compro_library
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test/library-checker/data-structure/vertex-set-path-composite.test.cpp
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- Last update: 2024-09-08 23:17:50+09:00
- Problem: https://judge.yosupo.jp/problem/vertex_set_path_composite
Depends on
- data-structure/monoid/affine.hpp
- Segment Tree
(data-structure/segtree/segtree.hpp)
- グラフ構造体
(graph/graph_template.hpp)
- HL分解
(graph/tree/hld.hpp)
- modint/modint.hpp
- template/template.cpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"
#include "../../../template/template.cpp"
#include "../../../data-structure/monoid/affine.hpp"
#include "../../../data-structure/segtree/segtree.hpp"
#include "../../../graph/tree/hld.hpp"
#include "../../../modint/modint.hpp"
using mint = ModInt<MOD2>;
using AffineLeft = MonoidAffine<mint, false>;
using AffineRight = MonoidAffine<mint, true>;
int main() {
int N, Q;
cin >> N >> Q;
vector<pair<mint, mint>> af(N);
REP(i, N) {
mint a, b;
cin >> a >> b;
af[i] = {a, b};
}
HeavyLightDecomposition hld(N);
REP(_, N-1) {
int u, v;
cin >> u >> v;
hld.add_edge(u, v);
}
hld.build();
Segtree<AffineLeft> seg(N);
Segtree<AffineRight> seg_rev(N);
REP(i, N) {
seg.set(hld[i], af[i]);
seg_rev.set(hld[i], af[i]);
}
while(Q--) {
int type;
cin >> type;
if(type == 0) {
int p;
mint c, d;
cin >> p >> c >> d;
seg.set(hld[p], make_pair(c, d));
seg_rev.set(hld[p], make_pair(c, d));
} else {
int u, v;
mint x;
cin >> u >> v >> x;
pair<mint, mint> res_l = AffineLeft::e(), res_r = AffineRight::e();
auto f = [&](int l, int r) {
res_l = AffineLeft::op(seg.prod(l, r), res_l);
};
auto f_rev = [&](int l, int r) {
res_r = AffineRight::op(seg_rev.prod(l, r), res_r);
};
hld.path_query<decltype(f), decltype(f_rev)>(u, v, f, f_rev);
auto [a, b] = AffineLeft::op(res_r, res_l);
mint ans = a * x + b;
cout << ans << '\n';
}
}
}#line 1 "test/library-checker/data-structure/vertex-set-path-composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/vertex_set_path_composite"
#line 1 "template/template.cpp"
#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
// input output utils
namespace siro53_io {
// https://maspypy.github.io/library/other/io_old.hpp
struct has_val_impl {
template <class T>
static auto check(T &&x) -> decltype(x.val(), std::true_type{});
template <class T> static auto check(...) -> std::false_type;
};
template <class T>
class has_val : public decltype(has_val_impl::check<T>(std::declval<T>())) {
};
// debug
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void dump(const T t) {
cerr << t;
}
template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
void dump(const T t) {
cerr << t;
}
template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
void dump(const T &t) {
cerr << t.val();
}
void dump(__int128_t n) {
if(n == 0) {
cerr << '0';
return;
} else if(n < 0) {
cerr << '-';
n = -n;
}
string s;
while(n > 0) {
s += (char)('0' + n % 10);
n /= 10;
}
reverse(s.begin(), s.end());
cerr << s;
}
void dump(const string &s) { cerr << s; }
void dump(const char *s) {
int n = (int)strlen(s);
for(int i = 0; i < n; i++) cerr << s[i];
}
template <class T1, class T2> void dump(const pair<T1, T2> &p) {
cerr << '(';
dump(p.first);
cerr << ',';
dump(p.second);
cerr << ')';
}
template <class T> void dump(const vector<T> &v) {
cerr << '{';
for(int i = 0; i < (int)v.size(); i++) {
dump(v[i]);
if(i < (int)v.size() - 1) cerr << ',';
}
cerr << '}';
}
template <class T> void dump(const set<T> &s) {
cerr << '{';
for(auto it = s.begin(); it != s.end(); it++) {
dump(*it);
if(next(it) != s.end()) cerr << ',';
}
cerr << '}';
}
template <class Key, class Value> void dump(const map<Key, Value> &mp) {
cerr << '{';
for(auto it = mp.begin(); it != mp.end(); it++) {
dump(*it);
if(next(it) != mp.end()) cerr << ',';
}
cerr << '}';
}
template <class Key, class Value>
void dump(const unordered_map<Key, Value> &mp) {
cerr << '{';
for(auto it = mp.begin(); it != mp.end(); it++) {
dump(*it);
if(next(it) != mp.end()) cerr << ',';
}
cerr << '}';
}
template <class T> void dump(const deque<T> &v) {
cerr << '{';
for(int i = 0; i < (int)v.size(); i++) {
dump(v[i]);
if(i < (int)v.size() - 1) cerr << ',';
}
cerr << '}';
}
template <class T> void dump(queue<T> q) {
cerr << '{';
while(!q.empty()) {
dump(q.front());
if((int)q.size() > 1) cerr << ',';
q.pop();
}
cerr << '}';
}
void debug_print() { cerr << endl; }
template <class Head, class... Tail>
void debug_print(const Head &h, const Tail &...t) {
dump(h);
if(sizeof...(Tail)) dump(' ');
debug_print(t...);
}
// print
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void print_single(const T t) {
cout << t;
}
template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
void print_single(const T t) {
cout << t;
}
template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
void print_single(const T t) {
cout << t.val();
}
void print_single(__int128_t n) {
if(n == 0) {
cout << '0';
return;
} else if(n < 0) {
cout << '-';
n = -n;
}
string s;
while(n > 0) {
s += (char)('0' + n % 10);
n /= 10;
}
reverse(s.begin(), s.end());
cout << s;
}
void print_single(const string &s) { cout << s; }
void print_single(const char *s) {
int n = (int)strlen(s);
for(int i = 0; i < n; i++) cout << s[i];
}
template <class T1, class T2> void print_single(const pair<T1, T2> &p) {
print_single(p.first);
cout << ' ';
print_single(p.second);
}
template <class T> void print_single(const vector<T> &v) {
for(int i = 0; i < (int)v.size(); i++) {
print_single(v[i]);
if(i < (int)v.size() - 1) cout << ' ';
}
}
template <class T> void print_single(const set<T> &s) {
for(auto it = s.begin(); it != s.end(); it++) {
print_single(*it);
if(next(it) != s.end()) cout << ' ';
}
}
template <class T> void print_single(const deque<T> &v) {
for(int i = 0; i < (int)v.size(); i++) {
print_single(v[i]);
if(i < (int)v.size() - 1) cout << ' ';
}
}
template <class T> void print_single(queue<T> q) {
while(!q.empty()) {
print_single(q.front());
if((int)q.size() > 1) cout << ' ';
q.pop();
}
}
void print() { cout << '\n'; }
template <class Head, class... Tail>
void print(const Head &h, const Tail &...t) {
print_single(h);
if(sizeof...(Tail)) print_single(' ');
print(t...);
}
// input
template <class T, enable_if_t<is_integral<T>::value, int> = 0>
void input_single(T &t) {
cin >> t;
}
template <class T, enable_if_t<is_floating_point<T>::value, int> = 0>
void input_single(T &t) {
cin >> t;
}
template <class T, typename enable_if<has_val<T>::value>::type * = nullptr>
void input_single(T &t) {
cin >> t;
}
void input_single(__int128_t &n) {
string s;
cin >> s;
if(s == "0") {
n = 0;
return;
}
bool is_minus = false;
if(s[0] == '-') {
s = s.substr(1);
is_minus = true;
}
n = 0;
for(int i = 0; i < (int)s.size(); i++) n = n * 10 + (int)(s[i] - '0');
if(is_minus) n = -n;
}
void input_single(string &s) { cin >> s; }
template <class T1, class T2> void input_single(pair<T1, T2> &p) {
input_single(p.first);
input_single(p.second);
}
template <class T> void input_single(vector<T> &v) {
for(auto &e : v) input_single(e);
}
void input() {}
template <class Head, class... Tail> void input(Head &h, Tail &...t) {
input_single(h);
input(t...);
}
}; // namespace siro53_io
#ifdef DEBUG
#define debug(...) \
cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debug_print(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
// io setup
struct Setup {
Setup() {
cin.tie(0);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
}
} __Setup;
using namespace siro53_io;
// types
using ll = long long;
using i128 = __int128_t;
// input macros
#define INT(...) \
int __VA_ARGS__; \
input(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
input(__VA_ARGS__)
#define STRING(...) \
string __VA_ARGS__; \
input(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
input(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
input(__VA_ARGS__)
#define LD(...) \
long double __VA_ARGS__; \
input(__VA_ARGS__)
#define UINT(...) \
unsigned int __VA_ARGS__; \
input(__VA_ARGS__)
#define ULL(...) \
unsigned long long __VA_ARGS__; \
input(__VA_ARGS__)
#define VEC(name, type, len) \
vector<type> name(len); \
input(name);
#define VEC2(name, type, len1, len2) \
vector name(len1, vector<type>(len2)); \
input(name);
// other macros
// https://trap.jp/post/1224/
#define OVERLOAD3(_1, _2, _3, name, ...) name
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()
#define REP1(i, n) for(int i = 0; i < int(n); i++)
#define REP2(i, a, b) for(int i = (a); i < int(b); i++)
#define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1)(__VA_ARGS__)
#define SORT(v) sort(ALL(v))
#define RSORT(v) sort(RALL(v))
#define UNIQUE(v) \
sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()), v.shrink_to_fit()
#define REV(v) reverse(ALL(v))
#define SZ(v) ((int)(v).size())
#define MIN(v) (*min_element(ALL(v)))
#define MAX(v) (*max_element(ALL(v)))
// util const
const int INF = 1 << 30;
const ll LLINF = 1LL << 60;
constexpr int MOD = 1000000007;
constexpr int MOD2 = 998244353;
const int dx[4] = {1, 0, -1, 0};
const int dy[4] = {0, 1, 0, -1};
// util functions
void Case(int i) { cout << "Case #" << i << ": "; }
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
template <class T> inline bool chmax(T &a, T b) {
return (a < b ? a = b, true : false);
}
template <class T> inline bool chmin(T &a, T b) {
return (a > b ? a = b, true : false);
}
template <class T, int dim>
auto make_vector_impl(vector<int>& sizes, const T &e) {
if constexpr(dim == 1) {
return vector(sizes[0], e);
} else {
int n = sizes[dim - 1];
sizes.pop_back();
return vector(n, make_vector_impl<T, dim - 1>(sizes, e));
}
}
template <class T, int dim>
auto make_vector(const int (&sizes)[dim], const T &e = T()) {
vector<int> s(dim);
for(int i = 0; i < dim; i++) s[i] = sizes[dim - i - 1];
return make_vector_impl<T, dim>(s, e);
}
vector<int> iota_gen(int n, int start = 0) {
vector<int> ord(n);
iota(ord.begin(), ord.end(), start);
return ord;
}
template<typename T>
vector<int> ord_sort(const vector<T>& v, bool greater = false) {
auto ord = iota_gen((int)v.size());
sort(ALL(ord), [&](int i, int j) {
if(greater) return v[i] > v[j];
return v[i] < v[j];
});
return ord;
}
#pragma endregion Macros
#line 2 "data-structure/monoid/affine.hpp"
#line 4 "data-structure/monoid/affine.hpp"
template <typename T, bool rev = false> struct MonoidAffine {
using S = std::pair<T, T>;
using value_type = S;
inline static S op(const S &l, const S &r) {
if(rev) return S(r.first * l.first, r.first * l.second + r.second);
return S(l.first * r.first, l.first * r.second + l.second);
}
inline static S e() { return S(T(1), T(0)); }
};
#line 2 "data-structure/segtree/segtree.hpp"
#line 5 "data-structure/segtree/segtree.hpp"
template <class Monoid> class Segtree {
public:
using T = typename Monoid::value_type;
Segtree() : Segtree(0) {}
explicit Segtree(int n) : Segtree(std::vector<T>(n, Monoid::e())) {}
explicit Segtree(const std::vector<T> &v) : N((int)v.size()), sz(1) {
while(sz < N) sz <<= 1;
node.resize(sz * 2, Monoid::e());
for(int i = 0; i < N; i++) node[i + sz] = v[i];
for(int i = sz - 1; i >= 1; i--) {
node[i] = Monoid::op(node[i << 1], node[i << 1 | 1]);
}
}
void set(int pos, T val) {
assert(0 <= pos && pos < N);
pos += sz;
node[pos] = val;
while(pos > 1) {
pos >>= 1;
node[pos] = Monoid::op(node[pos << 1], node[pos << 1 | 1]);
}
}
T get(int pos) const {
assert(0 <= pos && pos < N);
return node[pos + sz];
}
void apply(int pos, T val) {
this->set(pos, Monoid::op(this->get(pos), val));
}
T prod(int l, int r) const {
assert(0 <= l && l <= r && r <= N);
T value_l = Monoid::e(), value_r = Monoid::e();
l += sz;
r += sz;
while(l < r) {
if(l & 1) value_l = Monoid::op(value_l, node[l++]);
if(r & 1) value_r = Monoid::op(node[--r], value_r);
l >>= 1;
r >>= 1;
}
return Monoid::op(value_l, value_r);
}
T all_prod() const { return node[1]; }
template <class F> int max_right(int l, F f) const {
assert(0 <= l && l <= N);
assert(f(Monoid::e()));
if(l == N) return N;
l += sz;
T value_now = Monoid::e();
do {
while((l & 1) == 0) l >>= 1;
if(!f(Monoid::op(value_now, node[l]))) {
while(l < sz) {
l = 2 * l;
if(f(Monoid::op(value_now, node[l]))) {
value_now = Monoid::op(value_now, node[l]);
l++;
}
}
return (l - sz);
}
value_now = Monoid::op(value_now, node[l]);
l++;
} while((l & -l) != l);
return N;
}
template <class F> int min_left(int r, F f) const {
assert(0 <= r && r <= N);
assert(f(Monoid::e()));
if(r == 0) return 0;
r += sz;
T value_now = Monoid::e();
do {
r--;
while(r > 1 && (r & 1)) r >>= 1;
if(!f(Monoid::op(node[r], value_now))) {
while(r < sz) {
r = 2 * r + 1;
if(f(Monoid::op(node[r], value_now))) {
value_now = Monoid::op(node[r], value_now);
r--;
}
}
return ((r + 1) - sz);
}
value_now = Monoid::op(node[r], value_now);
} while((r & -r) != r);
return 0;
}
private:
int N, sz;
std::vector<T> node;
};
#line 2 "graph/tree/hld.hpp"
#line 4 "graph/tree/hld.hpp"
#line 2 "graph/graph_template.hpp"
#line 5 "graph/graph_template.hpp"
template <typename Cost = int> struct Edge {
int from, to;
Cost cost;
int id;
Edge() = default;
explicit Edge(int from, int to, Cost cost = 1, int id = -1)
: from(from), to(to), cost(cost), id(id) {}
operator int() const { return to; }
};
template <typename Cost = int> class Graph {
public:
Graph() = default;
explicit Graph(int N) : N(N), M(0), G(N) {}
inline void add_directed_edge(int from, int to, Cost cost = 1) {
assert(0 <= from && from < N);
assert(0 <= to && to < N);
G[from].emplace_back(from, to, cost, M++);
}
inline void add_undirected_edge(int from, int to, Cost cost = 1) {
assert(0 <= from && from < N);
assert(0 <= to && to < N);
G[from].emplace_back(from, to, cost, M);
G[to].emplace_back(to, from, cost, M++);
}
inline size_t size() const { return G.size(); }
inline std::vector<Edge<Cost>> &operator[](const int &i) { return G[i]; }
inline const std::vector<Edge<Cost>> &operator[](const int &i) const {
return G[i];
}
protected:
int N, M;
std::vector<std::vector<Edge<Cost>>> G;
};
template <class Cost = int> using Edges = std::vector<Edge<Cost>>;
#line 6 "graph/tree/hld.hpp"
template <typename Cost = int> class HeavyLightDecomposition {
public:
explicit HeavyLightDecomposition(int N)
: G(N), in(N), out(N), sz(N), head(N), par(N), dep(N), rev(N),
isBuilt(false) {}
explicit HeavyLightDecomposition(const Graph<Cost> &g)
: G(g), in(g.size()), out(g.size()), sz(g.size()), head(g.size()),
par(g.size()), dep(g.size()), rev(g.size()), isBuilt(false) {
build();
}
void add_edge(int from, int to, Cost cost = 1) {
G.add_undirected_edge(from, to, cost);
}
void build(int root = 0) {
dfs1(root, -1, 0);
head[root] = root;
int idx = 0;
dfs2(root, -1, idx);
isBuilt = true;
}
int lca(int u, int v) const {
assert(isBuilt);
assert(0 <= u && u < (int)G.size());
assert(0 <= v && v < (int)G.size());
while(1) {
if(in[u] > in[v]) std::swap(u, v);
if(head[u] == head[v]) return u;
v = par[head[v]];
}
}
int dist(int u, int v) const {
assert(isBuilt);
assert(0 <= u && u < (int)G.size());
assert(0 <= v && v < (int)G.size());
return (dep[u] + dep[v] - 2 * dep[lca(u, v)]);
}
int la(int u, int k) const {
assert(isBuilt);
assert(0 <= u && u < (int)G.size());
if(dep[u] < k) return -1;
while(1) {
if(in[u] - k >= in[head[u]]) {
return rev[in[u] - k];
}
k -= (in[u] - in[head[u]] + 1);
u = par[head[u]];
}
}
template<class F>
void path_query(int u, int v, const F& f, bool edge = false) const {
assert(isBuilt);
assert(0 <= u && u < (int)G.size());
assert(0 <= v && v < (int)G.size());
while(1) {
if(in[u] > in[v]) std::swap(u, v);
if(head[u] == head[v]) {
f(in[u] + (int)(edge), in[v] + 1);
break;
} else {
f(in[head[v]], in[v] + 1);
}
v = par[head[v]];
}
}
template<class F, class F_rev>
void path_query(int u, int v, const F& f, const F_rev& f_rev, bool edge = false) const {
assert(isBuilt);
assert(0 <= u && u < (int)G.size());
assert(0 <= v && v < (int)G.size());
int L = lca(u, v);
path_query<F>(u, L, f, edge);
path_query<F_rev>(L, v, f_rev, true);
}
template<class F>
void subtree_query(int u, const F& f) const {
assert(isBuilt);
assert(0 <= u && u < (int)G.size());
f(in[u], out[u]);
}
int operator[](int u) const {
assert(isBuilt);
assert(0 <= u && u < (int)G.size());
return in[u];
}
private:
Graph<Cost> G;
std::vector<int> in, out, sz, head, par, dep, rev;
bool isBuilt;
void dfs1(int u, int p, int d) {
dep[u] = d;
sz[u] = 1;
if(!G[u].empty() && G[u].front().to == p) {
std::swap(G[u].front(), G[u].back());
}
for(auto &e : G[u]) {
if(e.to == p) continue;
dfs1(e.to, u, d + 1);
sz[u] += sz[e.to];
if(sz[e.to] > sz[G[u].front().to]) { std::swap(G[u].front(), e); }
}
}
void dfs2(int u, int p, int &idx) {
par[u] = p;
in[u] = idx++;
rev[in[u]] = u;
for(const auto &e : G[u]) {
if(e.to == p) continue;
head[e.to] = (e.to == G[u].front().to ? head[u] : e.to);
dfs2(e.to, u, idx);
}
out[u] = idx;
}
};
#line 2 "modint/modint.hpp"
#line 6 "modint/modint.hpp"
template <int mod> class ModInt {
public:
ModInt() : x(0) {}
ModInt(long long y)
: x(y >= 0 ? y % umod() : (umod() - (-y) % umod()) % umod()) {}
unsigned int val() const { return x; }
ModInt &operator+=(const ModInt &p) {
if((x += p.x) >= umod()) x -= umod();
return *this;
}
ModInt &operator-=(const ModInt &p) {
if((x += umod() - p.x) >= umod()) x -= umod();
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (unsigned int)(1ULL * x * p.x % umod());
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inv();
return *this;
}
ModInt operator-() const { return ModInt(-(long long)x); }
ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
bool operator==(const ModInt &p) const { return x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inv() const {
long long a = x, b = mod, u = 1, v = 0, t;
while(b > 0) {
t = a / b;
std::swap(a -= t * b, b);
std::swap(u -= t * v, v);
}
return ModInt(u);
}
ModInt pow(unsigned long long n) const {
ModInt ret(1), mul(x);
while(n > 0) {
if(n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
friend std::ostream &operator<<(std::ostream &os, const ModInt &p) {
return os << p.x;
}
friend std::istream &operator>>(std::istream &is, ModInt &a) {
long long t;
is >> t;
a = ModInt<mod>(t);
return (is);
}
static constexpr int get_mod() { return mod; }
private:
unsigned int x;
static constexpr unsigned int umod() { return mod; }
};
#line 7 "test/library-checker/data-structure/vertex-set-path-composite.test.cpp"
using mint = ModInt<MOD2>;
using AffineLeft = MonoidAffine<mint, false>;
using AffineRight = MonoidAffine<mint, true>;
int main() {
int N, Q;
cin >> N >> Q;
vector<pair<mint, mint>> af(N);
REP(i, N) {
mint a, b;
cin >> a >> b;
af[i] = {a, b};
}
HeavyLightDecomposition hld(N);
REP(_, N-1) {
int u, v;
cin >> u >> v;
hld.add_edge(u, v);
}
hld.build();
Segtree<AffineLeft> seg(N);
Segtree<AffineRight> seg_rev(N);
REP(i, N) {
seg.set(hld[i], af[i]);
seg_rev.set(hld[i], af[i]);
}
while(Q--) {
int type;
cin >> type;
if(type == 0) {
int p;
mint c, d;
cin >> p >> c >> d;
seg.set(hld[p], make_pair(c, d));
seg_rev.set(hld[p], make_pair(c, d));
} else {
int u, v;
mint x;
cin >> u >> v >> x;
pair<mint, mint> res_l = AffineLeft::e(), res_r = AffineRight::e();
auto f = [&](int l, int r) {
res_l = AffineLeft::op(seg.prod(l, r), res_l);
};
auto f_rev = [&](int l, int r) {
res_r = AffineRight::op(seg_rev.prod(l, r), res_r);
};
hld.path_query<decltype(f), decltype(f_rev)>(u, v, f, f_rev);
auto [a, b] = AffineLeft::op(res_r, res_l);
mint ans = a * x + b;
cout << ans << '\n';
}
}
}