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test/mytest/cf702_F_splay.test.cpp
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- Last update: 2024-03-30 00:47:55+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
Depends on
- alg/monoid/add_pair.hpp
- ds/splaytree/splaytree.hpp
- ds/splaytree/splaytree_acted_set.hpp
- my_template.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "alg/monoid/add_pair.hpp"
#include "ds/splaytree/splaytree_acted_set.hpp"
// (所持金, 操作回数, query index)
struct AS {
using Monoid_A = Monoid_Add_Pair<int>;
using A = Monoid_A::value_type;
using S = tuple<int, int, int>;
static S act(const S& s, const A& x) {
auto [a, b, c] = s;
return {a + x.fi, b + x.se, c};
}
};
vc<int> solve_cf702F(vc<pair<int, int>> CQ, vc<int> query) {
const int Q = len(query);
sort(all(CQ), [&](auto& a, auto& b) -> bool {
if (a.se != b.se) return a.se > b.se;
return a.fi < b.fi;
});
using T = tuple<int, int, int>;
vc<T> dat(Q);
FOR(q, Q) {
int x = query[q];
dat[q] = {x, 0, q};
}
sort(all(dat));
const int MAX = 500'000;
SplayTree_ActedSet<AS, MAX> X;
using np = decltype(X)::np;
using S = typename AS::S;
np root = X.new_node(dat);
FOR(i, len(CQ)) {
ll c = CQ[i].fi;
np nm, nr;
tie(root, nr)
= X.split_max_right(root, [&](S& s) { return get<0>(s) < c; });
X.apply(nr, {-c, 1});
tie(nm, nr) = X.split_max_right(nr, [&](S& s) { return get<0>(s) < c; });
for (auto&& [aa, bb, cc]: X.get_all(nm)) assert(aa < c);
for (auto&& [aa, bb, cc]: X.get_all(nr)) assert(aa >= c);
for (auto [val, cnt, idx]: X.get_all(nm)) {
ll t = val;
auto [l_root, r_root]
= X.split_max_right(root, [&](S& s) { return get<0>(s) < t; });
root = X.merge(l_root, X.new_node({val, cnt, idx}));
root = X.merge(root, r_root);
}
root = X.merge(root, nr);
}
vc<int> ANS(Q);
for (auto [val, cnt, idx]: X.get_all(root)) { ANS[idx] = cnt; }
return ANS;
}
void test_1() {
vc<pair<int, int>> CQ;
CQ.eb(7, 5);
CQ.eb(3, 5);
CQ.eb(4, 3);
vc<int> query = {13, 14};
vc<int> ANS = solve_cf702F(CQ, query);
assert(ANS == vc<int>({2, 3}));
}
void test_2() {
vc<pair<int, int>> CQ;
CQ.eb(100, 500);
CQ.eb(50, 499);
vc<int> query = {50, 200, 150, 100};
vc<int> ANS = solve_cf702F(CQ, query);
assert(ANS == vc<int>({1, 2, 2, 1}));
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test_1();
test_2();
solve();
return 0;
}#line 1 "test/mytest/cf702_F_splay.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")
#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 "alg/monoid/add_pair.hpp"
template <typename E>
struct Monoid_Add_Pair {
using value_type = pair<E, E>;
using X = value_type;
static constexpr X op(const X &x, const X &y) {
return {x.fi + y.fi, x.se + y.se};
}
static constexpr X inverse(const X &x) { return {-x.fi, -x.se}; }
static constexpr X unit() { return {0, 0}; }
static constexpr bool commute = true;
};
#line 2 "ds/splaytree/splaytree.hpp"
// Node 型を別に定義して使う
template <typename Node, int NODES = 1'000'000>
struct SplayTree {
Node *pool;
int pid;
using np = Node *;
using X = typename Node::value_type;
using A = typename Node::operator_type;
vc<np> FREE;
SplayTree() : pid(0) { pool = new Node[NODES]; }
void free_subtree(np c) {
auto dfs = [&](auto &dfs, np c) -> void {
if (c->l) dfs(dfs, c->l);
if (c->r) dfs(dfs, c->r);
FREE.eb(c);
};
dfs(dfs, c);
}
void reset() {
pid = 0;
FREE.clear();
}
np new_root() { return nullptr; }
np new_node(const X &x) {
np n = (FREE.empty() ? &(pool[pid++]) : POP(FREE));
Node::new_node(n, x);
return n;
}
np new_node(const vc<X> &dat) {
auto dfs = [&](auto &dfs, int l, int r) -> np {
if (l == r) return nullptr;
if (r == l + 1) return new_node(dat[l]);
int m = (l + r) / 2;
np l_root = dfs(dfs, l, m);
np r_root = dfs(dfs, m + 1, r);
np root = new_node(dat[m]);
root->l = l_root, root->r = r_root;
if (l_root) l_root->p = root;
if (r_root) r_root->p = root;
root->update();
return root;
};
return dfs(dfs, 0, len(dat));
}
u32 get_size(np root) { return (root ? root->size : 0); }
np merge(np l_root, np r_root) {
if (!l_root) return r_root;
if (!r_root) return l_root;
assert((!l_root->p) && (!r_root->p));
splay_kth(r_root, 0); // splay したので prop 済
r_root->l = l_root;
l_root->p = r_root;
r_root->update();
return r_root;
}
np merge3(np a, np b, np c) { return merge(merge(a, b), c); }
np merge4(np a, np b, np c, np d) { return merge(merge(merge(a, b), c), d); }
pair<np, np> split(np root, u32 k) {
assert(!root || !root->p);
if (k == 0) return {nullptr, root};
if (k == (root->size)) return {root, nullptr};
splay_kth(root, k - 1);
np right = root->r;
root->r = nullptr, right->p = nullptr;
root->update();
return {root, right};
}
tuple<np, np, np> split3(np root, u32 l, u32 r) {
np nm, nr;
tie(root, nr) = split(root, r);
tie(root, nm) = split(root, l);
return {root, nm, nr};
}
tuple<np, np, np, np> split4(np root, u32 i, u32 j, u32 k) {
np d;
tie(root, d) = split(root, k);
auto [a, b, c] = split3(root, i, j);
return {a, b, c, d};
}
// 部分木が区間 [l,r) に対応するようなノードを作って返す
// そのノードが root になるわけではないので、
// このノードを参照した後にすぐに splay して根に持ち上げること
void goto_between(np &root, u32 l, u32 r) {
if (l == 0 && r == root->size) return;
if (l == 0) {
splay_kth(root, r);
root = root->l;
return;
}
if (r == root->size) {
splay_kth(root, l - 1);
root = root->r;
return;
}
splay_kth(root, r);
np rp = root;
root = rp->l;
root->p = nullptr;
splay_kth(root, l - 1);
root->p = rp;
rp->l = root;
rp->update();
root = root->r;
}
vc<X> get_all(const np &root) {
vc<X> res;
auto dfs = [&](auto &dfs, np root) -> void {
if (!root) return;
root->prop();
dfs(dfs, root->l);
res.eb(root->get());
dfs(dfs, root->r);
};
dfs(dfs, root);
return res;
}
X get(np &root, u32 k) {
assert(root == nullptr || !root->p);
splay_kth(root, k);
return root->get();
}
void set(np &root, u32 k, const X &x) {
assert(root != nullptr && !root->p);
splay_kth(root, k);
root->set(x);
}
void multiply(np &root, u32 k, const X &x) {
assert(root != nullptr && !root->p);
splay_kth(root, k);
root->multiply(x);
}
X prod(np &root, u32 l, u32 r) {
assert(root == nullptr || !root->p);
using Mono = typename Node::Monoid_X;
if (l == r) return Mono::unit();
assert(0 <= l && l < r && r <= root->size);
goto_between(root, l, r);
X res = root->prod;
splay(root);
return res;
}
X prod(np &root) {
assert(root == nullptr || !root->p);
using Mono = typename Node::Monoid_X;
return (root ? root->prod : Mono::unit());
}
void apply(np &root, u32 l, u32 r, const A &a) {
if (l == r) return;
assert(0 <= l && l < r && r <= root->size);
goto_between(root, l, r);
root->apply(a);
splay(root);
}
void apply(np &root, const A &a) {
if (!root) return;
root->apply(a);
}
void reverse(np &root, u32 l, u32 r) {
assert(root == nullptr || !root->p);
if (l == r) return;
assert(0 <= l && l < r && r <= root->size);
goto_between(root, l, r);
root->reverse();
splay(root);
}
void reverse(np root) {
if (!root) return;
root->reverse();
}
void rotate(Node *n) {
// n を根に近づける。prop, update は rotate の外で行う。
Node *pp, *p, *c;
p = n->p;
pp = p->p;
if (p->l == n) {
c = n->r;
n->r = p;
p->l = c;
} else {
c = n->l;
n->l = p;
p->r = c;
}
if (pp && pp->l == p) pp->l = n;
if (pp && pp->r == p) pp->r = n;
n->p = pp;
p->p = n;
if (c) c->p = p;
}
void splay(Node *me) {
// これを呼ぶ時点で、me の祖先（me を除く）は既に prop 済であることを仮定
// 特に、splay 終了時点で me は upd / prop 済である
me->prop();
while (me->p) {
np p = me->p;
np pp = p->p;
if (!pp) {
rotate(me);
p->update();
break;
}
bool same = (p->l == me && pp->l == p) || (p->r == me && pp->r == p);
if (same) rotate(p), rotate(me);
if (!same) rotate(me), rotate(me);
pp->update(), p->update();
}
// me の update は最後だけでよい
me->update();
}
void splay_kth(np &root, u32 k) {
assert(0 <= k && k < (root->size));
while (1) {
u32 sl = (root->l ? root->l->size : 0);
if (k == sl) break;
root->prop();
if (k < sl)
root = root->l;
else {
k -= sl + 1;
root = root->r;
}
}
splay(root);
}
// check(x), 左側のノード全体が check を満たすように切る
template <typename F>
pair<np, np> split_max_right(np root, F check) {
if (!root) return {nullptr, nullptr};
assert(!root->p);
np c = find_max_right(root, check);
if (!c) {
splay(root);
return {nullptr, root};
}
splay(c);
np right = c->r;
if (!right) return {c, nullptr};
right->p = nullptr;
c->r = nullptr;
c->update();
return {c, right};
}
// 左側のノード全体の prod が check を満たすように切る
template <typename F>
pair<np, np> split_max_right_prod(np root, F check) {
if (!root) return {nullptr, nullptr};
assert(!root->p);
np c = find_max_right_prod(root, check);
if (!c) {
splay(root);
return {nullptr, root};
}
splay(c);
np right = c->r;
if (!right) return {c, nullptr};
right->p = nullptr;
c->r = nullptr;
c->update();
return {c, right};
}
template <typename F>
np find_max_right(np root, const F &check) {
// 最後に見つけた ok の点、最後に探索した点
np last_ok = nullptr, last = nullptr;
while (root) {
last = root;
root->prop();
if (check(root->x)) {
last_ok = root;
root = root->r;
} else {
root = root->l;
}
}
splay(last);
return last_ok;
}
template <typename F>
np find_max_right_prod(np root, const F &check) {
using Mono = typename Node::Monoid_X;
X prod = Mono::unit();
// 最後に見つけた ok の点、最後に探索した点
np last_ok = nullptr, last = nullptr;
while (root) {
last = root;
root->prop();
X lprod = prod;
if (root->l) lprod = Mono::op(lprod, root->l->prod);
lprod = Mono::op(lprod, root->x);
if (check(lprod)) {
prod = lprod;
last_ok = root;
root = root->r;
} else {
root = root->l;
}
}
splay(last);
return last_ok;
}
};
#line 2 "ds/splaytree/splaytree_acted_set.hpp"
namespace SplayTreeNodes {
template <typename ActedSet>
struct Node_AS {
using Monoid_A = typename ActedSet::Monoid_A;
using A = typename ActedSet::A;
using S = typename ActedSet::S;
using value_type = S;
using operator_type = A;
using np = Node_AS *;
np p, l, r;
S x;
A lazy;
u32 size;
bool rev;
static void new_node(np n, const S &x) {
n->p = n->l = n->r = nullptr;
n->x = x;
n->lazy = Monoid_A::unit();
n->size = 1;
n->rev = 0;
}
void update() {
size = 1;
if (l) { size += l->size; }
if (r) { size += r->size; }
}
void prop() {
if (lazy != Monoid_A::unit()) {
if (l) { l->apply(lazy); }
if (r) { r->apply(lazy); }
lazy = Monoid_A::unit();
}
if (rev) {
if (l) {
l->rev ^= 1;
swap(l->l, l->r);
}
if (r) {
r->rev ^= 1;
swap(r->l, r->r);
}
rev = 0;
}
}
// update, prop 以外で呼ばれるものは、splay 後であることが想定されている。
// したがってその時点で update, prop 済であることを仮定してよい。
S get() { return x; }
void set(const S &xx) {
x = xx;
update();
}
void apply(const A &a) {
x = ActedSet::act(x, a);
lazy = Monoid_A::op(lazy, a);
}
void reverse() {
swap(l, r);
rev ^= 1;
}
};
template <typename ActedSet, int NODES>
using SplayTree_ActedSet = SplayTree<Node_AS<ActedSet>, NODES>;
} // namespace SplayTreeNodes
using SplayTreeNodes::SplayTree_ActedSet;
#line 5 "test/mytest/cf702_F_splay.test.cpp"
// (所持金, 操作回数, query index)
struct AS {
using Monoid_A = Monoid_Add_Pair<int>;
using A = Monoid_A::value_type;
using S = tuple<int, int, int>;
static S act(const S& s, const A& x) {
auto [a, b, c] = s;
return {a + x.fi, b + x.se, c};
}
};
vc<int> solve_cf702F(vc<pair<int, int>> CQ, vc<int> query) {
const int Q = len(query);
sort(all(CQ), [&](auto& a, auto& b) -> bool {
if (a.se != b.se) return a.se > b.se;
return a.fi < b.fi;
});
using T = tuple<int, int, int>;
vc<T> dat(Q);
FOR(q, Q) {
int x = query[q];
dat[q] = {x, 0, q};
}
sort(all(dat));
const int MAX = 500'000;
SplayTree_ActedSet<AS, MAX> X;
using np = decltype(X)::np;
using S = typename AS::S;
np root = X.new_node(dat);
FOR(i, len(CQ)) {
ll c = CQ[i].fi;
np nm, nr;
tie(root, nr)
= X.split_max_right(root, [&](S& s) { return get<0>(s) < c; });
X.apply(nr, {-c, 1});
tie(nm, nr) = X.split_max_right(nr, [&](S& s) { return get<0>(s) < c; });
for (auto&& [aa, bb, cc]: X.get_all(nm)) assert(aa < c);
for (auto&& [aa, bb, cc]: X.get_all(nr)) assert(aa >= c);
for (auto [val, cnt, idx]: X.get_all(nm)) {
ll t = val;
auto [l_root, r_root]
= X.split_max_right(root, [&](S& s) { return get<0>(s) < t; });
root = X.merge(l_root, X.new_node({val, cnt, idx}));
root = X.merge(root, r_root);
}
root = X.merge(root, nr);
}
vc<int> ANS(Q);
for (auto [val, cnt, idx]: X.get_all(root)) { ANS[idx] = cnt; }
return ANS;
}
void test_1() {
vc<pair<int, int>> CQ;
CQ.eb(7, 5);
CQ.eb(3, 5);
CQ.eb(4, 3);
vc<int> query = {13, 14};
vc<int> ANS = solve_cf702F(CQ, query);
assert(ANS == vc<int>({2, 3}));
}
void test_2() {
vc<pair<int, int>> CQ;
CQ.eb(100, 500);
CQ.eb(50, 499);
vc<int> query = {50, 200, 150, 100};
vc<int> ANS = solve_cf702F(CQ, query);
assert(ANS == vc<int>({1, 2, 2, 1}));
}
void solve() {
int a, b;
cin >> a >> b;
cout << a + b << "\n";
}
signed main() {
test_1();
test_2();
solve();
return 0;
}