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test/mytest/range_closest_pair.test.cpp
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- Last update: 2023-11-22 02:53:14+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
Depends on
- alg/monoid/min.hpp
- ds/hashmap.hpp
- ds/segtree/dual_segtree.hpp
- geo/range_closest_pair_query.hpp
- my_template.hpp
- random/base.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "random/base.hpp"
#include "geo/range_closest_pair_query.hpp"
void test() {
FOR(N, 2, 100) {
FOR(Q, 1, 100) {
vc<pair<int, int>> point(N), query(Q);
FOR(i, N) {
int x = RNG(0, 20);
int y = RNG(0, 20);
point[i] = {x, y};
}
FOR(q, Q) {
while (1) {
int L = RNG(0, N);
int R = RNG(0, N);
if (L + 1 <= R) {
query[q] = {L, R + 1};
break;
}
}
}
Range_Closest_Pair_Query X;
for (auto&& [a, b]: point) X.add_point(a, b);
for (auto&& [l, r]: query) X.add_query(l, r);
vi ANS = X.calc();
FOR(q, Q) {
ll ans = infty<ll>;
auto [L, R] = query[q];
FOR(i, L, R) FOR(j, L, R) {
if (i == j) continue;
auto [x1, y1] = point[i];
auto [x2, y2] = point[j];
ll dx = x1 - x2, dy = y1 - y2;
chmin(ans, dx * dx + dy * dy);
}
assert(ans == ANS[q]);
}
}
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test();
solve();
return 0;
}#line 1 "test/mytest/range_closest_pair.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
#endif
#line 2 "random/base.hpp"
u64 RNG_64() {
static uint64_t x_
= uint64_t(chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count())
* 10150724397891781847ULL;
x_ ^= x_ << 7;
return x_ ^= x_ >> 9;
}
u64 RNG(u64 lim) { return RNG_64() % lim; }
ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 2 "ds/hashmap.hpp"
// u64 -> Val
template <typename Val, int LOG = 20, bool KEEP_IDS = false>
struct HashMap {
static constexpr int N = (1 << LOG);
u64* key;
Val* val;
vc<int> IDS;
bitset<N> used;
const int shift;
const u64 r = 11995408973635179863ULL;
HashMap() : key(new u64[N]), val(new Val[N]), shift(64 - LOG) {}
u32 hash(u64 x) {
static const u64 FIXED_RANDOM
= std::chrono::steady_clock::now().time_since_epoch().count();
return (u64(x + FIXED_RANDOM) * r) >> shift;
}
int index(const u64& k) {
int i = 0;
for (i = hash(k); used[i] && key[i] != k; (i += 1) &= (N - 1)) {}
return i;
}
Val& operator[](const u64& k) {
int i = index(k);
if (!used[i]) {
used[i] = 1, key[i] = k, val[i] = Val{};
if constexpr (KEEP_IDS) IDS.eb(i);
}
return val[i];
}
Val get(const u64& k, Val default_value) {
int i = index(k);
if (!used[i]) return default_value;
return val[i];
}
bool count(const u64& k) {
int i = index(k);
return used[i] && key[i] == k;
}
void reset() {
static_assert(KEEP_IDS);
for (auto&& i: IDS) used[i] = 0;
IDS.clear();
}
// f(key, val)
template <typename F>
void enumerate_all(F f) {
static_assert(KEEP_IDS);
for (auto&& i: IDS) f(key[i], val[i]);
}
};
#line 2 "ds/segtree/dual_segtree.hpp"
template <typename Monoid>
struct Dual_SegTree {
using MA = Monoid;
using A = typename MA::value_type;
int n, log, size;
vc<A> laz;
Dual_SegTree() : Dual_SegTree(0) {}
Dual_SegTree(int n) { build(n); }
void build(int m) {
n = m;
log = 1;
while ((1 << log) < n) ++log;
size = 1 << log;
laz.assign(size << 1, MA::unit());
}
A get(int p) {
assert(0 <= p && p < n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return laz[p];
}
vc<A> get_all() {
FOR(i, size) push(i);
return {laz.begin() + size, laz.begin() + size + n};
}
void apply(int l, int r, const A& a) {
assert(0 <= l && l <= r && r <= n);
if (l == r) return;
l += size, r += size;
if (!MA::commute) {
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
}
while (l < r) {
if (l & 1) all_apply(l++, a);
if (r & 1) all_apply(--r, a);
l >>= 1, r >>= 1;
}
}
private:
void push(int k) {
if (laz[k] == MA::unit()) return;
all_apply(2 * k, laz[k]), all_apply(2 * k + 1, laz[k]);
laz[k] = MA::unit();
}
void all_apply(int k, A a) { laz[k] = MA::op(laz[k], a); }
};
#line 2 "alg/monoid/min.hpp"
template <typename E>
struct Monoid_Min {
using X = E;
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return min(x, y); }
static constexpr X unit() { return infty<E>; }
static constexpr bool commute = true;
};
#line 4 "geo/range_closest_pair_query.hpp"
// 点群 {p_i | i in [l, r)} に対する最近点対の計算を行うクエリ
// O(KNlogKN + QlogN)
// https://qoj.ac/problem/5463
// https://codeforces.com/gym/104172/attachments/download/18933/Hong_Kong_Tutorial.pdf
struct Range_Closest_Pair_Query {
/*
・R を増やしながら、L ごとの答を管理する
・2^{k-1} <= ANS[L:R] < 2^{k} となる L ：レベル k （レベル 0：距離 0）
・レベル 0, 1, 2, ..., 29 のグリッドを用意する
・幅は 2^k
・一辺 1.99 の正方形内で点対距離が 1 以上 → 8 個までありうる
・レベル 29, 28, ..., 0 の順に探索する：9 近傍
・答が見つかったらレベルを下げる。左向きに伝搬。
・レベルの減少は 30N 回までしか起きない
*/
const int LOG = 30;
vc<pair<int, int>> point;
vc<pair<int, int>> query;
void add_point(int x, int y) {
assert(0 <= x && x < (1 << LOG));
assert(0 <= y && y < (1 << LOG));
point.eb(x, y);
}
void add_query(int L, int R) {
assert(R - L >= 2);
query.eb(L, R);
}
ll dist(int i, int j) {
ll dx = point[i].fi - point[j].fi;
ll dy = point[i].se - point[j].se;
return dx * dx + dy * dy;
}
vc<ll> calc() {
static HashMap<int, 20, true> MP;
MP.reset();
const int K = LOG;
const int N = len(point), Q = len(query);
using A9 = array<int, 9>;
// それぞれのレベルのときのセル番号
vv(int, IDX, K, N, -1);
// 各セル番号に対する近傍
vc<A9> nbd;
FOR(k, 1, K) {
MP.reset();
auto to_64 = [&](int x, int y) -> u64 { return u64(x) << 30 | y; };
int off = len(nbd);
int p = off;
FOR(i, N) {
int x = point[i].fi >> (k);
int y = point[i].se >> (k);
u64 key = to_64(x, y);
int idx = MP.index(key);
if (!MP.used[idx]) {
MP.used[idx] = 1, MP.IDS.eb(idx), MP.key[idx] = key,
MP.val[idx] = p++;
}
IDX[k][i] = MP.val[idx];
}
nbd.resize(p);
FOR(i, N) {
int x = point[i].fi >> (k);
int y = point[i].se >> (k);
int me = MP[to_64(x, y)];
int s = 0;
FOR(dx, -1, 2) FOR(dy, -1, 2) {
u64 key = to_64(x + dx, y + dy);
nbd[me][s++] = (MP.count(key) ? MP[key] : -1);
}
}
}
vc<array<int, 8>> dat(len(nbd), {-1, -1, -1, -1, -1, -1, -1, -1});
auto add = [&](int k, int i) -> void {
int idx = IDX[k][i];
for (auto&& j: dat[idx]) {
if (j == -1) {
j = i;
return;
}
}
};
auto rm = [&](int k, int i) -> void {
int idx = IDX[k][i];
for (auto&& j: dat[idx]) {
if (j == i) {
j = -1;
return;
}
}
};
auto solve_level = [&](int k, int i) -> vc<pair<int, ll>> {
// レベル k の点群に対する答の計算
vc<pair<int, ll>> res;
int me = IDX[k][i];
for (auto&& idx: nbd[me]) {
if (idx == -1) continue;
for (auto&& j: dat[idx]) {
if (j == -1) continue;
res.eb(j, dist(i, j));
}
}
return res;
};
Dual_SegTree<Monoid_Min<ll>> seg(N);
vc<int> LEVEL(N, -1);
auto get_lv = [&](ll d) -> int {
if (d == 0) return 0;
return topbit(d) / 2 + 1;
};
vc<int> left(Q);
vvc<int> query_at(N);
FOR(qid, Q) {
auto [L, R] = query[qid];
left[qid] = L;
query_at[--R].eb(qid);
}
vi ANS(Q);
FOR(R, N) {
// R 番目の点を用いた答の更新
vc<pair<int, ll>> upd;
FOR(k, 1, K) {
auto res = solve_level(k, R);
upd.insert(upd.end(), all(res));
}
for (auto [i, d]: upd) {
int lv = get_lv(d);
if (seg.get(i) < d) continue;
// 答えの更新
seg.apply(0, i + 1, d);
// レベルの更新
while (i >= 0 && LEVEL[i] > lv) {
rm(LEVEL[i], i);
LEVEL[i] = lv;
if (lv) add(lv, i);
--i;
}
}
LEVEL[R] = K - 1;
add(K - 1, R);
for (auto&& qid: query_at[R]) { ANS[qid] = seg.get(left[qid]); }
}
return ANS;
}
};
#line 5 "test/mytest/range_closest_pair.test.cpp"
void test() {
FOR(N, 2, 100) {
FOR(Q, 1, 100) {
vc<pair<int, int>> point(N), query(Q);
FOR(i, N) {
int x = RNG(0, 20);
int y = RNG(0, 20);
point[i] = {x, y};
}
FOR(q, Q) {
while (1) {
int L = RNG(0, N);
int R = RNG(0, N);
if (L + 1 <= R) {
query[q] = {L, R + 1};
break;
}
}
}
Range_Closest_Pair_Query X;
for (auto&& [a, b]: point) X.add_point(a, b);
for (auto&& [l, r]: query) X.add_query(l, r);
vi ANS = X.calc();
FOR(q, Q) {
ll ans = infty<ll>;
auto [L, R] = query[q];
FOR(i, L, R) FOR(j, L, R) {
if (i == j) continue;
auto [x1, y1] = point[i];
auto [x2, y2] = point[j];
ll dx = x1 - x2, dy = y1 - y2;
chmin(ans, dx * dx + dy * dy);
}
assert(ans == ANS[q]);
}
}
}
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test();
solve();
return 0;
}