#include "parks.h"
#include <bits/stdc++.h>
using namespace std;
typedef pair<int, int> ii;
typedef tuple<int, int, int> iii;
const int dx[] = {-1,0,0,1};
const int dy[] = {0,1,-1,0};
vector<int> AdjList[200005];
ii EdgeList[800005];
ii EdgeList2[800005];
map<ii, int> indx;
map<ii, int> indxEdge;
map<ii, int> indxBench;
vector<int> AdjListBench[800005];
set<int> AdjListRoad[200005];
int degBench[800005];
ii benchXY[800005];
mt19937 rng(1);
struct Dinic{
static const int MAX_E = 1000005;
static const int MAX_V = 1000005;
// Edge List
ii EdgeList[MAX_E<<1];
int flow[MAX_E<<1];
int capacity[MAX_E<<1];
vector<int> AdjList[MAX_V];
int level[MAX_V];
int ptr[MAX_V];
int E = 0;
int s, t;
Dinic(int _s, int _t){
s = _s;
t = _t;
}
void add_edge(int u, int v, int c){
EdgeList[E] = ii(u, v);
EdgeList[E+1] = ii(v, u);
flow[E] = 0;
flow[E+1] = 0;
capacity[E] = c;
capacity[E+1] = 0;
AdjList[u].push_back(E);
AdjList[v].push_back(E+1);
E += 2;
}
bool bfs(){
memset(level, -1, sizeof(level));
queue<int> q;
level[s] = 0;
q.push(s);
while(!q.empty()){
int u = q.front(); q.pop();
for(int indx: AdjList[u]){
int v = EdgeList[indx].second;
if(level[v] == -1 && capacity[indx] > flow[indx]){
level[v] = level[u] + 1;
q.push(v);
}
}
}
return level[t] != -1;
}
int dfs(int u, int flowToSend){
if(u == t){return flowToSend;}
if(flowToSend == 0){return 0;}
while(ptr[u] < (int)AdjList[u].size()){
int indx = AdjList[u][ptr[u]];
int v = EdgeList[indx].second;
if(capacity[indx] > flow[indx] && level[v] == level[u] + 1){
int nxtFlow = min(flowToSend, capacity[indx] - flow[indx]);
int flowSent = dfs(v, nxtFlow);
if(flowSent > 0){
flow[indx] += flowSent; // flow from u to v
flow[indx^1] -= flowSent; // flow from v to u
return flowSent;
}
}
ptr[u] ++;
}
return 0;
}
int findMaxFlow(){
int maxFlow = 0;
while(1){
if(!bfs()){return maxFlow;}
memset(ptr, 0, sizeof(ptr));
while(1){
int temp = dfs(s, INT_MAX);
maxFlow += temp;
if(temp == 0){break;}
}
}
}
};
struct UnionFind{
vector<int> p;
vector<int> rank1;
void init(int n){
p.assign(n, 0);
rank1.assign(n, 0);
for(int i = 0; i < n; i ++){
p[i] = i;
rank1[i] = 0;
}
}
int findSet(int i){
return (p[i] == i) ? i : (p[i] = findSet(p[i]));
}
bool isSameSet(int i, int j){
return findSet(i) == findSet(j);
}
void unionSet(int i, int j){
int x = findSet(i);
int y = findSet(j);
if(x != y){
if(rank1[x] > rank1[y]){
p[y] = x;
}else{
p[x] = y;
if(rank1[x] == rank1[y]){
rank1[y] ++;
}
}
}
}
};
int p[200005];
int construct_roads(std::vector<int> x, std::vector<int> y) {
int n = (int)x.size();
if (n == 1) {
build({}, {}, {}, {});
return 1;
}
vector<int> U(n-1);
vector<int> V(n-1);
vector<int> A(n-1);
vector<int> B(n-1);
for(int i = 0; i < n; i ++){
indx[ii(x[i], y[i])] = i;
}
int cnt3 = 0;
for(pair<ii, int> temp: indx){
p[cnt3 ++] = temp.second;
}
int m = 0;
for(int i = 0; i < n; i ++){
int i2 = p[i];
for(int k = 0; k < 4; k ++){
int nx = x[i2] + 2*dx[k];
int ny = y[i2] + 2*dy[k];
if(indx.find(ii(nx, ny)) != indx.end()){
int j = indx[ii(nx, ny)];
EdgeList[m ++] = ii(i2, j);
}
}
}
UnionFind* uf = new UnionFind();
while(1){
uf->init(n);
int cnt = 0;
for(int i = 0; i < m; i ++){
int u, v;
tie(u, v) = EdgeList[i];
if(!uf->isSameSet(u, v)){
uf->unionSet(u, v);
AdjList[u].push_back(v);
AdjList[v].push_back(u);
EdgeList2[cnt] = ii(u, v);
indxEdge[ii(u, v)] = cnt;
cnt ++;
}
}
if(cnt != n-1){
return 0;
}
int benches = 0;
memset(degBench, 0, sizeof(degBench));
for(int i = 0; i < n-1; i ++){
int u, v;
tie(u, v) = EdgeList2[i];
int x2 = (x[u] + x[v])/2;
int y2 = (y[u] + y[v])/2;
for(int k = 0; k < 4; k ++){
int nx = x2 + dx[k];
int ny = y2 + dy[k];
if(nx%2 == 1 && ny%2 == 1){
int indx2 = benches;
if(indxBench.find(ii(nx, ny)) != indxBench.end()){
indx2 = indxBench[ii(nx, ny)];
}else{
benchXY[benches] = ii(nx, ny);
indxBench[ii(nx, ny)] = benches;
//printf("bench %d; (%d, %d)\n", benches, nx, ny);
benches ++;
}
AdjListBench[indx2].push_back(i);
AdjListRoad[i].insert(indx2);
//printf("road %d; bench %d\n", i, indx2);
degBench[i] ++;
}
}
}
int S = n+benches;
int T = n+benches+1;
Dinic* mf = new Dinic(S, T);
for(int i = 0; i < n; i ++){
mf->add_edge(S, i, 1);
}
for(int i = 0; i < benches; i ++){
mf->add_edge(n+i, T, 1);
}
for(int i = 0; i < n; i ++){
for(int j: AdjListRoad[i]){
mf->add_edge(i, n+j, 1);
}
}
int res = mf->findMaxFlow();
//printf("res=%d\n", res);
assert(res == n-1);
int cnt2 = 0;
for(int i = 0; i < mf->E; i ++){
int u, v;
tie(u, v) = mf->EdgeList[i];
//printf("u=%d v=%d\n", u, v);
if(u >= n){continue;}
if(mf->flow[i] > 0){
tie(U[cnt2], V[cnt2]) = EdgeList2[u];
tie(A[cnt2], B[cnt2]) = benchXY[v-n];
cnt2 ++;
}
}
if(cnt2 == n-1){
build(U, V, A, B);
return 1;
}
shuffle(EdgeList, EdgeList+m, rng);
}
}
