#include "simurgh.h"
#include <vector>
#include <iostream>
#include <set>
#include <algorithm>
using namespace std;
const int maxN = 500;
const int maxM = 500*499/2;
int N, M;
vector< vector<int> > edge_index(maxN, vector<int>(maxN, -1)); //index of edge in graph
vector<int> edge[maxN]; //list of edge destinations of each node in maain graph
vector<bool> edge_in_tree(maxM, 0); //is this edge index in the tree?
set<int> treeset; //set of edge indices in the basic spanning tree
vector<int> parent(maxN, -1); //parent of node in basic spanning tree
vector<int> depth(maxN, 0); //depth of node in basic spanning tree
const int unclear = -1;
const int good = 1;
const int bad = 0;
vector<bool> extra_visited(maxM, 0);
vector<int> state(maxM, unclear); //state of each edge.
void dfs(int u)
{
// cerr << "u = " << u << '\n';
for(int v: edge[u])
{
// cerr << u << " -> " << v << '\n';
if(parent[u] == v || parent[v] != -1) continue;
parent[v] = u;
depth[v] = depth[u] + 1;
edge_in_tree[ edge_index[u][v] ] = 1;
treeset.insert(edge_index[u][v]);
dfs(v);
}
}
vector<int> findtree_ans(maxM, -1);
vector<int> get_vector(set<int> S)
{
vector<int> K;
for(int s:S) K.push_back(s);
return K;
}
struct disjoint_set
{
int N;
vector<int> parent;
vector<int> subtree;
disjoint_set()
{
;
}
disjoint_set(int N_)
{
N = N_;
parent = vector<int>(N);
subtree = vector<int>(N, 1);
for(int i = 0; i < N; i++) parent[i] = i;
}
int root(int u)
{
while(parent[u] != u) u = parent[u];
return u;
}
bool connected(int u, int v)
{
return root(u) == root(v);
}
void join(int u, int v)
{
u = root(u);
v = root(v);
if(connected(u, v)) return;
if(subtree[u] < subtree[v]) swap(u, v);
parent[v] = u;
subtree[u] += subtree[v];
}
};
vector<int> find_roads(int n, vector<int> u, vector<int> v)
{
// cerr << "check zero\n";
//PART ONE
N = n;
M = (int)u.size();
for(int j = 0; j < M; j++)
{
edge_index[ u[j] ][ v[j] ] = edge_index[ v[j] ][ u[j] ] = j;
edge[ u[j] ].push_back( v[j] );
edge[ v[j] ].push_back( u[j] );
}
// cerr << "check2\n";
parent[0] = 0;
dfs(0);
// cerr << "check3\n";
vector<int> Q;
for(int j = 0; j < M; j++)
if(edge_in_tree[j])
Q.push_back(j);
int basic_query = count_common_roads(Q);
Q.clear();
// cerr << "check 1\n";
// cerr << "check4\n";
for(int j = 0; j < M; j++)
{
if(edge_in_tree[j]) continue;
// cerr << "check5 " << j << '\n';
vector<int> tree_path;
int U = u[j], V = v[j];
if(depth[U] > depth[V]) swap(U, V);
// cerr << depth[V] - depth[U] << '\n';
while(depth[V] != depth[U])
{
// cerr << "k = " << k << '\n';
tree_path.push_back( edge_index[ V ][ parent[V] ] );
V = parent[V];
}
// cerr << "check6 " << j << '\n';
// cerr << U << ' ' << V << ' ' << depth[U] << ' ' << depth[V] << '\n';
while(U != V)
{
tree_path.push_back( edge_index[U][ parent[U] ] );
tree_path.push_back(edge_index[V][parent[V]]);
U = parent[U];
V = parent[V];
}
for(int t: tree_path)
extra_visited[t] = 1;
// cerr << "check7 " << j << '\n';
vector<int> known;
vector<int> unknown;
int known_count = 0;
for(int t: tree_path)
{
if(state[t] != unclear)
{
known.push_back(t);
known_count++;
}
else
{
unknown.push_back(t);
}
}
// cerr << "check8 " << j << '\n';
if(known_count == (int)tree_path.size())
continue;
else if(known_count != 0)
{
treeset.insert(j);
treeset.erase(known[0]);
int this_basic = count_common_roads(get_vector(treeset));
int cycle_weight = this_basic + state[known[0]];
treeset.insert(known[0]);
for(int u: unknown)
{
treeset.erase(u);
state[u] = cycle_weight - count_common_roads(get_vector(treeset));
treeset.insert(u);
}
treeset.erase(j);
}
else if(known_count == 0)
{
vector< pair<int, int> > cycle_elements;
cycle_elements.push_back(make_pair(basic_query, j));
for(int t: tree_path)
{
treeset.erase(t);
treeset.insert(j);
findtree_ans[t] = count_common_roads(get_vector(treeset));
cycle_elements.push_back(make_pair(findtree_ans[t], t));
treeset.erase(j);
treeset.insert(t);
}
sort(cycle_elements.begin(), cycle_elements.end());
bool good_flag = 0;
for(int x = (int)cycle_elements.size() - 1; x >= 0; x--)
{
if(x < (int)cycle_elements.size() - 1 && cycle_elements[x].first != cycle_elements[x+1].first)
good_flag = 1;
if(good_flag)
state[ cycle_elements[x].second ] = good;
else
state[ cycle_elements[x].second ] = bad;
}
}
// cerr << "check9 " << j << '\n';
}
for(int e: treeset)
if(extra_visited[e] == 0)
state[e] = good;
// cerr << "tree and states: \n";
//
// for(int j = 0; j < M; j++)
// {
// if(edge_in_tree[j])
// {
// cerr << u[j] << ' ' << v[j] << ' ' << state[j] << '\n';
// }
// }
// cerr << "check 2\n";
//PART TWO
set<int> potential_new_neighbors[N];
vector<int> new_neighbors_count(N, 0);
for(int U = 0; U < N; U++)
{
for(int V = 0; V < N; V++)
{
if(U == V) continue;
if(state[ edge_index[U][V] ] == unclear)
{
potential_new_neighbors[U].insert(V);
}
}
}
// cerr << "check 3\n";
//
// for(int t: treeset) cerr << t << ' ';
// cerr << '\n';
for(int U = 0; U < N; U++)
{
// cerr << "U = " << U << '\n';
vector<int> query_vector;
disjoint_set DSU(N);
for(int V = 0; V < N; V++)
{
if(U == V) continue;
if(edge_index[U][V] != -1)
{
if(state[ edge_index[U][V] ] == good)
new_neighbors_count[U]--;
DSU.join(U, V);
query_vector.push_back(edge_index[U][V]);
}
}
// cerr << "qv = ";
// for(int qv: query_vector) cerr << qv << ' ';
// cerr << '\n';
//
// for(int i = 0; i < N; i++)
// cerr << DSU.root(i) << ' ';
// cerr << '\n';
for(int t: treeset)
{
// cerr << u[t] << ' ' << v[t] << ' ' << DSU.connected(u[t], v[t]) << '\n';
if(!DSU.connected(u[t], v[t]))
{
// cerr << "joined!\n";
DSU.join(u[t], v[t]);
// cerr << u[t] << ' ' << v[t] << ' ' << DSU.connected(u[t], v[t]) << '\n';
query_vector.push_back(t);
if(state[t] == good)
new_neighbors_count[U]--;
// for(int i = 0; i < N; i++)
// cerr << DSU.root(i) << ' ';
// cerr << '\n';
}
// cerr << "\n";
}
// for(int i = 0; i < N; i++)
// cerr << DSU.root(i) << ' ';
// cerr << '\n';
new_neighbors_count[U] += count_common_roads(query_vector);
}
// cerr << "check 4\n";
for(int Z = 1; Z <= N; Z++)
{
int U = -1;
for(int y = 0; y < N; y++)
{
if(new_neighbors_count[y] == 1)
{
U = y;
break;
}
}
if(U == -1) break;
vector<int> candidates;
for(int V = 0; V < N; V++)
{
if(U == V) continue;
if(edge_index[U][V] == -1) continue;
if(state[ edge_index[U][V] ] == unclear)
candidates.push_back(V);
}
int lo = 0;
int hi = (int)candidates.size() - 1;
while(lo != hi)
{
int mid = (lo+hi)/2;
int prefix_candidates = 0;
disjoint_set DSU(N);
vector<int> query_vector;
for(int i = 0; i <= mid; i++)
{
DSU.join(U, candidates[i]);
query_vector.push_back( edge_index[U][candidates[i]] );
}
for(int t: treeset)
{
if(DSU.connected(u[t], v[t])) continue;
prefix_candidates -= state[ edge_index[u[t]][v[t]] ];
DSU.join(u[t], v[t]);
query_vector.push_back(t);
}
prefix_candidates += count_common_roads(query_vector);
if(prefix_candidates >= 1) hi = mid;
else lo = mid+1;
}
for(int c: candidates)
{
if(c == candidates[lo])
{
state[ edge_index[U][c] ] = good;
new_neighbors_count[c]--;
}
else
{
state[ edge_index[U][c] ] = bad;
}
potential_new_neighbors[c].erase(U);
potential_new_neighbors[U].erase(c);
new_neighbors_count[U]--;
}
}
// cerr << "check 5\n";
// for(int j = 0; j < M; j++) cerr << state[j] << ' ';
// cerr << '\n';
vector<int> res;
for(int j = 0; j < M; j++)
if(state[j] == good)
{
// cerr << "adding " << j << '\n';
res.push_back(j);
}
return res;
}
