LightOJ - 1380 Teleport(最小树形图)

题目大意：给你一个有向图，问这个有向图中，以k为根的最小树形图

解题思路：模版题

#include <cstdio>
#include <cstring>

const int MAXNODE = 1010;
const int MAXEDGE = 10010;
typedef int Type;
const Type INF = 0x3f3f3f3f;

struct Edge {
    int u, v;
    Type dis;
    Edge() {}
    Edge(int u, int v, Type dis): u(u), v(v), dis(dis) {}
};

struct Directed_MT{
    int n, m;
    Edge edges[MAXEDGE];
    int vis[MAXNODE];
    int pre[MAXNODE];
    int id[MAXNODE];
    Type in[MAXNODE];

    void init(int n) {
        this->n = n;
        m = 0;
    }

    void AddEdge(int u, int v, Type dis) {
        edges[m++] = Edge(u, v, dis);
    }

    Type DirMt(int root) {
        Type ans = 0;
        while (1) {
            //初始化
            for (int i = 0; i < n; i++) in[i] = INF;

            for (int i = 0; i < m; i++) {
                int u = edges[i].u;
                int v = edges[i].v;
                //找寻最小入边，删除自环
                if (edges[i].dis < in[v] && u != v) {
                    in[v] = edges[i].dis;
                    pre[v] = u;
                }
            }

            //如果没有最小入边，表示该点不连通，则最小树形图形成失败
            for (int i = 0; i < n; i++) {
                if (i == root) continue;
                if (in[i] == INF) return -1;
            }

            int cnt = 0;//记录缩点
            memset(id, -1, sizeof(id));
            memset(vis, -1, sizeof(vis));
            in[root] = 0;//树根不能有入边
            for (int i = 0; i < n; i++) {
                ans += in[i];
                int v = i;
                //找寻自环
                while (vis[v] != i && id[v] == -1 && v != root) {
                    vis[v] = i;
                    v = pre[v];
                }
                //找到自环
                if (v != root && id[v] == -1) {
                    for (int u = pre[v]; u != v; u = pre[u]) 
                        id[u] = cnt;
                    id[v] = cnt++;
                }
            }

            //如果没有自环了，表示最小树形图形成成功了
            if (cnt == 0) break;

            //找到那些不是自环的，重新给那些点进行标记
            for (int i = 0; i < n; i++) 
                if (id[i] == -1) id[i] = cnt++;

            for (int i = 0; i < m; i++) {
                int v = edges[i].v;
                edges[i].v = id[edges[i].v];
                edges[i].u = id[edges[i].u];
                if (edges[i].u != edges[i].v) 
                    edges[i].dis -= in[v];
            }
            //缩点完后，点的数量就边了
            n = cnt;
            root = id[root];
        }
        return ans;
    }
}MT;

int cas = 1;
void init() {
    int n, m, k;
    scanf("%d%d%d", &n, &m, &k);
    MT.init(n);

    int u, v, dis;
    for (int i = 0; i < m; i++) {
        scanf("%d%d%d", &u, &v, &dis);
        MT.AddEdge(u, v, dis);
    }
    int ans = MT.DirMt(k);
    if (ans == -1) printf("Case %d: impossible\n", cas++);
    else printf("Case %d: %d\n", cas++, ans);

}

int main() {
    int test;
    scanf("%d", &test);
    while (test--) init();
    return 0;
}