].to] );
            }
            else {
                edges[i].cost = INF;
            }
        }
        double ans = Directed_MST( 0, n, m );
        if( ans == -1 ) printf( "poor snoopy\n" );
        else printf( "%.2f\n", ans );
    }

    return 0;
}