結果
問題 | No.2531 Coloring Vertices on Namori |
ユーザー |
![]() |
提出日時 | 2023-11-03 21:50:42 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 263 ms / 2,000 ms |
コード長 | 18,881 bytes |
コンパイル時間 | 2,537 ms |
コンパイル使用メモリ | 203,572 KB |
実行使用メモリ | 53,512 KB |
最終ジャッジ日時 | 2024-09-25 20:00:21 |
合計ジャッジ時間 | 9,352 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 31 |
ソースコード
#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <chrono>#include <cmath>#include <complex>#include <deque>#include <forward_list>#include <fstream>#include <functional>#include <iomanip>#include <ios>#include <iostream>#include <limits>#include <list>#include <map>#include <memory>#include <numeric>#include <optional>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <string>#include <tuple>#include <type_traits>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>using namespace std;using lint = long long;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v<< ','; os << ']'; return os; }template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);},tpl); return is; }template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) {((os << args << ','), ...);}, tpl); return os << ')'; }template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os<< v << ','; os << '}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}';return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os <<'}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v <<','; os << '}'; return os; }template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for(auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }#ifdef HITONANODE_LOCALconst string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET<< std::endl#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " <<__FILE__ << COLOR_RESET << std::endl : std::cerr)#else#define dbg(x) ((void)0)#define dbgif(cond, x) ((void)0)#endiftemplate <int md> struct ModInt {using lint = long long;constexpr static int mod() { return md; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&]() {std::set<int> fac;int v = md - 1;for (lint i = 2; i * i <= v; i++)while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < md; g++) {bool ok = true;for (auto i : fac)if (ModInt(g).pow((md - 1) / i) == 1) {ok = false;break;}if (ok) return g;}return -1;}();}return primitive_root;}int val_;int val() const noexcept { return val_; }constexpr ModInt() : val_(0) {}constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }constexpr ModInt(lint v) { _setval(v % md + md); }constexpr explicit operator bool() const { return val_ != 0; }constexpr ModInt operator+(const ModInt &x) const {return ModInt()._setval((lint)val_ + x.val_);}constexpr ModInt operator-(const ModInt &x) const {return ModInt()._setval((lint)val_ - x.val_ + md);}constexpr ModInt operator*(const ModInt &x) const {return ModInt()._setval((lint)val_ * x.val_ % md);}constexpr ModInt operator/(const ModInt &x) const {return ModInt()._setval((lint)val_ * x.inv().val() % md);}constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }friend constexpr ModInt operator+(lint a, const ModInt &x) {return ModInt()._setval(a % md + x.val_);}friend constexpr ModInt operator-(lint a, const ModInt &x) {return ModInt()._setval(a % md - x.val_ + md);}friend constexpr ModInt operator*(lint a, const ModInt &x) {return ModInt()._setval(a % md * x.val_ % md);}friend constexpr ModInt operator/(lint a, const ModInt &x) {return ModInt()._setval(a % md * x.inv().val() % md);}constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }constexpr bool operator<(const ModInt &x) const {return val_ < x.val_;} // To use std::map<ModInt, T>friend std::istream &operator>>(std::istream &is, ModInt &x) {lint t;return is >> t, x = ModInt(t), is;}constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {return os << x.val_;}constexpr ModInt pow(lint n) const {ModInt ans = 1, tmp = *this;while (n) {if (n & 1) ans *= tmp;tmp *= tmp, n >>= 1;}return ans;}static constexpr int cache_limit = std::min(md, 1 << 21);static std::vector<ModInt> facs, facinvs, invs;constexpr static void _precalculation(int N) {const int l0 = facs.size();if (N > md) N = md;if (N <= l0) return;facs.resize(N), facinvs.resize(N), invs.resize(N);for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;facinvs[N - 1] = facs.back().pow(md - 2);for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];}constexpr ModInt inv() const {if (this->val_ < cache_limit) {if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return invs[this->val_];} else {return this->pow(md - 2);}}constexpr ModInt fac() const {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return facs[this->val_];}constexpr ModInt facinv() const {while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);return facinvs[this->val_];}constexpr ModInt doublefac() const {lint k = (this->val_ + 1) / 2;return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()): ModInt(k).fac() * ModInt(2).pow(k);}constexpr ModInt nCr(int r) const {if (r < 0 or this->val_ < r) return ModInt(0);return this->fac() * (*this - r).facinv() * ModInt(r).facinv();}constexpr ModInt nPr(int r) const {if (r < 0 or this->val_ < r) return ModInt(0);return this->fac() * (*this - r).facinv();}static ModInt binom(int n, int r) {static long long bruteforce_times = 0;if (r < 0 or n < r) return ModInt(0);if (n <= bruteforce_times or n < (int)facs.size()) return ModInt(n).nCr(r);r = std::min(r, n - r);ModInt ret = ModInt(r).facinv();for (int i = 0; i < r; ++i) ret *= n - i;bruteforce_times += r;return ret;}// Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)// Complexity: O(sum(ks))template <class Vec> static ModInt multinomial(const Vec &ks) {ModInt ret{1};int sum = 0;for (int k : ks) {assert(k >= 0);ret *= ModInt(k).facinv(), sum += k;}return ret * ModInt(sum).fac();}// Catalan number, C_n = binom(2n, n) / (n + 1)// C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...// https://oeis.org/A000108// Complexity: O(n)static ModInt catalan(int n) {if (n < 0) return ModInt(0);return ModInt(n * 2).fac() * ModInt(n + 1).facinv() * ModInt(n).facinv();}ModInt sqrt() const {if (val_ == 0) return 0;if (md == 2) return val_;if (pow((md - 1) / 2) != 1) return 0;ModInt b = 1;while (b.pow((md - 1) / 2) == 1) b += 1;int e = 0, m = md - 1;while (m % 2 == 0) m >>= 1, e++;ModInt x = pow((m - 1) / 2), y = (*this) * x * x;x *= (*this);ModInt z = b.pow(m);while (y != 1) {int j = 0;ModInt t = y;while (t != 1) j++, t *= t;z = z.pow(1LL << (e - j - 1));x *= z, z *= z, y *= z;e = j;}return ModInt(std::min(x.val_, md - x.val_));}};template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};using mint = ModInt<998244353>;// UnionFind Tree (0-indexed), based on size of each disjoint setstruct UnionFind {std::vector<int> par, cou;UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); }int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); }bool unite(int x, int y) {x = find(x), y = find(y);if (x == y) return false;if (cou[x] < cou[y]) std::swap(x, y);par[y] = x, cou[x] += cou[y];return true;}int count(int x) { return cou[find(x)]; }bool same(int x, int y) { return find(x) == find(y); }std::vector<std::vector<int>> groups() {std::vector<std::vector<int>> ret(par.size());for (int i = 0; i < int(par.size()); ++i) ret[find(i)].push_back(i);ret.erase(std::remove_if(ret.begin(), ret.end(),[&](const std::vector<int> &v) { return v.empty(); }),ret.end());return ret;}};// lowest common ancestor (LCA) for undirected weighted treetemplate <typename T> struct UndirectedWeightedTree {int INVALID = -1;int V, lgV;int E;int root;std::vector<std::vector<std::pair<int, int>>> adj; // (nxt_vertex, edge_id)// vector<pint> edge; // edges[edge_id] = (vertex_id, vertex_id)std::vector<T> weight; // w[edge_id]std::vector<int> par; // parent_vertex_id[vertex_id]std::vector<int> depth; // depth_from_root[vertex_id]std::vector<T> acc_weight; // w_sum_from_root[vertex_id]void _fix_root_dfs(int now, int prv, int prv_edge_id) {par[now] = prv;if (prv_edge_id != INVALID) acc_weight[now] = acc_weight[prv] + weight[prv_edge_id];for (auto nxt : adj[now])if (nxt.first != prv) {depth[nxt.first] = depth[now] + 1;_fix_root_dfs(nxt.first, now, nxt.second);}}UndirectedWeightedTree() = default;UndirectedWeightedTree(int N) : V(N), E(0), adj(N) {lgV = 1;while (1 << lgV < V) lgV++;}void add_edge(int u, int v, T w) {adj[u].emplace_back(v, E);adj[v].emplace_back(u, E);// edge.emplace_back(u, v);weight.emplace_back(w);E++;}std::vector<std::vector<int>> doubling;void _doubling_precalc() {doubling.assign(lgV, std::vector<int>(V));doubling[0] = par;for (int d = 0; d < lgV - 1; d++)for (int i = 0; i < V; i++) {if (doubling[d][i] == INVALID)doubling[d + 1][i] = INVALID;elsedoubling[d + 1][i] = doubling[d][doubling[d][i]];}}void fix_root(int r) {root = r;par.resize(V);depth.resize(V);depth[r] = 0;acc_weight.resize(V);acc_weight[r] = 0;_fix_root_dfs(root, INVALID, INVALID);_doubling_precalc();}int kth_parent(int x, int k) const {if (depth[x] < k) return INVALID;for (int d = 0; d < lgV; d++) {if (x == INVALID) return INVALID;if (k & (1 << d)) x = doubling[d][x];}return x;}int lowest_common_ancestor(int u, int v) const {if (depth[u] > depth[v]) std::swap(u, v);v = kth_parent(v, depth[v] - depth[u]);if (u == v) return u;for (int d = lgV - 1; d >= 0; d--) {if (doubling[d][u] != doubling[d][v]) u = doubling[d][u], v = doubling[d][v];}return par[u];}T path_length(int u, int v) const {// Not distance, but the sum of weightsint r = lowest_common_ancestor(u, v);return (acc_weight[u] - acc_weight[r]) + (acc_weight[v] - acc_weight[r]);}int s_to_t_by_k_steps(int s, int t, int k) const {int l = lowest_common_ancestor(s, t);int dsl = depth[s] - depth[l], dtl = depth[t] - depth[l];if (k > dsl + dtl) {return INVALID;} else if (k < dsl) {return kth_parent(s, k);} else if (k == dsl) {return l;} else {return kth_parent(t, dsl + dtl - k);}}};int main() {int N, K;cin >> N >> K;vector<vector<int>> to(N);UnionFind uf(N);UndirectedWeightedTree<int> tree(N);int p = -1, q = -1;REP(i, N) {int a, b;cin >> a >> b;--a, --b;if (uf.unite(a, b)) {to[a].push_back(b);to[b].push_back(a);tree.add_edge(a, b, 1);} else {p = a, q = b;}}tree.fix_root(0);dbg(to);dbg(make_tuple(p, q));int d = tree.path_length(p, q);dbg(d);const int v = d + 1;vector<mint> dp0(v), dp1(v);dp0.at(0) = 1;FOR(i, 1, v) {dp0.at(i) += dp1.at(i - 1);dp1.at(i) += dp0.at(i - 1) * (K - 1);dp1.at(i) += dp1.at(i - 1) * (K - 2);}dbg(dp0);dbg(dp1);cout << dp1.back() * mint(K - 1).pow(N - v) * K << endl;}