This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define FIXED_FLOAT(x) std::fixed <<std::setprecision(20) << (x)
#define all(v) (v).begin(), (v).end()
using namespace std;
#define forn(i,n) for (int i = 0; i < (n); ++i)
#define rforn(i, n) for(int i = (n) - 1;i >= 0;--i)
#define sz(x) (int)x.size()
#define ff first
#define se second
#define mp make_pair
using ll = long long;
int MOD = 998244353;
const int INF = 1e9 + 1;
const int N = 2e5 + 10;
const double eps = 1e-7;
template <class T> using V = vector<T>;
template <class T> using VV = V<V<T>>;
template<class T, size_t SZ> using AR = array<T, SZ>;
template<class T> using PR = pair<T, T>;
template <typename XPAX>
bool ckma(XPAX &x, XPAX y) {
return (x < y ? x = y, 1 : 0);
}
template <typename XPAX>
bool ckmi(XPAX &x, XPAX y) {
return (x > y ? x = y, 1 : 0);
}
void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
int n, m, w, h;
double dist(int x1, int y1, int x2, int y2) {
long long dx = x1-x2, dy = y1-y2;
return double(sqrt(dx * dx + dy * dy));
}
struct DSU {
vector<int> e;
DSU(int N) { e = vector<int>(N, -1); }
// get representive component (uses path compression)
int get(int x) { return e[x] < 0 ? x : e[x] = get(e[x]); }
bool same_set(int a, int b) { return get(a) == get(b); }
int size(int x) { return -e[get(x)]; }
bool unite(int x, int y) { // union by size
x = get(x), y = get(y);
if (x == y) return false;
if (e[x] > e[y]) swap(x, y);
e[x] += e[y]; e[y] = x; return true;
}
};
void solve() {
cin >> n >> m >> w >> h;
vector<int> x(n), y(n);
V<double> r(n);
forn(i, n) cin >> y[i] >> x[i] >> r[i];
vector<array<int, 3>> Q(m);
forn(i, m) {
cin >> Q[i][0] >> Q[i][1];
Q[i][1]--;
Q[i][2] = i;
}
vector<pair<double, pair<int, int>>> E;
for(int i = 0;i < n;++i) {
for(int j = i + 1;j < n;++j) {
E.push_back({dist(x[i], y[i], x[j], y[j])-r[i]-r[j], {i, j}});
}
E.push_back({y[i]-r[i], {i, n}});
E.push_back({x[i]-r[i], {i, n+1}});
E.push_back({w-y[i]-r[i], {i, n+2}});
E.push_back({h-x[i]-r[i], {i, n+3}});
}
DSU D(n + 5);
V<string> ret(m);
sort(begin(Q), end(Q), [&](array<int, 3> one, array<int, 3> two) {
return one[0] < two[0];
});
sort(begin(E), end(E), [&](pair<double, pair<int, int>> one, pair<double, pair<int, int>> two) {
return one.ff < two.ff;
});
//debug(E);
int k = 0;
auto can = [&](int f, int g) {
if(f == g) return true;
if(f > g) swap(f, g);
if(D.same_set(n+f, n+(f+1)%4))return false;
if(D.same_set(n+g, n+(g+1)%4))return false;
if(f == 0 && g == 3)
return !D.same_set(n, n+2);
else if(f+1==g) {
return !D.same_set(n+(f+1)%4, n+(f+3)%4);
}
else {
if(D.same_set(n+f, n+(f+2)%4))return false;
if(D.same_set(n+(f+1)%4, n+(f+3)%4))return false;
return true;
}
};
for(auto [R, cor, i] : Q) {
while(k < sz(E) && E[k].ff < R * 2.0) {
D.unite(E[k].se.ff, E[k].se.se);
++k;
}
string res = "";
forn(j, 4) if(can(cor, j)) res += '0' + j + 1;
ret[i] = res;
}
forn(i, m) cout << ret[i] << '\n';
}
void test_case() {
int t;
cin >> t;
forn(p, t) {
//cout << "Case #" << p + 1 << ": ";
solve();
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
solve();
}
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