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ds/randomized_bst/rbst_acted_monoid.hpp
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- Last update: 2024-09-09 05:21:21+09:00
- Include:
#include "ds/randomized_bst/rbst_acted_monoid.hpp"
Verified with
- test/1_mytest/ARC30D.test.cpp
- test/1_mytest/rbst_am.test.cpp
- test/1_mytest/rbst_am_2.test.cpp
- test/1_mytest/rbst_am_persistent.test.cpp
- test/2_library_checker/data_structure/dynamic_sequence_range_affine_range_sum_rbst.test.cpp
- test/3_yukicoder/686.test.cpp
Code
template <typename ActedMonoid, bool PERSISTENT>
struct RBST_ActedMonoid {
using Monoid_X = typename ActedMonoid::Monoid_X;
using Monoid_A = typename ActedMonoid::Monoid_A;
using X = typename Monoid_X::value_type;
using A = typename Monoid_A::value_type;
struct Node {
Node *l, *r;
X x, prod; // lazy, rev 反映済
A lazy;
u32 size;
bool rev;
};
Node *pool;
const int NODES;
int pid;
using np = Node *;
RBST_ActedMonoid(int NODES) : NODES(NODES), pid(0) { pool = new Node[NODES]; }
~RBST_ActedMonoid() { delete[] pool; }
void reset() { pid = 0; }
np new_node(const X &x) {
pool[pid].l = pool[pid].r = nullptr;
pool[pid].x = x;
pool[pid].prod = x;
pool[pid].lazy = Monoid_A::unit();
pool[pid].size = 1;
pool[pid].rev = 0;
return &(pool[pid++]);
}
np new_node(const vc<X> &dat) {
auto dfs = [&](auto &dfs, u32 l, u32 r) -> np {
if (l == r) return nullptr;
if (r == l + 1) return new_node(dat[l]);
u32 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;
update(root);
return root;
};
return dfs(dfs, 0, len(dat));
}
np copy_node(np &n) {
if (!n || !PERSISTENT) return n;
pool[pid].l = n->l, pool[pid].r = n->r;
pool[pid].x = n->x;
pool[pid].prod = n->prod;
pool[pid].lazy = n->lazy;
pool[pid].size = n->size;
pool[pid].rev = n->rev;
return &(pool[pid++]);
}
np merge(np l_root, np r_root) { return merge_rec(l_root, 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) {
if (!root) {
assert(k == 0);
return {nullptr, nullptr};
}
assert(0 <= k && k <= root->size);
return split_rec(root, k);
}
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};
}
X prod(np root, u32 l, u32 r) {
if (l == r) return Monoid_X::unit();
return prod_rec(root, l, r, false);
}
X prod(np root) { return (root ? root->prod : Monoid_X::unit()); }
np reverse(np root, u32 l, u32 r) {
assert(Monoid_X::commute);
assert(0 <= l && l <= r && r <= root->size);
if (r - l <= 1) return root;
auto [nl, nm, nr] = split3(root, l, r);
nm->rev ^= 1;
swap(nm->l, nm->r);
return merge3(nl, nm, nr);
}
np apply(np root, u32 l, u32 r, const A a) {
assert(0 <= l && l <= r && r <= root->size);
return apply_rec(root, l, r, a);
}
np apply(np root, const A a) {
if (!root) return root;
return apply_rec(root, 0, root->size, a);
}
np set(np root, u32 k, const X &x) { return set_rec(root, k, x); }
np multiply(np root, u32 k, const X &x) { return multiply_rec(root, k, x); }
X get(np root, u32 k) { return get_rec(root, k, false, Monoid_A::unit()); }
vc<X> get_all(np root) {
vc<X> res;
auto dfs = [&](auto &dfs, np root, bool rev, A lazy) -> void {
if (!root) return;
X me = ActedMonoid::act(root->x, lazy, 1);
lazy = Monoid_A::op(root->lazy, lazy);
dfs(dfs, (rev ? root->r : root->l), rev ^ root->rev, lazy);
res.eb(me);
dfs(dfs, (rev ? root->l : root->r), rev ^ root->rev, lazy);
};
dfs(dfs, root, 0, Monoid_A::unit());
return res;
}
template <typename F>
pair<np, np> split_max_right(np root, const F check) {
assert(check(Monoid_X::unit()));
X x = Monoid_X::unit();
return split_max_right_rec(root, check, x);
}
private:
inline u32 xor128() {
static u32 x = 123456789;
static u32 y = 362436069;
static u32 z = 521288629;
static u32 w = 88675123;
u32 t = x ^ (x << 11);
x = y;
y = z;
z = w;
return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
}
void prop(np c) {
// 自身をコピーする必要はない。
// 子をコピーする必要がある。複数の親を持つ可能性があるため。
bool bl_lazy = (c->lazy != Monoid_A::unit());
bool bl_rev = c->rev;
if (bl_lazy || bl_rev) {
c->l = copy_node(c->l);
c->r = copy_node(c->r);
}
if (c->lazy != Monoid_A::unit()) {
if (c->l) {
c->l->x = ActedMonoid::act(c->l->x, c->lazy, 1);
c->l->prod = ActedMonoid::act(c->l->prod, c->lazy, c->l->size);
c->l->lazy = Monoid_A::op(c->l->lazy, c->lazy);
}
if (c->r) {
c->r->x = ActedMonoid::act(c->r->x, c->lazy, 1);
c->r->prod = ActedMonoid::act(c->r->prod, c->lazy, c->r->size);
c->r->lazy = Monoid_A::op(c->r->lazy, c->lazy);
}
c->lazy = Monoid_A::unit();
}
if (c->rev) {
if (c->l) {
c->l->rev ^= 1;
swap(c->l->l, c->l->r);
}
if (c->r) {
c->r->rev ^= 1;
swap(c->r->l, c->r->r);
}
c->rev = 0;
}
}
void update(np c) {
// データを保ったまま正常化するだけなので、コピー不要
c->size = 1;
c->prod = c->x;
if (c->l) {
c->size += c->l->size;
c->prod = Monoid_X::op(c->l->prod, c->prod);
}
if (c->r) {
c->size += c->r->size;
c->prod = Monoid_X::op(c->prod, c->r->prod);
}
}
np merge_rec(np l_root, np r_root) {
if (!l_root) return r_root;
if (!r_root) return l_root;
u32 sl = l_root->size, sr = r_root->size;
if (xor128() % (sl + sr) < sl) {
prop(l_root);
l_root = copy_node(l_root);
l_root->r = merge_rec(l_root->r, r_root);
update(l_root);
return l_root;
}
prop(r_root);
r_root = copy_node(r_root);
r_root->l = merge_rec(l_root, r_root->l);
update(r_root);
return r_root;
}
pair<np, np> split_rec(np root, u32 k) {
if (!root) return {nullptr, nullptr};
prop(root);
u32 sl = (root->l ? root->l->size : 0);
if (k <= sl) {
auto [nl, nr] = split_rec(root->l, k);
root = copy_node(root);
root->l = nr;
update(root);
return {nl, root};
}
auto [nl, nr] = split_rec(root->r, k - (1 + sl));
root = copy_node(root);
root->r = nl;
update(root);
return {root, nr};
}
np set_rec(np root, u32 k, const X &x) {
if (!root) return root;
prop(root);
u32 sl = (root->l ? root->l->size : 0);
if (k < sl) {
root = copy_node(root);
root->l = set_rec(root->l, k, x);
update(root);
return root;
}
if (k == sl) {
root = copy_node(root);
root->x = x;
update(root);
return root;
}
root = copy_node(root);
root->r = set_rec(root->r, k - (1 + sl), x);
update(root);
return root;
}
np multiply_rec(np root, u32 k, const X &x) {
if (!root) return root;
prop(root);
u32 sl = (root->l ? root->l->size : 0);
if (k < sl) {
root = copy_node(root);
root->l = multiply_rec(root->l, k, x);
update(root);
return root;
}
if (k == sl) {
root = copy_node(root);
root->x = Monoid_X::op(root->x, x);
update(root);
return root;
}
root = copy_node(root);
root->r = multiply_rec(root->r, k - (1 + sl), x);
update(root);
return root;
}
X prod_rec(np root, u32 l, u32 r, bool rev) {
if (l == 0 && r == root->size) { return root->prod; }
np left = (rev ? root->r : root->l);
np right = (rev ? root->l : root->r);
u32 sl = (left ? left->size : 0);
X res = Monoid_X::unit();
if (l < sl) {
X y = prod_rec(left, l, min(r, sl), rev ^ root->rev);
res = Monoid_X::op(res, ActedMonoid::act(y, root->lazy, min(r, sl) - l));
}
if (l <= sl && sl < r) res = Monoid_X::op(res, root->x);
u32 k = 1 + sl;
if (k < r) {
X y = prod_rec(right, max(k, l) - k, r - k, rev ^ root->rev);
res = Monoid_X::op(res, ActedMonoid::act(y, root->lazy, r - max(k, l)));
}
return res;
}
X get_rec(np root, u32 k, bool rev, A lazy) {
np left = (rev ? root->r : root->l);
np right = (rev ? root->l : root->r);
u32 sl = (left ? left->size : 0);
if (k == sl) return ActedMonoid::act(root->x, lazy, 1);
lazy = Monoid_A::op(root->lazy, lazy);
rev ^= root->rev;
if (k < sl) return get_rec(left, k, rev, lazy);
return get_rec(right, k - (1 + sl), rev, lazy);
}
np apply_rec(np root, u32 l, u32 r, const A &a) {
prop(root);
root = copy_node(root);
if (l == 0 && r == root->size) {
root->x = ActedMonoid::act(root->x, a, 1);
root->prod = ActedMonoid::act(root->prod, a, root->size);
root->lazy = a;
return root;
}
u32 sl = (root->l ? root->l->size : 0);
if (l < sl) root->l = apply_rec(root->l, l, min(r, sl), a);
if (l <= sl && sl < r) root->x = ActedMonoid::act(root->x, a, 1);
u32 k = 1 + sl;
if (k < r) root->r = apply_rec(root->r, max(k, l) - k, r - k, a);
update(root);
return root;
}
template <typename F>
pair<np, np> split_max_right_rec(np root, F check, X &x) {
if (!root) return {nullptr, nullptr};
prop(root);
root = copy_node(root);
X y = Monoid_X::op(x, root->prod);
if (check(y)) {
x = y;
return {root, nullptr};
}
np left = root->l, right = root->r;
if (left) {
X y = Monoid_X::op(x, root->l->prod);
if (!check(y)) {
auto [n1, n2] = split_max_right_rec(left, check, x);
root->l = n2;
update(root);
return {n1, root};
}
x = y;
}
y = Monoid_X::op(x, root->x);
if (!check(y)) {
root->l = nullptr;
update(root);
return {left, root};
}
x = y;
auto [n1, n2] = split_max_right_rec(right, check, x);
root->r = n1;
update(root);
return {root, n2};
}
};#line 1 "ds/randomized_bst/rbst_acted_monoid.hpp"
template <typename ActedMonoid, bool PERSISTENT>
struct RBST_ActedMonoid {
using Monoid_X = typename ActedMonoid::Monoid_X;
using Monoid_A = typename ActedMonoid::Monoid_A;
using X = typename Monoid_X::value_type;
using A = typename Monoid_A::value_type;
struct Node {
Node *l, *r;
X x, prod; // lazy, rev 反映済
A lazy;
u32 size;
bool rev;
};
Node *pool;
const int NODES;
int pid;
using np = Node *;
RBST_ActedMonoid(int NODES) : NODES(NODES), pid(0) { pool = new Node[NODES]; }
~RBST_ActedMonoid() { delete[] pool; }
void reset() { pid = 0; }
np new_node(const X &x) {
pool[pid].l = pool[pid].r = nullptr;
pool[pid].x = x;
pool[pid].prod = x;
pool[pid].lazy = Monoid_A::unit();
pool[pid].size = 1;
pool[pid].rev = 0;
return &(pool[pid++]);
}
np new_node(const vc<X> &dat) {
auto dfs = [&](auto &dfs, u32 l, u32 r) -> np {
if (l == r) return nullptr;
if (r == l + 1) return new_node(dat[l]);
u32 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;
update(root);
return root;
};
return dfs(dfs, 0, len(dat));
}
np copy_node(np &n) {
if (!n || !PERSISTENT) return n;
pool[pid].l = n->l, pool[pid].r = n->r;
pool[pid].x = n->x;
pool[pid].prod = n->prod;
pool[pid].lazy = n->lazy;
pool[pid].size = n->size;
pool[pid].rev = n->rev;
return &(pool[pid++]);
}
np merge(np l_root, np r_root) { return merge_rec(l_root, 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) {
if (!root) {
assert(k == 0);
return {nullptr, nullptr};
}
assert(0 <= k && k <= root->size);
return split_rec(root, k);
}
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};
}
X prod(np root, u32 l, u32 r) {
if (l == r) return Monoid_X::unit();
return prod_rec(root, l, r, false);
}
X prod(np root) { return (root ? root->prod : Monoid_X::unit()); }
np reverse(np root, u32 l, u32 r) {
assert(Monoid_X::commute);
assert(0 <= l && l <= r && r <= root->size);
if (r - l <= 1) return root;
auto [nl, nm, nr] = split3(root, l, r);
nm->rev ^= 1;
swap(nm->l, nm->r);
return merge3(nl, nm, nr);
}
np apply(np root, u32 l, u32 r, const A a) {
assert(0 <= l && l <= r && r <= root->size);
return apply_rec(root, l, r, a);
}
np apply(np root, const A a) {
if (!root) return root;
return apply_rec(root, 0, root->size, a);
}
np set(np root, u32 k, const X &x) { return set_rec(root, k, x); }
np multiply(np root, u32 k, const X &x) { return multiply_rec(root, k, x); }
X get(np root, u32 k) { return get_rec(root, k, false, Monoid_A::unit()); }
vc<X> get_all(np root) {
vc<X> res;
auto dfs = [&](auto &dfs, np root, bool rev, A lazy) -> void {
if (!root) return;
X me = ActedMonoid::act(root->x, lazy, 1);
lazy = Monoid_A::op(root->lazy, lazy);
dfs(dfs, (rev ? root->r : root->l), rev ^ root->rev, lazy);
res.eb(me);
dfs(dfs, (rev ? root->l : root->r), rev ^ root->rev, lazy);
};
dfs(dfs, root, 0, Monoid_A::unit());
return res;
}
template <typename F>
pair<np, np> split_max_right(np root, const F check) {
assert(check(Monoid_X::unit()));
X x = Monoid_X::unit();
return split_max_right_rec(root, check, x);
}
private:
inline u32 xor128() {
static u32 x = 123456789;
static u32 y = 362436069;
static u32 z = 521288629;
static u32 w = 88675123;
u32 t = x ^ (x << 11);
x = y;
y = z;
z = w;
return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
}
void prop(np c) {
// 自身をコピーする必要はない。
// 子をコピーする必要がある。複数の親を持つ可能性があるため。
bool bl_lazy = (c->lazy != Monoid_A::unit());
bool bl_rev = c->rev;
if (bl_lazy || bl_rev) {
c->l = copy_node(c->l);
c->r = copy_node(c->r);
}
if (c->lazy != Monoid_A::unit()) {
if (c->l) {
c->l->x = ActedMonoid::act(c->l->x, c->lazy, 1);
c->l->prod = ActedMonoid::act(c->l->prod, c->lazy, c->l->size);
c->l->lazy = Monoid_A::op(c->l->lazy, c->lazy);
}
if (c->r) {
c->r->x = ActedMonoid::act(c->r->x, c->lazy, 1);
c->r->prod = ActedMonoid::act(c->r->prod, c->lazy, c->r->size);
c->r->lazy = Monoid_A::op(c->r->lazy, c->lazy);
}
c->lazy = Monoid_A::unit();
}
if (c->rev) {
if (c->l) {
c->l->rev ^= 1;
swap(c->l->l, c->l->r);
}
if (c->r) {
c->r->rev ^= 1;
swap(c->r->l, c->r->r);
}
c->rev = 0;
}
}
void update(np c) {
// データを保ったまま正常化するだけなので、コピー不要
c->size = 1;
c->prod = c->x;
if (c->l) {
c->size += c->l->size;
c->prod = Monoid_X::op(c->l->prod, c->prod);
}
if (c->r) {
c->size += c->r->size;
c->prod = Monoid_X::op(c->prod, c->r->prod);
}
}
np merge_rec(np l_root, np r_root) {
if (!l_root) return r_root;
if (!r_root) return l_root;
u32 sl = l_root->size, sr = r_root->size;
if (xor128() % (sl + sr) < sl) {
prop(l_root);
l_root = copy_node(l_root);
l_root->r = merge_rec(l_root->r, r_root);
update(l_root);
return l_root;
}
prop(r_root);
r_root = copy_node(r_root);
r_root->l = merge_rec(l_root, r_root->l);
update(r_root);
return r_root;
}
pair<np, np> split_rec(np root, u32 k) {
if (!root) return {nullptr, nullptr};
prop(root);
u32 sl = (root->l ? root->l->size : 0);
if (k <= sl) {
auto [nl, nr] = split_rec(root->l, k);
root = copy_node(root);
root->l = nr;
update(root);
return {nl, root};
}
auto [nl, nr] = split_rec(root->r, k - (1 + sl));
root = copy_node(root);
root->r = nl;
update(root);
return {root, nr};
}
np set_rec(np root, u32 k, const X &x) {
if (!root) return root;
prop(root);
u32 sl = (root->l ? root->l->size : 0);
if (k < sl) {
root = copy_node(root);
root->l = set_rec(root->l, k, x);
update(root);
return root;
}
if (k == sl) {
root = copy_node(root);
root->x = x;
update(root);
return root;
}
root = copy_node(root);
root->r = set_rec(root->r, k - (1 + sl), x);
update(root);
return root;
}
np multiply_rec(np root, u32 k, const X &x) {
if (!root) return root;
prop(root);
u32 sl = (root->l ? root->l->size : 0);
if (k < sl) {
root = copy_node(root);
root->l = multiply_rec(root->l, k, x);
update(root);
return root;
}
if (k == sl) {
root = copy_node(root);
root->x = Monoid_X::op(root->x, x);
update(root);
return root;
}
root = copy_node(root);
root->r = multiply_rec(root->r, k - (1 + sl), x);
update(root);
return root;
}
X prod_rec(np root, u32 l, u32 r, bool rev) {
if (l == 0 && r == root->size) { return root->prod; }
np left = (rev ? root->r : root->l);
np right = (rev ? root->l : root->r);
u32 sl = (left ? left->size : 0);
X res = Monoid_X::unit();
if (l < sl) {
X y = prod_rec(left, l, min(r, sl), rev ^ root->rev);
res = Monoid_X::op(res, ActedMonoid::act(y, root->lazy, min(r, sl) - l));
}
if (l <= sl && sl < r) res = Monoid_X::op(res, root->x);
u32 k = 1 + sl;
if (k < r) {
X y = prod_rec(right, max(k, l) - k, r - k, rev ^ root->rev);
res = Monoid_X::op(res, ActedMonoid::act(y, root->lazy, r - max(k, l)));
}
return res;
}
X get_rec(np root, u32 k, bool rev, A lazy) {
np left = (rev ? root->r : root->l);
np right = (rev ? root->l : root->r);
u32 sl = (left ? left->size : 0);
if (k == sl) return ActedMonoid::act(root->x, lazy, 1);
lazy = Monoid_A::op(root->lazy, lazy);
rev ^= root->rev;
if (k < sl) return get_rec(left, k, rev, lazy);
return get_rec(right, k - (1 + sl), rev, lazy);
}
np apply_rec(np root, u32 l, u32 r, const A &a) {
prop(root);
root = copy_node(root);
if (l == 0 && r == root->size) {
root->x = ActedMonoid::act(root->x, a, 1);
root->prod = ActedMonoid::act(root->prod, a, root->size);
root->lazy = a;
return root;
}
u32 sl = (root->l ? root->l->size : 0);
if (l < sl) root->l = apply_rec(root->l, l, min(r, sl), a);
if (l <= sl && sl < r) root->x = ActedMonoid::act(root->x, a, 1);
u32 k = 1 + sl;
if (k < r) root->r = apply_rec(root->r, max(k, l) - k, r - k, a);
update(root);
return root;
}
template <typename F>
pair<np, np> split_max_right_rec(np root, F check, X &x) {
if (!root) return {nullptr, nullptr};
prop(root);
root = copy_node(root);
X y = Monoid_X::op(x, root->prod);
if (check(y)) {
x = y;
return {root, nullptr};
}
np left = root->l, right = root->r;
if (left) {
X y = Monoid_X::op(x, root->l->prod);
if (!check(y)) {
auto [n1, n2] = split_max_right_rec(left, check, x);
root->l = n2;
update(root);
return {n1, root};
}
x = y;
}
y = Monoid_X::op(x, root->x);
if (!check(y)) {
root->l = nullptr;
update(root);
return {left, root};
}
x = y;
auto [n1, n2] = split_max_right_rec(right, check, x);
root->r = n1;
update(root);
return {root, n2};
}
};