cpp-library
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util/random_tree.hpp
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- Last update: 2024-11-09 00:49:07+00:00
- Include:
#include "util/random_tree.hpp"
Depends on
graph.hpp
util/rand.hppCode
#pragma once
#include "graph.hpp"
#include "util/rand.hpp"
vector<vector<int>> random_tree(int n, const vector<int>& code) {
vector<int> degree(n, 1);
for (int i : code) degree[i]++;
set<int> leaves;
for (int i = 0; i < n; i++)
if (degree[i] == 1) leaves.insert(i);
vector<vector<int>> G(n);
for (int v : code) {
int leaf = *leaves.begin();
leaves.erase(leaves.begin());
G[leaf].push_back(v);
G[v].push_back(leaf);
if (--degree[v] == 1) leaves.insert(v);
}
G[*leaves.begin()].push_back(n-1);
G[n-1].push_back(*leaves.begin());
return G;
}
vector<vector<int>> random_tree(int n) {
vector<int> code(n - 2);
rep(i, n - 2) code[i] = rand32() % n;
return random_tree(n, code);
}
#line 2 "prelude.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using vc = vector<char>;
#define rep2(i, m, n) for (auto i = (m); i < (n); i++)
#define rep(i, n) rep2(i, 0, n)
#define repr2(i, m, n) for (auto i = (n); i-- > (m);)
#define repr(i, n) repr2(i, 0, n)
#define all(x) begin(x), end(x)
auto ndvec(int n, auto e) { return vector(n, e); }
auto ndvec(int n, auto ...e) { return vector(n, ndvec(e...)); }
auto comp_key(auto&& f) { return [&](auto&& a, auto&& b) { return f(a) < f(b); }; }
auto& max(const auto& a, const auto& b) { return a < b ? b : a; }
auto& min(const auto& a, const auto& b) { return b < a ? b : a; }
#if __cpp_lib_ranges
namespace R = std::ranges;
namespace V = std::views;
#endif
#line 3 "graph/traits.hpp"
struct unit_edge {
int to;
operator int() const { return to; }
int w() const { return 1; }
};
template <class Weight>
struct weighted_edge {
int to;
Weight weight;
operator int() const { return to; }
Weight w() const { return weight; }
};
template <class Inner>
struct basic_graph {
using weight_type = void;
const Inner& inner;
basic_graph(const Inner& g) : inner(g) { }
template <class F>
void adj(int v, F f) const {
for (auto u : inner[v]) f(unit_edge{u});
}
int deg(int v) const { return inner[v].size(); }
};
template <class Inner, class Weight>
struct basic_weighted_graph {
using weight_type = Weight;
const Inner& inner;
basic_weighted_graph(const Inner& g) : inner(g) { }
template <class F>
void adj(int v, F f) const {
for (auto [u, w] : inner[v]) f(weighted_edge<weight_type>{u, w});
}
int deg(int v) const { return inner[v].size(); }
};
template <class Inner>
struct graph_trait {
using weight_type = typename Inner::weight_type;
const Inner& g;
graph_trait(const Inner& g) : g(g) { }
int size() const { return g.size(); }
template <class F>
void adj(int v, F f) const {
g.adj(v, f);
}
decltype(auto) operator[](int v) const { return g[v]; }
};
template <class T>
constexpr bool is_weighted_v =
!is_same_v<typename graph_trait<T>::weight_type, void>;
template <class T>
using weight_t =
conditional_t<is_weighted_v<T>, typename graph_trait<T>::weight_type, int>;
template <class T>
using edge_t =
conditional_t<is_weighted_v<T>, weighted_edge<weight_t<T>>, unit_edge>;
template <size_t N>
struct graph_trait<vector<int>[N]> : basic_graph<vector<int>[N]> {
using basic_graph<vector<int>[N]>::basic_graph;
int size() const { return N; }
};
template <>
struct graph_trait<vector<vector<int>>> : basic_graph<vector<vector<int>>> {
using basic_graph<vector<vector<int>>>::basic_graph;
int size() const { return this->inner.size(); }
};
template <size_t N, class Weight>
struct graph_trait<vector<pair<int, Weight>>[N]>
: basic_weighted_graph<vector<pair<int, Weight>>[N], Weight> {
using basic_weighted_graph<
vector<pair<int, Weight>>[N], Weight>::basic_weighted_graph;
int size() const { return N; }
};
template <class Weight>
struct graph_trait<vector<vector<pair<int, Weight>>>>
: basic_weighted_graph<vector<vector<pair<int, Weight>>>, Weight> {
using basic_weighted_graph<
vector<vector<pair<int, Weight>>>, Weight>::basic_weighted_graph;
int size() const { return this->inner.size(); }
};
#line 3 "range.hpp"
template <class It>
struct range : pair<It, It> {
using pair<It, It>::pair;
It begin() const { return this->first; }
It end() const { return this->second; }
It cbegin() const { return begin(); }
It cend() const { return end(); }
int size() const { return this->second - this->first; }
};
#line 4 "graph/csr.hpp"
template <size_t>
struct stdin_reader;
template <class Weight = void>
class csr_graph {
private:
struct directed_t {};
public:
using weight_type = Weight;
csr_graph() = default;
template <class It>
csr_graph(int n, It e, It e_last) : n(n), m(distance(e, e_last)) {
init<false>(e, e_last);
}
template <size_t Size = 1 << 26>
csr_graph(int n, int m, stdin_reader<Size>& read) : n(n), m(m) {
auto e = read_e(read);
init<false>(all(e));
}
template <class It>
static csr_graph directed(int n, It e, It e_last) {
return csr_graph(directed_t{}, n, e, e_last);
}
template <size_t Size = 1 << 26>
static csr_graph directed(int n, int m, stdin_reader<Size>& read) {
return csr_graph(directed_t{}, n, m, read);
}
template <size_t Size = 1 << 26>
static csr_graph tree(int n, stdin_reader<Size>& read) {
return csr_graph(n, n - 1, read);
}
template <size_t Size = 1 << 26>
static csr_graph tree(stdin_reader<Size>& read) {
int n = read;
return csr_graph(n, n - 1, read);
}
int size() const { return n; }
range<typename vector<edge_t<csr_graph>>::iterator> operator[](int v) const {
return {ls[v], rs[v]};
}
int deg(int v) { return rs[v] - ls[v]; }
template <class F>
void adj(int v, F f) const {
for_each(ls[v], rs[v], f);
}
private:
template <class It>
csr_graph(directed_t, int n, It e, It e_last) : n(n), m(distance(e, e_last)) {
init<true>(e, e_last);
}
template <size_t Size = 1 << 26>
csr_graph(directed_t, int n, int m, stdin_reader<Size>& read) : n(n), m(m) {
auto e = read_e(read);
init<true>(all(e));
}
vector<typename vector<edge_t<csr_graph>>::iterator> ls, rs;
int n, m;
vector<edge_t<csr_graph>> es;
template <bool OneBased = true, size_t Size = 1 << 26>
auto read_e(stdin_reader<Size>& read) {
using E = conditional_t<is_weighted_v<csr_graph>, tuple<int, int, Weight>,
pair<int, int>>;
vector<E> res(m);
for (auto& e : res) {
read(e);
if (OneBased) get<0>(e)--, get<1>(e)--;
}
return res;
}
template <bool Directed, class It>
void init(It e, It e_last) {
if (!Directed) m *= 2;
es.resize(m);
ls.resize(n), rs.resize(n);
vector<int> sz(n);
for (auto it = e; it != e_last; it++) {
int from = get<0>(*it), to = get<1>(*it);
sz[from]++;
if (!Directed) sz[to]++;
}
partial_sum(all(sz), sz.begin());
rep(v, n) ls[v] = rs[v] = es.begin() + sz[v];
for (auto it = e; it != e_last; it++) {
int from = get<0>(*it), to = get<1>(*it);
if constexpr (is_weighted_v<csr_graph>)
*--ls[from] = edge_t<csr_graph>{to, get<2>(*it)};
else
*--ls[from] = edge_t<csr_graph>{to};
if (!Directed) {
if constexpr (is_weighted_v<csr_graph>)
*--ls[to] = edge_t<csr_graph>{from, get<2>(*it)};
else
*--ls[to] = edge_t<csr_graph>{from};
}
}
}
};
#line 3 "util/seed.hpp"
auto seed() {
#if defined(LOCAL) && !defined(NO_FIX_SEED)
return 314169265258979;
#endif
return chrono::steady_clock::now().time_since_epoch().count();
}
#line 3 "util/rand.hpp"
uint32_t rand32() {
static uint32_t x = seed();
x ^= x << 13;
x ^= x >> 17;
x ^= x << 5;
return x;
}
uint64_t rand64() {
return uint64_t(rand32()) << 32 | rand32();
}
#line 4 "util/random_tree.hpp"
vector<vector<int>> random_tree(int n, const vector<int>& code) {
vector<int> degree(n, 1);
for (int i : code) degree[i]++;
set<int> leaves;
for (int i = 0; i < n; i++)
if (degree[i] == 1) leaves.insert(i);
vector<vector<int>> G(n);
for (int v : code) {
int leaf = *leaves.begin();
leaves.erase(leaves.begin());
G[leaf].push_back(v);
G[v].push_back(leaf);
if (--degree[v] == 1) leaves.insert(v);
}
G[*leaves.begin()].push_back(n-1);
G[n-1].push_back(*leaves.begin());
return G;
}
vector<vector<int>> random_tree(int n) {
vector<int> code(n - 2);
rep(i, n - 2) code[i] = rand32() % n;
return random_tree(n, code);
}