#677779 (C++17) No.1600 Many Shortest Path Problems

• 問題: No.1600 Many Shortest Path Problems
• ユーザー: hitonanode
• 提出日時: 2021-07-13 00:21:33
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: WA
• 実行時間: -
• コード長: 21,540 bytes
• コンパイル時間: 2,579 ms
• コンパイル使用メモリ: 178,112 KB
• 最終ジャッジ日時: 2025-01-23 00:51:49
• ジャッジサーバーID （参考情報）: judge2 / judge5

ファイルパターン	結果
sample	AC * 3
other	AC * 33 WA * 18

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 <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

template <int md> struct ModInt {
#if __cplusplus >= 201402L
#define MDCONST constexpr
#else
#define MDCONST
#endif
    using lint = long long;
    MDCONST 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;
    MDCONST ModInt() : val(0) {}
    MDCONST ModInt &_setval(lint v) { return val = (v >= md ? v - md : v), *this; }
    MDCONST ModInt(lint v) { _setval(v % md + md); }
    MDCONST explicit operator bool() const { return val != 0; }
    MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
    MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + md); }
    MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % md); }
    MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % md); }
    MDCONST ModInt operator-() const { return ModInt()._setval(md - val); }
    MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val); }
    friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val + md); }
    friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val % md); }
    friend MDCONST ModInt operator/(lint a, const ModInt &x) {
        return ModInt()._setval(a % md * x.inv() % md);
    }
    MDCONST bool operator==(const ModInt &x) const { return val == x.val; }
    MDCONST bool operator!=(const ModInt &x) const { return val != x.val; }
    MDCONST 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;
    }
    MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; }
    MDCONST ModInt pow(lint n) const {
        ModInt ans = 1, tmp = *this;
        while (n) {
            if (n & 1) ans *= tmp;
            tmp *= tmp, n >>= 1;
        }
        return ans;
    }

    static std::vector<ModInt> facs, facinvs, invs;
    MDCONST static void _precalculation(int N) {
        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];
    }
    MDCONST lint inv() const {
        if (this->val < std::min(md >> 1, 1 << 21)) {
            while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
            return invs[this->val].val;
        } else {
            return this->pow(md - 2).val;
        }
    }
    MDCONST ModInt fac() const {
        while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
        return facs[this->val];
    }
    MDCONST ModInt facinv() const {
        while (this->val >= int(facs.size())) _precalculation(facs.size() * 2);
        return facinvs[this->val];
    }
    MDCONST 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);
    }
    MDCONST ModInt nCr(const ModInt &r) const {
        return (this->val < r.val) ? 0 : this->fac() * (*this - r).facinv() * r.facinv();
    }
    MDCONST ModInt nPr(const ModInt &r) const {
        return (this->val < r.val) ? 0 : this->fac() * (*this - r).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<1000000007>;

// 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); }
};


// Incremental Bridge-Connectivity
// two-edge-connected components
// Reference: <https://scrapbox.io/data-structures/Incremental_Bridge-Connectivity>
//            <https://ei1333.github.io/library/graph/connected-components/incremental-bridge-connectivity.cpp>
struct IncrementalBridgeConnectivity {
    int V;
    int nb_bridge;
    UnionFind con, bicon;
    std::vector<int> bbf;

    int _bicon_par(int x) { return bbf[x] == -1 ? -1 : bicon.find(bbf[x]); }
    int _lca(int x, int y) {
        std::unordered_set<int> us;
        while (true) {
            if (x != -1) {
                if (!us.insert(x).second) { return x; }
                x = _bicon_par(x);
            }
            std::swap(x, y);
        }
    }
    void _compress(int now, int lca) {
        while (bicon.find(now) != bicon.find(lca)) {
            int nxt = _bicon_par(now);
            bbf[now] = bbf[lca], bicon.unite(now, lca), now = nxt, nb_bridge--;
        }
    }

    IncrementalBridgeConnectivity(int v = 0) : V(v), nb_bridge(0), con(v), bicon(v), bbf(v, -1) {}

    void add_edge(int u, int v) {
        assert(u >= 0 and u < V);
        assert(v >= 0 and v < V);
        u = bicon.find(u), v = bicon.find(v);
        if (con.find(u) == con.find(v)) {
            int lca = _lca(u, v);
            _compress(u, lca), _compress(v, lca);
        } else {
            if (con.count(u) > con.count(v)) std::swap(u, v);
            for (int now = u, pre = v; now != -1;) {
                int nxt = _bicon_par(now);
                bbf[now] = pre, pre = now, now = nxt;
            }
            con.unite(u, v), nb_bridge++;
        }
    }
    int count_bridge() const { return nb_bridge; }
    bool two_edge_connected(int x, int y) { return bicon.same(x, y); }
    int find(int x) { return bicon.find(x); }
};

// lowest common ancestor (LCA) class for undirected weighted tree
// 無向重み付きグラフの最小共通祖先
// <https://yukicoder.me/submissions/392383>
struct UndirectedWeightedTree {
    using T = long long; // Arbitrary data structure (operator+, operator- must be defined)
    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++;
    }

    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);
    }

    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;
                else
                    doubling[d + 1][i] = doubling[d][doubling[d][i]];
            }
    }

    int kth_parent(int x, int k) {
        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) {
        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) {
        // Not distance, but the sum of weights
        int r = lowest_common_ancestor(u, v);
        return (acc_weight[u] - acc_weight[r]) + (acc_weight[v] - acc_weight[r]);
    }
};


// 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 lca3(int a, int b, int c) {
        return lca(a, b) ^ lca(b, c) ^ lca(c, a);
    }
    int distance(int u, int v) {
        return depth[u] + depth[v] - 2 * depth[lca(u, v)];
    }
};


int main() {
    int N, M;
    cin >> N >> M;
    UndirectedWeightedTree tree(N);
    TreeLCA tree1(N);
    vector<pint> edges, tree_edges;
    vector<mint> pow2{1};
    UnionFind uf(N);
    vector<int> additional_eids;
    REP(e, M) {
        int a, b;
        cin >> a >> b;
        a--, b--;
        edges.emplace_back(a, b);
        auto p = pow2.back() * 2;
        pow2.push_back(p);
        if (uf.unite(a, b)) {
            tree.add_edge(a, b, p.val);
            tree1.add_edge(a, b);
            tree_edges.emplace_back(a, b);
        } else {
            additional_eids.push_back(e);
        }
    }
    tree.fix_root(0);
    tree1.build();
    tree.doubling_precalc();

    int Q;
    cin >> Q;
    vector<int> x(Q), y(Q), z(Q), u(Q), v(Q);
    vector<int> ret(Q, -1);
    vector<int> lo(Q, -1), hi(Q, additional_eids.size() + 1);
    REP(q, Q) {
        cin >> x[q] >> y[q] >> z[q];
        x[q]--, y[q]--, z[q]--;
        bool edge_on_line = false;
        if (!binary_search(additional_eids.begin(), additional_eids.end(), z[q])) {
            tie(u[q], v[q]) = edges[z[q]];
            if (tree1.lca3(x[q], y[q], u[q]) == u[q] and tree1.lca3(x[q], y[q], v[q]) == v[q]) {
                edge_on_line = true;
            }
        }
        if (!edge_on_line) {
            lo[q] = -1, hi[q] = 0;
            ret[q] = mint(tree.path_length(x[q], y[q])).val;
        } else {
            lo[q] = 0;
        }
    }
    dbg("OK");
    IncrementalBridgeConnectivity conn_(N);
    for (auto [a, b] : tree_edges) conn_.add_edge(a, b);

    while (true) {
        vector<pint> t2q;
        REP(q, Q) {
            if (lo[q] + 1 < hi[q]) {
                int n = (lo[q] + hi[q]) / 2;
                t2q.emplace_back(n, q);
            }
        }
        if (t2q.empty()) break;
        sort(t2q.begin(), t2q.end());
        int added = 0;
        auto conn = conn_;
        for (auto [t, q] : t2q) {
            while (added < t) {
                auto [u, v] = edges[additional_eids[added++]];
                conn.add_edge(u, v);
            }
            (conn.two_edge_connected(u[q], v[q]) ? hi[q] : lo[q]) = t;
        }
    }
    REP(q, Q) if (ret[q] < 0) {
        if (lo[q] < int(additional_eids.size())) {
            int e = additional_eids[lo[q]];
            auto [u, v] = edges[e];
            if (tree1.distance(x[q], u) > tree1.distance(x[q], v)) swap(u, v);
            ret[q] = mint(tree.path_length(x[q], u) + tree.path_length(y[q], v) + pow2[e + 1]).val;
        }
    }

    for (auto x : ret) cout << x << '\n';
}