結果

問題 No.1833 Subway Planning
ユーザー hitonanodehitonanode
提出日時 2022-02-04 22:45:12
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,300 ms / 4,000 ms
コード長 10,460 bytes
コンパイル時間 2,929 ms
コンパイル使用メモリ 204,684 KB
実行使用メモリ 122,116 KB
最終ジャッジ日時 2024-06-11 12:13:53
合計ジャッジ時間 13,705 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 1 ms
5,376 KB
testcase_02 AC 1 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 317 ms
121,296 KB
testcase_05 AC 715 ms
122,116 KB
testcase_06 AC 216 ms
118,480 KB
testcase_07 AC 348 ms
118,148 KB
testcase_08 AC 375 ms
113,060 KB
testcase_09 AC 976 ms
121,788 KB
testcase_10 AC 270 ms
102,088 KB
testcase_11 AC 733 ms
102,216 KB
testcase_12 AC 1,300 ms
105,720 KB
testcase_13 AC 281 ms
102,216 KB
testcase_14 AC 222 ms
101,296 KB
testcase_15 AC 844 ms
105,192 KB
testcase_16 AC 323 ms
101,424 KB
testcase_17 AC 379 ms
101,568 KB
testcase_18 AC 358 ms
95,592 KB
testcase_19 AC 287 ms
99,252 KB
testcase_20 AC 217 ms
77,560 KB
testcase_21 AC 810 ms
114,476 KB
testcase_22 AC 554 ms
106,668 KB
testcase_23 AC 2 ms
5,376 KB
testcase_24 AC 2 ms
5,376 KB
testcase_25 AC 2 ms
5,376 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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 <numeric>
#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, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
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; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename 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 <typename 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 <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const 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) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr)
#else
#define dbg(x) (x)
#define dbgif(cond, x) 0
#endif


// Range Minimum Query for static sequence by sparse table
// Complexity: (N \log N)$ for precalculation, (1)$ per query
template <typename T> struct StaticRMQ {
    inline T func(const T &l, const T &r) const noexcept { return std::min<T>(l, r); }
    int N, lgN;
    T defaultT;
    std::vector<std::vector<T>> data;
    std::vector<int> lgx_table;
    StaticRMQ() = default;
    StaticRMQ(const std::vector<T> &sequence, T defaultT)
        : N(sequence.size()), defaultT(defaultT) {
        lgx_table.resize(N + 1);
        for (int i = 2; i < N + 1; i++) lgx_table[i] = lgx_table[i >> 1] + 1;
        lgN = lgx_table[N] + 1;
        data.assign(lgN, std::vector<T>(N, defaultT));
        data[0] = sequence;
        for (int d = 1; d < lgN; d++) {
            for (int i = 0; i + (1 << d) <= N; i++) {
                data[d][i] = func(data[d - 1][i], data[d - 1][i + (1 << (d - 1))]);
            }
        }
    }
    T get(int l, int r) const { // [l, r), 0-indexed
        assert(l >= 0 and r <= N);
        if (l >= r) return defaultT;
        int d = lgx_table[r - l];
        return func(data[d][l], data[d][r - (1 << d)]);
    }
};

struct TreeLCA {
    const int N;
    std::vector<std::vector<int>> to;
    bool built;
    TreeLCA(int V = 0) : N(V), to(V), built(false) {}

    void add_edge(int u, int v) {
        assert(0 <= u and u < N);
        assert(0 <= v and v < N);
        assert(u != v);
        to[u].push_back(v);
        to[v].push_back(u);
    }

    using P = std::pair<int, int>;
    std::vector<int> subtree_begin;
    std::vector<P> vis_order;
    std::vector<int> depth;
    void _build_dfs(int now, int prv, int dnow) {
        subtree_begin[now] = vis_order.size();
        vis_order.emplace_back(dnow, now);
        depth[now] = dnow;
        for (auto &&nxt : to[now]) {
            if (nxt != prv) {
                _build_dfs(nxt, now, dnow + 1);
                vis_order.emplace_back(dnow, now);
            }
        }
    }

    StaticRMQ<P> rmq;
    void build(int root = 0) {
        assert(root >= 0 and root < N);
        built = true;
        subtree_begin.resize(N);
        vis_order.reserve(N * 2);
        depth.resize(N);
        _build_dfs(root, -1, 0);
        rmq = {vis_order, P{N, -1}};
    }

    int lca(int u, int v) {
        assert(0 <= u and u < N);
        assert(0 <= v and v < N);
        if (!built) build();

        auto a = subtree_begin[u], b = subtree_begin[v];
        if (a > b) std::swap(a, b);
        return rmq.get(a, b + 1).second;
    };

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

// UnionFind Tree (0-indexed), based on size of each disjoint set
struct 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); }
};

int main() {
    int N;
    cin >> N;
    vector<tuple<int, int, int>> edges;

    TreeLCA graph(N);

    int ng = -1, ok = 0;
    vector<vector<pint>> to(N);
    REP(i, N - 1) {
        int a, b, c;
        cin >> a >> b >> c;
        --a, --b;
        edges.emplace_back(a, b, c);
        chmax(ok, c);
        graph.add_edge(a, b);
        to[a].emplace_back(b, c);
        to[b].emplace_back(a, c);
    }
    const int maxi = ok;

    const int root = 0;
    graph.build(root);
    vector<pint> par(N, pint(-1, -1));

    auto rec = [&](auto &&self, int now, int prv) -> void {
        for (auto [nxt, w] : to[now]) {
            if (nxt == prv) continue;
            par[nxt] = pint(now, w);
            self(self, nxt, now);
        }
    };
    rec(rec, root, -1);
    dbg(par);

    while (ok > ng + 1) {
        const int m = (ok + ng) / 2;
        UnionFind uf(N);
        vector<pint> dvs;
        int lca = -1;
        for (auto [a, b, w] : edges) {
            if (w > m) {
                if (lca < 0) lca = a;
                lca = graph.lca(lca, a);
                lca = graph.lca(lca, b);
                uf.unite(a, b);
                dvs.emplace_back(graph.depth[a], a);
                dvs.emplace_back(graph.depth[b], b);
            }
        }
        dvs = sort_unique(dvs);
        reverse(ALL(dvs));

        vector<int> vis(N);
        vector<int> deg(N);
        if (lca >= 0) deg[lca] -= 1;
        bool failed = false;
        for (auto [d, v] : dvs) {
            if (vis[v]) continue;
            vis[v] = 1;
            while (v != lca) {
                if (par[v].second < maxi - m) {
                    failed = true;
                    break;
                }
                v = par[v].first;
                deg[v]++;
                vis[v] = 1;
            }
        }
        dbgif(m == 8, vis);
        dbgif(m == 8, deg);
        dbgif(m == 8, failed);
        dbgif(m == 8, dvs);
        if (*max_element(ALL(deg)) > 1) failed = true;
        (failed ? ng : ok) = m;
    }
    cout << ok << '\n';
}
0