noya2_Library

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:warning: misc/random_tree.hpp

Depends on

Code

#pragma once

#include"../template/template.hpp"

#include"../misc/rng.hpp"

namespace noya2 {

// input: [c \in [0, n)] * (n-2), n >= 3
vector<vector<int>> pruefer_code(const vector<int>& code) {
    int n = code.size() + 2;
    assert(n > 2);
    vector<vector<int>> g(n);
    vector<int> deg(n, 1);
    int e = 0;
    for (auto& x : code) deg[x]++;
    set<int> ps;
    for (int j = 0; j < n; j++) {
        if (deg[j] == 1) ps.insert(j);
    }
    for (auto& i : code) {
        if (ps.empty()) break;
        int j = *begin(ps);
        ps.erase(j);
        g[i].push_back(j);
        g[j].push_back(i);
        if (deg[i] == 1) ps.erase(i);
        deg[i]--, deg[j]--;
        if (deg[i] == 1) ps.insert(i);
        e++;
    }
    int u = -1, v = -1;
    for (int i = 0; i < n; i++) {
        if (deg[i] == 1) (u == -1 ? u : v) = i;
    }
    assert(u != -1 and v != -1);
    g[u].push_back(v);
    g[v].push_back(u);
    e++;
    assert(e == n - 1);
    return g;
}

vector<vector<int>> random_tree(int n) {
    if (n <= 2) {
        vector<vector<int>> g(n);
        if (n == 2) {
            g[0].push_back(1);
            g[1].push_back(0);
        }
        return g;
    }
    vector<int> pruefer(n - 2);
    for (auto& x : pruefer) x = randint(0,n);
    return pruefer_code(pruefer);
}

} // namespace noya2
#line 2 "misc/random_tree.hpp"

#line 2 "template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "template/utils.hpp"

#line 6 "template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 4 "misc/random_tree.hpp"

#line 2 "misc/rng.hpp"

#line 4 "misc/rng.hpp"

namespace noya2 {

// [0, 2^64 - 1)
ull rng() {
  static ull _x = 88172645463325252UL;
  return _x ^= _x << 7, _x ^= _x >> 9;
}

// [l, r]
ll rng(ll l, ll r) {
  assert(l <= r);
  return l + rng() % ull(r - l + 1);
}

// [l, r)
ll randint(ll l, ll r) {
  assert(l < r);
  return l + rng() % ull(r - l);
}

// [0.0, 1.0)
ld rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
ld rnd(ld l, ld r) {
  assert(l < r);
  return l + rnd() * (r - l);
}

} // namespace noya2
#line 6 "misc/random_tree.hpp"

namespace noya2 {

// input: [c \in [0, n)] * (n-2), n >= 3
vector<vector<int>> pruefer_code(const vector<int>& code) {
    int n = code.size() + 2;
    assert(n > 2);
    vector<vector<int>> g(n);
    vector<int> deg(n, 1);
    int e = 0;
    for (auto& x : code) deg[x]++;
    set<int> ps;
    for (int j = 0; j < n; j++) {
        if (deg[j] == 1) ps.insert(j);
    }
    for (auto& i : code) {
        if (ps.empty()) break;
        int j = *begin(ps);
        ps.erase(j);
        g[i].push_back(j);
        g[j].push_back(i);
        if (deg[i] == 1) ps.erase(i);
        deg[i]--, deg[j]--;
        if (deg[i] == 1) ps.insert(i);
        e++;
    }
    int u = -1, v = -1;
    for (int i = 0; i < n; i++) {
        if (deg[i] == 1) (u == -1 ? u : v) = i;
    }
    assert(u != -1 and v != -1);
    g[u].push_back(v);
    g[v].push_back(u);
    e++;
    assert(e == n - 1);
    return g;
}

vector<vector<int>> random_tree(int n) {
    if (n <= 2) {
        vector<vector<int>> g(n);
        if (n == 2) {
            g[0].push_back(1);
            g[1].push_back(0);
        }
        return g;
    }
    vector<int> pruefer(n - 2);
    for (auto& x : pruefer) x = randint(0,n);
    return pruefer_code(pruefer);
}

} // namespace noya2
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