【洛谷 P2783】 有机化学之神偶尔会做作弊 （双联通分量）

题目链接

可能是除了《概率论》的最水的黑题了吧

用\(Tarjan\)缩点（点双联通分量），然后就是树上两点之间的距离了，跑\(LCA\)就好了。

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
int s; char ch;
inline int read(){
    s = 0; ch = getchar();
    while(ch < '0' || ch > '9') ch = getchar();
    while(ch >= '0' && ch <= '9') { s = s * 10 + ch - '0'; ch = getchar(); }
    return s;
}
const int MAXN = 10010;
const int MAXM = 50010;
int dfn[MAXN], low[MAXN], id, bridge[MAXM << 1], dcc, belong[MAXN], top, vis[MAXN];
int n, m, a, b, head[MAXN], num = 1, f[MAXN][20], dep[MAXN], t, stack[MAXN];
struct Edge{
    int from, next, to;
}e[MAXM << 2];
inline void Add(int from, int to){
    e[++num].to = to; e[num].from = from; e[num].next = head[from]; head[from] = num;
    e[++num].to = from; e[num].from = to; e[num].next = head[to]; head[to] = num;
}
void Tarjan(int u, int fa){
    dfn[u] = low[u] = ++id; stack[++top] = u; vis[u] = 1;
    for(int i = head[u]; i; i = e[i].next)
       if(e[i].to != fa)
         if(!dfn[e[i].to]){
           Tarjan(e[i].to, u);
           low[u] = min(low[u], low[e[i].to]);
         }
         else if(vis[e[i].to])
           low[u] = min(low[u], dfn[e[i].to]);
    if(dfn[u] == low[u]){
      ++dcc;
      do
        belong[stack[top]] = dcc;
      while(stack[top--] != u);
    }
}
void getDF(int u, int fa){
    f[u][0] = fa; dep[u] = dep[fa] + 1;
    for(int i = head[u]; i; i = e[i].next)
       if(e[i].to != fa)
         getDF(e[i].to, u);
}
int LCA(int u, int v){
    if(dep[u] < dep[v]) swap(u, v);
    int cha = dep[u] - dep[v];
    if(cha)
      for(int i = 0; i <= 18; ++i)
         if((cha >> i) & 1)
           u = f[u][i];
    if(u != v){
      for(int i = 18; ~i; --i)
         if(f[u][i] != f[v][i])
           u = f[u][i], v = f[v][i];
      return f[u][0];
    }
    return u;
}
int dis(int u, int v){
    return dep[u] + dep[v] - (dep[LCA(u, v)] << 1) + 1;
}
void print(int x){
    if(x > 1) print(x >> 1);
    printf("%d", x & 1);
}
int main(){
    n = read(); m = read();
    for(int i = 1; i <= m; ++i)
       Add(read(), read());
    for(int i = 1; i <= n; ++i)
       if(!dfn[i])
         Tarjan(i, 0);
    memset(head, 0, sizeof head);
    int tmp = num;
    for(int i = 2; i <= tmp; i += 2)
       if(belong[e[i].from] != belong[e[i].to])
         Add(belong[e[i].from], belong[e[i].to]);
    getDF(1, 0);
    for(int j = 1; j <= 18; ++j)
       for(int i = 1; i <= dcc; ++i)
          f[i][j] = f[f[i][j - 1]][j - 1];
    t = read();
    while(t--) print(dis(belong[read()], belong[read()])), puts("");
    return 0;
}