相关链接
题目传送门：http://codeforces.com/problemset/problem/757/F
官方题解：http://codeforces.com/blog/entry/49743
中文题面及题解：https://blog.sengxian.com/solutions/cf-757f
解题报告
先搞出一个最短路径树，然后把一些非树边也给搞进来
我们发现这货是一个DAG，那么问题就转化为了：
给定一个DAG，问删掉一个点，最多使得多少点不可到达
然后我们就会想起这个题：BZOJ 2851
于是我们搞一个灾难树就可以啦！
Code
#include<bits/stdc++.h>
#define LL long long
using namespace std;
const int N = 200000+9;
const int M = 600000+9;
const LL INF = 1e9 * 1e9;
LL dis[N];
int n,m,s,E,vout,fa[N][20],done[N],in[N];
int head[N],to[M],nxt[M],cost[M],dep[N];
priority_queue<pair<LL,int> > que;
vector<int> anc[N],son[N];
inline int read() {
char c=getchar(); int f=1,ret=0;
while (c<'0'||c>'9') {if(c=='-')f=-1;c=getchar();}
while (c<='9'&&c>='0') {ret=ret*10+c-'0';c=getchar();}
return ret * f;
}
inline void Add_Edge(int u, int v, int c = 0) {
to[++E] = v; nxt[E] = head[u]; head[u] = E; cost[E] = c;
to[++E] = u; nxt[E] = head[v]; head[v] = E; cost[E] = c;
}
inline void Dijkstra() {
memset(dis,60,sizeof(dis));
dis[s] = 0; que.push(make_pair(0, s));
while (!que.empty()) {
int w = que.top().second; que.pop();
if (!done[w]) done[w] = 1;
else continue;
for (int i=head[w];i;i=nxt[i]) {
if (dis[to[i]] > dis[w] + cost[i]) {
dis[to[i]] = dis[w] + cost[i];
que.push(make_pair(-dis[to[i]], to[i]));
}
}
}
}
inline int LCA(int u, int v) {
if (dep[u] < dep[v]) swap(u, v);
for (int i=19;~i;i--) if (dep[fa[u][i]] >= dep[v]) u = fa[u][i];
if (u == v) return u;
for (int i=19;~i;i--) if (fa[u][i] != fa[v][i]) u = fa[u][i], v = fa[v][i];
return fa[u][0];
}
void solve(int w) {
done[w] = 1;
int f = anc[w][0];
for (int i=1;i<(int)anc[w].size();i++)
f = LCA(f, anc[w][i]);
Add_Edge(f, w);
fa[w][0] = f; dep[w] = dep[f] + 1;
for (int i=1;i<20;i++)
fa[w][i] = fa[fa[w][i-1]][i-1];
for (int i=son[w].size()-1,t;~i;i--) {
t = son[w][i];
if (--in[t] == 0 && !done[t]) {
solve(t);
}
}
}
int DFS(int w, int f) {
int sz = 1;
for (int i=head[w];i;i=nxt[i]) {
if (to[i] != f) {
sz += DFS(to[i], w);
}
}
if (w != s) vout = max(vout, sz);
return sz;
}
int main() {
n = read(); m = read(); s = read();
for (int i=1,u,v;i<=m;i++) {
u = read(); v = read();
Add_Edge(u, v, read());
}
Dijkstra();
for (int w=1;w<=n;w++) {
if (dis[w] > INF) continue;
for (int i=head[w];i;i=nxt[i]) {
if (dis[to[i]] == dis[w] + cost[i]) {
anc[to[i]].push_back(w);
son[w].push_back(to[i]);
in[to[i]] += (w != s);
}
}
}
memset(head,0,sizeof(head));
memset(done,0,sizeof(done));
done[s] = 1; E = 0;
for (int i=0;i<20;i++) fa[s][i] = s;
for (int i=1;i<=n;i++) {
if (!in[i] && !done[i] && dis[i] < INF) {
solve(i);
}
}
DFS(s, s);
printf("%d\n",vout);
return 0;
}
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