CP-templates

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View the Project on GitHub Misuki743/CP-templates

:heavy_check_mark: test/mytest_tree_diameter.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#include "../default/t.cpp"
#include "../tree/prufer_recover.cpp"
#include "../enumerate/enumerate_bit.cpp"
#include "../enumerate/enumerate_twelvefold.cpp"
#include "../enumerate/enumerate_label_tree.cpp"
#include "../enumerate/enumerate_unlabel_rooted_tree.cpp"
#include "../tree/tree.cpp"
#include "../tree/tree_diameter.cpp"

void check(vector<vector<int>> g) {
  const int n = ssize(g);
  vi dep;
  auto dfs = [&](int v, int p, auto &self) -> void {
    for(int x : g[v]) {
      if (x == p) continue;
      dep[x] = dep[v] + 1;
      self(x, v, self);
    }
  };

  int diameter = -1;
  for(int r = 0; r < n; r++) {
    vi(n, INT_MAX).swap(dep);
    dep[r] = 0;
    dfs(r, -1, dfs);
    chmax(diameter, ranges::max(dep));
  }

  vc<pii> e;
  for(int u = 0; u < n; u++)
    for(int v : g[u])
      if (u < v)
        e.emplace_back(u, v);

  set<pii> s;
  for(auto [u, v] : e)
    s.emplace(u, v), s.emplace(v, u);

  auto [diameter_2, path] = tree_diameter(e);

  assert(diameter == diameter_2);
  assert(ssize(path) == diameter + 1);
  for(int i = 1; i < ssize(path); i++)
    assert(s.contains(pair(path[i - 1], path[i])));
  Unique(path);
  assert(ssize(path) == diameter + 1);
}

auto random_relabel(vector<vector<int>> g) {
  mt19937 rng(clock);
  const int n = ssize(g);
  vector<int> p(n);
  iota(p.begin(), p.end(), 0);
  shuffle(p.begin(), p.end(), rng);
  vector<vector<int>> g2(n);
  for(int u = 0; u < n; u++)
    for(int v : g[u])
      g2[p[u]].eb(p[v]);
  return g2;
}

void a_plus_b() {
  int a, b; cin >> a >> b;
  cout << a + b << '\n';
}

int main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  mt19937 rng(clock);

  for(int n = 1; n <= 7; n++) {
    enumerate_label_tree(n, [&](vector<vector<int>> g) {
      check(g);
    });
  }

  for(int n = 1; n <= 15; n++) {
    enumerate_unlabel_rooted_tree(n, [&](vector<vector<int>> g) {
      check(g);
      check(random_relabel(g));
    });
  }

  //path
  for(int n = 1; n <= 100; n++) {
    vector<vector<int>> g(n);
    for(int i = 1; i < n; i++)
      g[i].emplace_back(i - 1), g[i - 1].emplace_back(i);
    check(g);
    check(random_relabel(g));
  }

  //star
  for(int n = 2; n <= 100; n++) {
    for(int root : {0, n / 2, n - 1}) {
      vector<vector<int>> g(n);
      for(int i = 0; i < n; i++)
        if (i != root)
          g[root].emplace_back(i), g[i].emplace_back(root);
      check(g);
    }
  }

  //almost path
  for(int tc = 0; tc < 30; tc++) {
    int n = 500;
    vector<vector<int>> g(n);
    for(int v = 1; v < n; v++) {
      int x = rng() % min(v, 5);
      g[v].emplace_back(x), g[x].emplace_back(v);
    }
    check(g);
    check(random_relabel(g));
  }

  a_plus_b();

  return 0;
}
#line 1 "test/mytest_tree_diameter.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#line 1 "default/t.cpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <variant>
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>

#define INT128_MAX (__int128)(((unsigned __int128) 1 << ((sizeof(__int128) * __CHAR_BIT__) - 1)) - 1)
#define INT128_MIN (-INT128_MAX - 1)

#define pb push_back
#define eb emplace_back
#define clock chrono::steady_clock::now().time_since_epoch().count()

using namespace std;

template<size_t I = 0, typename... args>
ostream& print_tuple(ostream& os, const tuple<args...> tu) {
  os << get<I>(tu);
  if constexpr (I + 1 != sizeof...(args)) {
    os << ' ';
    print_tuple<I + 1>(os, tu);
  }
  return os;
}
template<typename... args>
ostream& operator<<(ostream& os, const tuple<args...> tu) {
  return print_tuple(os, tu);
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2> pr) {
  return os << pr.first << ' ' << pr.second;
}
template<class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N> &arr) {
  for(size_t i = 0; T x : arr) {
    os << x;
    if (++i != N) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const vector<T> &vec) {
  for(size_t i = 0; T x : vec) {
    os << x;
    if (++i != size(vec)) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const set<T> &s) {
  for(size_t i = 0; T x : s) {
    os << x;
    if (++i != size(s)) os << ' ';
  }
  return os;
}
template<class T>
ostream& operator<<(ostream& os, const multiset<T> &s) {
  for(size_t i = 0; T x : s) {
    os << x;
    if (++i != size(s)) os << ' ';
  }
  return os;
}
template<class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2> &m) {
  for(size_t i = 0; pair<T1, T2> x : m) {
    os << x.first << " : " << x.second;
    if (++i != size(m)) os << ", ";
  }
  return os;
}

#ifdef DEBUG
#define dbg(...) cerr << '(', _do(#__VA_ARGS__), cerr << ") = ", _do2(__VA_ARGS__)
template<typename T> void _do(T &&x) { cerr << x; }
template<typename T, typename ...S> void _do(T &&x, S&&...y) { cerr << x << ", "; _do(y...); }
template<typename T> void _do2(T &&x) { cerr << x << endl; }
template<typename T, typename ...S> void _do2(T &&x, S&&...y) { cerr << x << ", "; _do2(y...); }
#else
#define dbg(...)
#endif

using ll = long long;
using ull = unsigned long long;
using ldb = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;

template<typename T> using vc = vector<T>;
template<typename T> using vvc = vc<vc<T>>;
template<typename T> using vvvc = vc<vvc<T>>;

using vi = vc<int>;
using vll = vc<ll>;
using vvi = vvc<int>;
using vvll = vvc<ll>;

template<typename T> using min_heap = priority_queue<T, vc<T>, greater<T>>;
template<typename T> using max_heap = priority_queue<T>;

template<typename R, typename F, typename... Args>
concept R_invocable = requires(F&& f, Args&&... args) {
  { std::invoke(std::forward<F>(f), std::forward<Args>(args)...) } -> std::same_as<R>;
};
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>, typename F>
requires R_invocable<T, F, T, T>
void pSum(rng &&v, F f) {
  if (!v.empty())
    for(T p = *v.begin(); T &x : v | views::drop(1))
      x = p = f(p, x);
}
template<ranges::forward_range rng, class T = ranges::range_value_t<rng>>
void pSum(rng &&v) {
  if (!v.empty())
    for(T p = *v.begin(); T &x : v | views::drop(1))
      x = p = p + x;
}

template<ranges::forward_range rng>
void Unique(rng &v) {
  ranges::sort(v);
  v.resize(unique(v.begin(), v.end()) - v.begin());
}

template<ranges::random_access_range rng>
rng invPerm(rng p) {
  rng ret = p;
  for(int i = 0; i < ssize(p); i++)
    ret[p[i]] = i;
  return ret;
}

template<ranges::random_access_range rng>
vi argSort(rng p) {
  vi id(size(p));
  iota(id.begin(), id.end(), 0);
  ranges::sort(id, {}, [&](int i) { return pair(p[i], i); });
  return id;
}

template<ranges::random_access_range rng, class T = ranges::range_value_t<rng>, typename F>
requires invocable<F, T&>
vi argSort(rng p, F proj) {
  vi id(size(p));
  iota(id.begin(), id.end(), 0);
  ranges::sort(id, {}, [&](int i) { return pair(proj(p[i]), i); });
  return id;
}

template<bool directed>
vvi read_graph(int n, int m, int base) {
  vvi g(n);
  for(int i = 0; i < m; i++) {
    int u, v; cin >> u >> v;
    u -= base, v -= base;
    g[u].emplace_back(v);
    if constexpr (!directed)
      g[v].emplace_back(u);
  }
  return g;
}

template<bool directed>
vvi adjacency_list(int n, vc<pii> e, int base) {
  vvi g(n);
  for(auto [u, v] : e) {
    u -= base, v -= base;
    g[u].emplace_back(v);
    if constexpr (!directed)
      g[v].emplace_back(u);
  }
  return g;
}

template<class T>
void setBit(T &msk, int bit, bool x) { (msk &= ~(T(1) << bit)) |= T(x) << bit; }
template<class T> void onBit(T &msk, int bit) { setBit(msk, bit, true); }
template<class T> void offBit(T &msk, int bit) { setBit(msk, bit, false); }
template<class T> void flipBit(T &msk, int bit) { msk ^= T(1) << bit; }
template<class T> bool getBit(T msk, int bit) { return msk >> bit & T(1); }

template<class T>
T floorDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? a / b : (a - b + 1) / b;
}
template<class T>
T ceilDiv(T a, T b) {
  if (b < 0) a *= -1, b *= -1;
  return a >= 0 ? (a + b - 1) / b : a / b;
}

template<class T> bool chmin(T &a, T b) { return a > b ? a = b, 1 : 0; }
template<class T> bool chmax(T &a, T b) { return a < b ? a = b, 1 : 0; }

#line 1 "tree/prufer_recover.cpp"
//empty vector would be assumed to be n = 2
vc<pii> prufer_recover(vi prufer_code) {
  const int n = ssize(prufer_code) + 2;
  assert(prufer_code.empty() or (ranges::min(prufer_code) >= 0 and ranges::max(prufer_code) < n));
  vi d(n, 1);
  for(int x : prufer_code) d[x]++;
  min_heap<int> leaf;
  for(int v = 0; v < n; v++)
    if (d[v] == 1)
      leaf.emplace(v);
  vc<pii> edges;
  for(int x : prufer_code) {
    int v = leaf.top(); leaf.pop();
    edges.emplace_back(v, x);
    if (--d[x] == 1)
      leaf.emplace(x);
  }
  int v = leaf.top(); leaf.pop();
  edges.emplace_back(v, leaf.top());
  return edges;
}
#line 1 "enumerate/enumerate_bit.cpp"

template<typename F, typename INT>
requires invocable<F, INT>
void enumerate_subset(INT msk, F f) {
  for(INT x = msk; x > 0; x = (x - 1) & msk)
    f(x);
  f(0);
}
#line 1 "enumerate/enumerate_twelvefold.cpp"
//#include "enumerate/bit.cpp"

template<typename F>
requires invocable<F, vector<int>>
void enumerate_cartesian_power(int n, int k, F f) {
  assert(min(n, k) >= 0);
  vector<int> p(k);
  auto dfs = [&](int i, auto &self) -> void {
    if (i == k) {
      f(p);
    } else {
      for(int x = 0; x < n; x++) {
        p[i] = x;
        self(i + 1, self);
      }
    }
  };
  dfs(0, dfs);
}

template<typename F>
requires invocable<F, vector<int>>
void enumerate_permutation(int n, F f) {
  assert(n >= 0);
  vector<int> p(n);
  iota(p.begin(), p.end(), 0);
  do { f(p); } while(next_permutation(p.begin(), p.end()));
}

template<typename F>
requires invocable<F, vector<int>>
void enumerate_combination(int n, int k, F f) {
  assert(min(n, k) >= 0);
  vector<int> p;
  auto dfs = [&](auto &self) -> void {
    if (ssize(p) == k) {
      f(p);
    } else {
      for(int x = (p.empty() ? 0 : p.back() + 1); x + k - ssize(p) <= n; x++) {
        p.emplace_back(x);
        self(self);
        p.pop_back();
      }
    }
  };
  dfs(dfs);
}

template<typename F>
requires invocable<F, vector<int>>
void enumerate_set_partition(int n, F f) {
  assert(n >= 0);
  vector<int> p;
  int msk = (1 << n) - 1;
  auto dfs = [&](auto &self) -> void {
    if (msk == 0) {
      f(p);
    } else {
      int x = msk & (-msk);
      msk ^= x;
      enumerate_subset(msk, [&](int sub) {
        p.emplace_back(sub | x);
        msk ^= sub;
        self(self);
        msk ^= sub;
        p.pop_back();
      });
      msk ^= x;
    }
  };
  dfs(dfs);
}

template<typename F>
requires invocable<F, vector<int>>
void enumerate_multisubset(int n, int sum, F f) {
  assert(min(n, sum) >= 0);
  vector<int> p(n);
  auto dfs = [&](int i, auto &self) -> void {
    if (i == n) {
      if (sum == 0) f(p);
    } else {
      for(int x = sum; x >= 0; x--) {
        p[i] = x, sum -= x;
        self(i + 1, self);
        sum += x;
      }
    }
  };
  dfs(0, dfs);
}

template<typename F>
requires invocable<F, vector<int>>
void enumerate_integer_partition(int n, F f) {
  assert(n >= 0);
  vector<int> p;
  auto dfs = [&](int s, auto &self) -> void {
    if (s == 0) {
      f(p);
    } else {
      for(int x = (p.empty() ? s : min(p.back(), s)); x > 0; x--) {
        p.emplace_back(x);
        self(s - x, self);
        p.pop_back();
      }
    }
  };
  dfs(n, dfs);
}
#line 1 "enumerate/enumerate_label_tree.cpp"
//#include "tree/prufer_recover.cpp"
//#include "enumerate/enumerate_bit.cpp"
//#include "enumerate/enumerate_twelvefold.cpp"

template<typename F>
requires invocable<F, vector<vector<int>>>
void enumerate_label_tree(int n, F f) {
  assert(n > 0);
  if (n == 1) {
    f(vector<vector<int>>(1));
  } else {
    enumerate_cartesian_power(n, n - 2, [n, f](vector<int> a) {
      f(adjacency_list<false>(n, prufer_recover(a), 0));
    });
  }
}
#line 1 "enumerate/enumerate_unlabel_rooted_tree.cpp"
//number of unlabel rooted tree (1-based)
//1, 1, 2, 4, 9,
//20, 48, 115, 286, 719,
//1842, 4766, 12486, 32973, 87811,
//235381, 634847, 1721159, 4688676, 12826228,
//35221832, 97055181, 268282855, 743724984, 2067174645

//root is 0
template<typename F>
requires invocable<F, vector<vector<int>>>
void enumerate_unlabel_rooted_tree(int n, F f) {
  const int LIM = 25;
  assert(0 < n and n <= LIM);

  vector hash(1, array<int, LIM>{-1});
  array<int, LIM + 2> st;
  fill(st.begin(), st.end(), INT_MAX);
  st[0] = -1, st[1] = 0;

  auto size = [&](int id) {
    int r = 1;
    while(st[r] <= id) r++;
    return r - 1;
  };

  for(int m = 2; m <= n; m++) {
    st[m] = ssize(hash);
    array<int, LIM> h;
    int nxt = 0;
    auto dfs = [&](int pre_id, int sum, auto &self) -> void {
      if (sum == 0) {
        h[nxt++] = -1;
        hash.emplace_back(h);
        nxt--;
      } else {
        for(int x = min(pre_id, st[sum + 1] - 1); x >= 0; x--) {
          h[nxt++] = x;
          self(x, sum - size(x), self);
          nxt--;
        }
      }
    };
    dfs(INT_MAX, m - 1, dfs);
  }
  st[n + 1] = ssize(hash);

  for(int id = st[n]; id < st[n + 1]; id++) {
    vector<vector<int>> g(n);
    int nxt = 0;
    auto dfs = [&](int v, int id, auto &self) -> void {
      if (id == 0) return;
      for(int i = 0; hash[id][i] != -1; i++) {
        g[v].emplace_back(nxt), g[nxt].emplace_back(v);
        self(nxt++, hash[id][i], self);
      }
    };
    dfs(nxt++, id, dfs);
    f(g);
  }
}
#line 1 "tree/tree.cpp"
class tree {
  using i32 = int32_t;

  vc<i32> ord;

  public:

  int n, root;
  vc<int> p, sz, dep, jp;

  void calc(vc<i32> d, vc<i32> adj) {
    sz = vi(n, 1);
    p = dep = jp = vi(n);

    ord.reserve(n - 1);
    for(int i = 0; i < n; i++) {
      int v = i;
      while(d[v] == 1) {
        ord.emplace_back(v);
        p[v] = adj[v], sz[p[v]] += sz[v];
        d[v] = 0, d[p[v]]--, adj[p[v]] ^= v;
        v = p[v];
      }
    }

    assert(ssize(ord) == n - 1);

    p[root] = jp[root] = root;
    for(i32 v : ord | views::reverse) {
      dep[v] = dep[p[v]] + 1;
      if (dep[p[v]] + dep[jp[jp[p[v]]]] == 2 * dep[jp[p[v]]])
        jp[v] = jp[jp[p[v]]];
      else
        jp[v] = p[v];
    }
  }

  tree(vc<pii> e, int _root = 0) : n(size(e) + 1), root(_root) {
    vc<i32> d(n), adj(n);
    for(auto [u, v] : e)
      d[u]++, d[v]++, adj[u] ^= v, adj[v] ^= u;
    d[root] = 0;
    calc(d, adj);
  }

  tree(vi pa) : n(size(pa)) {
    root = ranges::find(pa, -1) - pa.begin();
    vc<i32> d(n), adj(n);
    for(int v = 0; v < n; v++)
      if (pa[v] != -1)
        d[v]++, d[pa[v]]++, adj[v] ^= pa[v], adj[pa[v]] ^= v;
    d[root] = 0;
    calc(d, adj);
  }

  int jump(int v, int k) {
    k = min(k, dep[v]);
    while(k) {
      if (int d = dep[v] - dep[jp[v]]; d <= k)
        v = jp[v], k -= d;
      else
        v = p[v], k -= 1;
    }
    return v;
  }

  int lca(int u, int v) {
    if (dep[u] < dep[v])
      swap(u, v);
    u = jump(u, dep[u] - dep[v]);
    if (u == v) return u;
    while(p[u] != p[v]) {
      if (jp[u] != jp[v]) u = jp[u], v = jp[v];
      else u = p[u], v = p[v];
    }
    return p[u];
  }

  int kth(int s, int t, int k) {
    int m = lca(s, t);
    if (dep[s] + dep[t] - 2 * dep[m] < k)
      return -1;
    else if (dep[s] - dep[m] >= k)
      return jump(s, k);
    else
      return jump(t, dep[s] + dep[t] - 2 * dep[m] - k);
  }

  int dis(int u, int v) {
    return dep[u] + dep[v] - 2 * dep[lca(u, v)];
  }

  int median(int u, int v, int w) {
    return lca(u, v) ^ lca(u, w) ^ lca(v, w);
  }

  auto centroid() {
    array<int, 2> r = {-1, -1};
    vector<bool> ok(n, true);
    for(int v = 0; v < n; v++) {
      if (2 * (n - sz[v]) > n)
        ok[v] = false;
      if (v != root and 2 * sz[v] > n)
        ok[p[v]] = false;
    }
    for(int v = 0; v < n; v++)
      if (ok[v])
        r[1] = v, swap(r[0], r[1]);
    return r;
  }
};
#line 1 "tree/tree_diameter.cpp"
//#include "graph/tree.cpp"

auto tree_diameter(vc<pii> e) {
  auto d0 = tree(e).dep;
  int u = max_element(d0.begin(), d0.end()) - d0.begin();
  tree t(e, u);
  int v = max_element(t.dep.begin(), t.dep.end()) - t.dep.begin();
  vi path = {v};
  for(int i = t.dep[v]; i > 0; i--)
    path.emplace_back(t.p[path.back()]);
  return pair((int)(ssize(path) - 1), path);
}
#line 11 "test/mytest_tree_diameter.test.cpp"

void check(vector<vector<int>> g) {
  const int n = ssize(g);
  vi dep;
  auto dfs = [&](int v, int p, auto &self) -> void {
    for(int x : g[v]) {
      if (x == p) continue;
      dep[x] = dep[v] + 1;
      self(x, v, self);
    }
  };

  int diameter = -1;
  for(int r = 0; r < n; r++) {
    vi(n, INT_MAX).swap(dep);
    dep[r] = 0;
    dfs(r, -1, dfs);
    chmax(diameter, ranges::max(dep));
  }

  vc<pii> e;
  for(int u = 0; u < n; u++)
    for(int v : g[u])
      if (u < v)
        e.emplace_back(u, v);

  set<pii> s;
  for(auto [u, v] : e)
    s.emplace(u, v), s.emplace(v, u);

  auto [diameter_2, path] = tree_diameter(e);

  assert(diameter == diameter_2);
  assert(ssize(path) == diameter + 1);
  for(int i = 1; i < ssize(path); i++)
    assert(s.contains(pair(path[i - 1], path[i])));
  Unique(path);
  assert(ssize(path) == diameter + 1);
}

auto random_relabel(vector<vector<int>> g) {
  mt19937 rng(clock);
  const int n = ssize(g);
  vector<int> p(n);
  iota(p.begin(), p.end(), 0);
  shuffle(p.begin(), p.end(), rng);
  vector<vector<int>> g2(n);
  for(int u = 0; u < n; u++)
    for(int v : g[u])
      g2[p[u]].eb(p[v]);
  return g2;
}

void a_plus_b() {
  int a, b; cin >> a >> b;
  cout << a + b << '\n';
}

int main() {
  ios::sync_with_stdio(false), cin.tie(NULL);

  mt19937 rng(clock);

  for(int n = 1; n <= 7; n++) {
    enumerate_label_tree(n, [&](vector<vector<int>> g) {
      check(g);
    });
  }

  for(int n = 1; n <= 15; n++) {
    enumerate_unlabel_rooted_tree(n, [&](vector<vector<int>> g) {
      check(g);
      check(random_relabel(g));
    });
  }

  //path
  for(int n = 1; n <= 100; n++) {
    vector<vector<int>> g(n);
    for(int i = 1; i < n; i++)
      g[i].emplace_back(i - 1), g[i - 1].emplace_back(i);
    check(g);
    check(random_relabel(g));
  }

  //star
  for(int n = 2; n <= 100; n++) {
    for(int root : {0, n / 2, n - 1}) {
      vector<vector<int>> g(n);
      for(int i = 0; i < n; i++)
        if (i != root)
          g[root].emplace_back(i), g[i].emplace_back(root);
      check(g);
    }
  }

  //almost path
  for(int tc = 0; tc < 30; tc++) {
    int n = 500;
    vector<vector<int>> g(n);
    for(int v = 1; v < n; v++) {
      int x = rng() % min(v, 5);
      g[v].emplace_back(x), g[x].emplace_back(v);
    }
    check(g);
    check(random_relabel(g));
  }

  a_plus_b();

  return 0;
}
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