Aizu 2224 Save your cats

题目链接

题意

猫被困在围栏里，问最少去掉多长的边，使所有猫逃出来。
问题转化为将N个图转化为树，因为树不会成环，树加上一条边就可以成环

AC

• 并查集 + prim
  对于每个图，求它的最大生成树，总长度减去所有的最大生成树就是需要去掉的边

using namespace std;
int inf = 0x3f3f3f3f;
int n, m, pre[N];
double sum;
bool vis[N];
double dis[N];
struct ac{
    int v;
    double c;
};
vector<P> a(N);
vector<ac> g[N];
void init() {
    for (int i = 1; i <N; ++i) {
        pre[i] = i;
    }
}
int find(int x) {
    if (x == pre[x])    return x;
    else    return pre[x] = find(pre[x]);
}
void join(int x, int y) {
    int fx = find(x);
    int fy = find(y);
    if (fx == fy)   return;
    else if (fx < fy)   pre[fy] = fx;
    else    pre[fx] = fy;
}

// 求最大生成树
void prim(int x) {
    mem(dis, 0);
    mem(vis, false);
    for (int i = 0; i < g[x].size(); ++i) {
        ac t = g[x][i];
        dis[t.v] = t.c;
    }
    vis[x] = true;
    for (int i = 1; i < n; ++i) {
        double MAX = 0;
        int u = -1;
        for (int j = 1; j <= n; ++j) {
            if (vis[j]) continue;
            if (dis[j] > MAX) {
                MAX = dis[j];
                u = j;
            }
        }
        if (u == -1)    return;
        vis[u] = true;
        sum += MAX;
        for (int j = 0; j < g[u].size(); ++j) {
            ac t = g[u][j];
            if (vis[t.v])   continue;
            if (dis[t.v] < t.c ) {
                dis[t.v] = t.c;
            }
        }
    }
}

int main(){
// #ifndef ONLINE_JUDGE
//     freopen("in.txt", "r", stdin);
// #endif
    ios::sync_with_stdio(false);
    while (cin >> n >> m) {
        init();
        for (int i = 1; i <= n; ++i) {
            cin >> a[i].first >> a[i].second;
        }
        double ans = 0;
        for (int i = 0; i < m; ++i) {
            int u, v;
            cin >> u >> v;
            int dx = a[u].first - a[v].first;
            int dy = a[u].second - a[v].second;
            double temp = sqrt(dx * dx + dy * dy);
            ans += temp;
            // 建图
            g[u].push_back((ac){v, temp});
            g[v].push_back((ac){u, temp});
            join(u, v);
        }
        for (int i = 1; i <= n; ++i) {
            // 求这个并查集的最大生成树
            if (pre[i] == i) {
                sum = 0;
                prim(i);
                ans -= sum;
            }
        }
        printf("%.3lf\n",ans);
        for (int i = 1; i <= n; ++i) {
            g[i].clear();
        }
    }

    return 0;
}

• 贪心
  对所有边降序排列，如果两个边不连通，就减去这条边，剩下的就是需要去掉的边

using namespace std;
int inf = 0x3f3f3f3f;
int n, m, pre[N];
struct ac{
    int u, v;
    double c;
    bool operator < (const ac &x)const {
        return c > x.c;
    }
};
vector<P> a(N);
vector<ac> g;
void init() {
    for (int i = 1; i <N; ++i) {
        pre[i] = i;
    }
}
int find(int x) {
    if (x == pre[x])    return x;
    else    return pre[x] = find(pre[x]);
}
bool join(int x, int y) {
    int fx = find(x);
    int fy = find(y);
    if (fx == fy)   return false;
    else if (fx < fy)   pre[fy] = fx;
    else    pre[fx] = fy;
    return true;
}
double rm() {
    double sum = 0;
    for (int i = 0; i < g.size(); ++i) {
        ac t = g[i];
        if (join(t.u, t.v)) sum += t.c;
    }
    return sum;
}
int main(){
// #ifndef ONLINE_JUDGE
//     freopen("in.txt", "r", stdin);
// #endif
    ios::sync_with_stdio(false);
    while (cin >> n >> m) {
        init();
        for (int i = 1; i <= n; ++i) {
            cin >> a[i].first >> a[i].second;
        }
        double ans = 0;
        for (int i = 0; i < m; ++i) {
            int u, v;
            cin >> u >> v;
            int dx = a[u].first - a[v].first;
            int dy = a[u].second - a[v].second;
            double temp = sqrt(dx * dx + dy * dy);
            ans += temp;
            g.push_back((ac){u, v, temp});
        }
        sort(g.begin(), g.end());
        ans -= rm();
        printf("%.3lf\n",ans);
        g.clear();
    }

    return 0;
}