「CF1023F」Mobile Phone Network

「CF1023F」Mobile Phone Network

传送门

直接钦定那 \(k\) 条边在最小生成树中，然后把最小生成树树剖一下。

每条其它边的效果就是把该边端点路径上的边的权对该边边权取 \(\min\)。

不会区间取 \(\min\) 的看这里。

参考代码：

#include <algorithm>
#include <cstdio>
#define rg register
#define file(x) freopen(x".in", "r", stdin), freopen(x".out", "w", stdout)
using namespace std;
template < class T > inline void read(T& s) {
	s = 0; int f = 0; char c = getchar();
	while ('0' > c || c > '9') f |= c == '-', c = getchar();
	while ('0' <= c && c <= '9') s = s * 10 + c - 48, c = getchar();
	s = f ? -s : s;
}

typedef long long LL;
const int _ = 5e5 + 5, __ = 1e6 + 5, INF = 2e9;

int tot, head[_], nxt[_ << 1], ver[_ << 1], w[_ << 1];
inline void Add_edge(int u, int v, int d)
{ nxt[++tot] = head[u], head[u] = tot, ver[tot] = v, w[tot] = d; }

int n, k, m, tag[_], Fa[_], X[__], Y[__], V[__], vis[__];
int dep[_], siz[_], son[_], fa[_], top[_], rev[_], dfn[_], mn[_ << 2];

inline int Find(int x) { return Fa[x] == x ? x : Fa[x] = Find(Fa[x]); }

inline void merge(int x, int y) { Fa[Find(x)] = Find(y); }

inline int lc(int p) { return p << 1; }

inline int rc(int p) { return p << 1 | 1; }

inline void f(int p, int v) { mn[p] = min(mn[p], v); }

inline void pushdown(int p) { f(lc(p), mn[p]), f(rc(p), mn[p]), mn[p] = INF; }

inline void build(int p = 1, int l = 1, int r = n) {
	mn[p] = INF;
	if (l == r) { mn[p] = tag[rev[l]]; return ; }
	int mid = (l + r) >> 1;
	build(lc(p), l, mid), build(rc(p), mid + 1, r);
}

inline void update(int ql, int qr, int v, int p = 1, int l = 1, int r = n) {
	if (ql <= l && r <= qr) return f(p, v);
	int mid = (l + r) >> 1;
	pushdown(p);
	if (ql <= mid) update(ql, qr, v, lc(p), l, mid);
	if (qr > mid) update(ql, qr, v, rc(p), mid + 1, r);
}

inline int query(int id, int p = 1, int l = 1, int r = n) {
	if (l == r) return mn[p];
	int mid = (l + r) >> 1, res;
	pushdown(p);
	if (id <= mid) res = query(id, lc(p), l, mid);
	else res = query(id, rc(p), mid + 1, r);
	return res;
}

inline void dfs(int u, int f) {
	dep[u] = dep[f] + 1, siz[u] = 1, fa[u] = f;
	for (rg int i = head[u]; i; i = nxt[i]) {
		int v = ver[i]; if (v == f) continue ;
		tag[v] = w[i];
		dfs(v, u), siz[u] += siz[v];
		if (siz[son[u]] < siz[v]) son[u] = v;
	}
}

inline void dfs(int u, int f, int topf) {
	top[rev[dfn[u] = ++dfn[0]] = u] = topf;
	if (son[u]) dfs(son[u], u, topf);
	for (rg int i = head[u]; i; i = nxt[i]) {
		int v = ver[i]; if (v == f || v == son[u]) continue ;
		dfs(v, u, v);
	}
}

inline void uptChain(int x, int y, int v) {
	int fx = top[x], fy = top[y];
	while (fx != fy) {
		if (dep[fx] < dep[fy]) swap(x, y), swap(fx, fy);
		update(dfn[fx], dfn[x], v), x = fa[fx], fx = top[x];
	}
	if (dep[x] > dep[y]) swap(x, y);
	update(dfn[x] + 1, dfn[y], v);
}

int main() {
#ifndef ONLINE_JUDGE
	file("cpp");
#endif
	read(n), read(k), read(m);
	for (rg int i = 1; i <= n; ++i) Fa[i] = i;
	for (rg int u, v, i = 1; i <= k; ++i)
		read(u), read(v), merge(u, v), Add_edge(u, v, INF), Add_edge(v, u, INF);
	for (rg int i = 1; i <= m; ++i) {
		read(X[i]), read(Y[i]), read(V[i]);
		if (Find(X[i]) != Find(Y[i])) {
			vis[i] = 1, merge(X[i], Y[i]);
			Add_edge(X[i], Y[i], 0), Add_edge(Y[i], X[i], 0);
		}
	}
	dfs(1, 0), dfs(1, 0, 1), build();
	for (rg int i = 1; i <= m; ++i) if (!vis[i]) uptChain(X[i], Y[i], V[i]);
	LL ans = 0;
	for (rg int i = 2; i <= n; ++i) {
		int res = query(i);
		if (res == INF) return puts("-1"), 0; else ans += res;
	}
	printf("%lld\n", ans);
	return 0;
}