P2783 有机化学之神偶尔会做作弊
史上最水黑题
做法很暴力：tarjan算法求点双缩点，建新图，跑树剖或倍增，求LCA，通过深度算出答案即可。
点双的做法跟强连通分量的tarjan算法极其相似，唯一的一点不同就在于不能回到父节点。
要是回父节点的话那都有两个点大小的环咯
自己交上去45pts，原来是因为求LCA的时候下标弄错了。应该使用新图的下标。
代码：
/*************************************************************************
@Author: Garen
@Created Time : Thu 31 Jan 2019 05:21:10 PM CST
@File Name: P2783.cpp
@Description:
************************************************************************/
#include<bits/stdc++.h>
using std::cin;
using std::cout;
using std::endl;
#define ll long long
const int maxn = 50005, maxm = 100005;
struct Edges {
int next, to;
} e[maxm << 1], e2[maxn << 1];
int head[maxn], tot;
int head2[maxn], tot2;
int n, m, q;
//
int dfn[maxn], low[maxn], dtot;
int stack[maxn << 1], stop;
bool vis[maxn];
int col[maxn], ctot;
//
int dep[maxn], fa[maxn], size[maxn], wson[maxn];
int top[maxn];
void link(int u, int v) {
e[++tot] = (Edges){head[u], v};
head[u] = tot;
}
void link2(int u, int v) {
e2[++tot2] = (Edges){head2[u], v};
head2[u] = tot2;
}
void tarjan(int u, int f) {
dfn[u] = low[u] = ++dtot;
stack[++stop] = u; vis[u] = true;
for(int i = head[u]; i; i = e[i].next) {
int v = e[i].to;
if(v == f) continue;
if(!dfn[v]) {
tarjan(v, u); low[u] = std::min(low[u], low[v]);
} else if(vis[v]) {
low[u] = std::min(low[u], dfn[v]);
}
}
if(dfn[u] == low[u]) {
ctot++;
int sb;
do {
sb = stack[stop--]; vis[sb] = false;
col[sb] = ctot;
} while(sb != u);
}
}
void dfs1(int u, int f) {
dep[u] = dep[f] + 1; fa[u] = f; size[u] = 1;
for(int i = head2[u]; i; i = e2[i].next) {
int v = e2[i].to;
if(v == fa[u]) continue;
dfs1(v, u);
size[u] += size[v];
if(size[v] > size[wson[u]]) wson[u] = v;
}
}
void dfs2(int u, int topf) {
top[u] = topf;
if(wson[u]) dfs2(wson[u], topf);
for(int i = head2[u]; i; i = e2[i].next) {
int v = e2[i].to;
if(v == wson[u] || v == fa[u]) continue;
dfs2(v, v);
}
}
int get_lca(int u, int v) {
while(top[u] != top[v]) {
if(dep[top[u]] < dep[top[v]]) std::swap(u, v);
u = fa[top[u]];
}
if(dep[u] > dep[v]) std::swap(u, v);
return u;
}
void print(int x) {
std::vector<int> buf;
while(x) {
buf.push_back(x & 1);
x >>= 1;
}
for(int i = buf.size() - 1; i >= 0; i--) cout << buf[i];
}
int main() {
cin >> n >> m;
while(m--) {
int u, v; cin >> u >> v;
link(u, v), link(v, u);
}
for(int i = 1; i <= n; i++) if(!dfn[i]) tarjan(i, 0);
// print array col
//for(int i = 1; i <= n; i++) cout << col[i] << ' ';
//cout << endl;
for(int u = 1; u <= n; u++) {
for(int i = head[u]; i; i = e[i].next) {
int v = e[i].to;
if(col[u] != col[v]) {
link2(col[u], col[v]);
// print the new tree
//cout << col[u] << ' ' << col[v] << endl;
}
}
}
dfs1(1, 0); dfs2(1, 1);
cin >> q;
while(q--) {
int u, v; cin >> u >> v;
u = col[u], v = col[v];
int lca = get_lca(u, v);
//cout << dep[u] - dep[lca] + dep[v] - dep[lca] + 1 << endl;
print(dep[u] - dep[lca] + dep[v] - dep[lca] + 1);
cout << endl;
}
return 0;
}