#676614 (C++17) No.1600 Many Shortest Path Problems

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結果

問題	No.1600 Many Shortest Path Problems
コンテスト
ユーザー	yuto1115
提出日時	2021-07-09 23:55:46
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	1,993 ms / 4,000 ms
コード長	12,807 bytes
コンパイル時間	4,524 ms
コンパイル使用メモリ	232,724 KB
最終ジャッジ日時	2025-01-22 23:00:08
ジャッジサーバーID （参考情報）	judge3 / judge2
このコードへのチャレンジ
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ファイルパターン	結果
sample	AC * 3
other	AC * 51
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

raw source code
#include<bits/stdc++.h>
#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(i, n) for (ll i = 0; i < ll(n); ++i)
#define rep2(i, s, n) for (ll i = ll(s); i < ll(n); ++i)
#define rep3(i, s, n, d) for(ll i = ll(s); i < ll(n); i+=d)
#define rep(...) overload4(__VA_ARGS__,rep3,rep2,rep1)(__VA_ARGS__)
#define rrep1(i, n) for (ll i = ll(n)-1; i >= 0; i--)
#define rrep2(i, n, t) for (ll i = ll(n)-1; i >= (ll)t; i--)
#define rrep3(i, n, t, d) for (ll i = ll(n)-1; i >= (ll)t; i-=d)
#define rrep(...) overload4(__VA_ARGS__,rrep3,rrep2,rrep1)(__VA_ARGS__)
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define SUM(a) accumulate(all(a),0LL)
#define MIN(a) *min_element(all(a))
#define MAX(a) *max_element(all(a))
#define popcount(x) __builtin_popcountll(x)
#define pb push_back
#define eb emplace_back
#ifdef __LOCAL
#define debug(...) { cout << #__VA_ARGS__; cout << ": "; print(__VA_ARGS__); cout << flush; }
#else
#define debug(...) void(0)
#endif
#define INT(...) int __VA_ARGS__;scan(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;scan(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;scan(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;scan(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;scan(__VA_ARGS__)
using namespace std;
using ll = long long;
using ld = long double;
using P = pair<int, int>;
using LP = pair<ll, ll>;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vd = vector<double>;
using vvd = vector<vd>;
using vs = vector<string>;
using vc = vector<char>;
using vvc = vector<vc>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vp = vector<P>;
using vvp = vector<vp>;

template<class S, class T>
istream &operator>>(istream &is, pair<S, T> &p) { return is >> p.first >> p.second; }

template<class S, class T>
ostream &operator<<(ostream &os, const pair<S, T> &p) { return os << '{' << p.first << ", " << p.second << '}'; }

template<class S, class T, class U>
istream &operator>>(istream &is, tuple<S, T, U> &t) { return is >> get<0>(t) >> get<1>(t) >> get<2>(t); }

template<class S, class T, class U>
ostream &operator<<(ostream &os, const tuple<S, T, U> &t) {
    return os << '{' << get<0>(t) << ", " << get<1>(t) << ", " << get<2>(t) << '}';
}

template<class T>
istream &operator>>(istream &is, vector<T> &v) {
    for (T &t:v) { is >> t; }
    return is;
}

template<class T>
ostream &operator<<(ostream &os, const vector<T> &v) {
    os << '[';
    rep(i, v.size())os << v[i] << (i == int(v.size() - 1) ? "" : ", ");
    return os << ']';
}

template<class T>
void vecout(const vector<T> &v, char div = '\n') {
    rep(i, v.size()) cout << v[i] << (i == int(v.size() - 1) ? '\n' : div);
}

template<class T>
bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

void scan() {}

template<class Head, class... Tail>
void scan(Head &head, Tail &... tail) {
    cin >> head;
    scan(tail...);
}

template<class T>
void print(const T &t) { cout << t << '\n'; }

template<class Head, class... Tail>
void print(const Head &head, const Tail &... tail) {
    cout << head << ' ';
    print(tail...);
}

template<class... T>
void fin(const T &... a) {
    print(a...);
    exit(0);
}

struct Init_io {
    Init_io() {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout.tie(nullptr);
        cout << boolalpha << fixed << setprecision(15);
        cerr << boolalpha << fixed << setprecision(15);
    }
} init_io;

const string yes[] = {"no", "yes"};
const string Yes[] = {"No", "Yes"};
const string YES[] = {"NO", "YES"};
const int inf = 1001001001;
const ll linf = 1001001001001001001;

template<class T, class S>
vector<T> cumsum(const vector<S> &v, bool shift_one = true) {
    int n = v.size();
    vector<T> res;
    if (shift_one) {
        res.resize(n + 1);
        rep(i, n) res[i + 1] = res[i] + v[i];
    } else {
        res.resize(n);
        if (n) {
            res[0] = v[0];
            rep(i, 1, n) res[i] = res[i - 1] + v[i];
        }
    }
    return res;
}

vvi graph(int n, int m, bool directed = false, int origin = 1) {
    vvi G(n);
    rep(_, m) {
        INT(u, v);
        u -= origin, v -= origin;
        G[u].pb(v);
        if (!directed) G[v].pb(u);
    }
    return G;
}

template<class T>
vector<vector<pair<int, T>>> weighted_graph(int n, int m, bool directed = false, int origin = 1) {
    vector<vector<pair<int, T>>> G(n);
    rep(_, m) {
        int u, v;
        T w;
        scan(u, v, w);
        u -= origin, v -= origin;
        G[u].eb(v, w);
        if (!directed) G[v].eb(u, w);
    }
    return G;
}

template<int mod>
class modint {
    ll x;
public:
    constexpr modint(ll x = 0) : x((x % mod + mod) % mod) {}
    
    static constexpr int get_mod() { return mod; }
    
    constexpr int val() const { return x; }
    
    constexpr modint operator-() const { return modint(-x); }
    
    constexpr modint &operator+=(const modint &a) {
        if ((x += a.val()) >= mod) x -= mod;
        return *this;
    }
    
    constexpr modint &operator++() { return *this += 1; }
    
    constexpr modint &operator-=(const modint &a) {
        if ((x += mod - a.val()) >= mod) x -= mod;
        return *this;
    }
    
    constexpr modint &operator--() { return *this -= 1; }
    
    constexpr modint &operator*=(const modint &a) {
        (x *= a.val()) %= mod;
        return *this;
    }
    
    constexpr modint operator+(const modint &a) const {
        modint res(*this);
        return res += a;
    }
    
    constexpr modint operator-(const modint &a) const {
        modint res(*this);
        return res -= a;
    }
    
    constexpr modint operator*(const modint &a) const {
        modint res(*this);
        return res *= a;
    }
    
    constexpr modint pow(ll t) const {
        modint res = 1, a(*this);
        while (t > 0) {
            if (t & 1) res *= a;
            t >>= 1;
            a *= a;
        }
        return res;
    }
    
    template<int m>
    friend istream &operator>>(istream &, modint<m> &);
    
    // for prime mod
    constexpr modint inv() const { return pow(mod - 2); }
    
    constexpr modint &operator/=(const modint &a) { return *this *= a.inv(); }
    
    constexpr modint operator/(const modint &a) const {
        modint res(*this);
        return res /= a;
    }
};

using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;

template<int mod>
istream &operator>>(istream &is, modint<mod> &a) { return is >> a.x; }

template<int mod>
constexpr ostream &operator<<(ostream &os, const modint<mod> &a) { return os << a.val(); }

template<int mod>
constexpr bool operator==(const modint<mod> &a, const modint<mod> &b) { return a.val() == b.val(); }

template<int mod>
constexpr bool operator!=(const modint<mod> &a, const modint<mod> &b) { return a.val() != b.val(); }

template<int mod>
constexpr modint<mod> &operator++(modint<mod> &a) { return a += 1; }

template<int mod>
constexpr modint<mod> &operator--(modint<mod> &a) { return a -= 1; }

using mint = modint1000000007;

using vm = vector<mint>;
using vvm = vector<vm>;

class unionfind {
    int n;
    vector<int> par, rank;
public:
    unionfind(int n) : n(n), par(n, -1), rank(n, 0) {}
    
    int root(int x) {
        if (par[x] < 0) return x;
        else return par[x] = root(par[x]);
    }
    
    bool is_root(int x) { return root(x) == x; }
    
    bool same(int x, int y) { return root(x) == root(y); };
    
    bool merge(int x, int y) {
        x = root(x);
        y = root(y);
        if (x == y) return false;
        if (rank[x] < rank[y]) swap(x, y);
        if (rank[x] == rank[y]) rank[x]++;
        par[x] += par[y];
        par[y] = x;
        return true;
    }
    
    int size(int x) { return -par[root(x)]; };
    
    vi roots() {
        vi res;
        rep(i, n) if (root(i) == i) res.pb(i);
        return res;
    }
    
    bool connected() {
        return roots().size() == 1;
    }
};

class LCA {
    int n;
    vvi G;
    int root;
    vi depth;
    vvi par;
    
    void dfs(int v, int p, int d) {
        par[0][v] = p;
        depth[v] = d;
        for (int u : G[v]) if (u != p) dfs(u, v, d + 1);
    }
    
    void init() {
        n = G.size();
        depth.resize(n);
        par.resize(30);
        rep(i, 30) par[i].resize(n);
        dfs(root, -1, 0);
        rep(k, 29) rep(v, n) {
                if (par[k][v] < 0) par[k + 1][v] = -1;
                else par[k + 1][v] = par[k][par[k][v]];
            }
    }

public:
    LCA(vvi G, int root = 0) : G(G), root(root) { init(); }
    
    int operator()(int u, int v) {
        if (depth[u] > depth[v]) swap(u, v);
        rep(k, 30) if ((depth[v] - depth[u]) >> k & 1) v = par[k][v];
        if (u == v) return u;
        rrep(k, 30) {
            if (par[k][u] != par[k][v]) {
                u = par[k][u];
                v = par[k][v];
            }
        }
        return par[0][u];
    }
    
    int dist(int u, int v) {
        int w = this->operator()(u, v);
        return depth[u] + depth[v] - depth[w] * 2;
    }
};

int main() {
    INT(n, m);
    vi a(m), b(m);
    unionfind uf(n);
    vvi G(n);
    vector<vector<pair<int, mint>>> lg(n);
    // id, to
    vvp rev(n);
    vb used(m);
    rep(i, m) {
        scan(a[i], b[i]);
        a[i]--, b[i]--;
        if (!uf.same(a[i], b[i])) {
            uf.merge(a[i], b[i]);
            G[a[i]].pb(b[i]);
            G[b[i]].pb(a[i]);
            lg[a[i]].eb(b[i], mint(2).pow(i + 1));
            lg[b[i]].eb(a[i], mint(2).pow(i + 1));
            used[i] = true;
        } else {
            rev[a[i]].eb(i, b[i]);
            rev[b[i]].eb(i, a[i]);
        }
    }
    LCA lca(G);
    vm dep(n);
    vi in(n), out(n);
    vi cnt(n);
    int id = 0;
    auto f = [&](auto &f, int u, int p, mint d) -> int {
        dep[u] = d;
        in[u] = id++;
        cnt[u] = rev[u].size();
        for (auto[v, len] : lg[u]) {
            if (v == p) continue;
            cnt[u] += f(f, v, u, d + len);
        }
        out[u] = id;
        return cnt[u];
    };
    f(f, 0, -1, 0);
    using PQ = priority_queue<P, vp, greater<P>>;
    vi mn(n, inf);
    auto dfs = [&](auto &dfs, int u, int p, PQ &pq) -> void {
        int mx = -1, pos = -1;
        for (int v : G[u]) {
            if (v == p) continue;
            if (chmax(mx, cnt[v])) pos = v;
        }
        if (pos != -1) {
            dfs(dfs, pos, u, pq);
        }
        for (auto[id, to] : rev[u]) pq.emplace(id, to);
        for (int v : G[u]) {
            if (v == p or v == pos) continue;
            PQ tmp;
            dfs(dfs, v, u, tmp);
            while (tmp.size()) {
                auto np = tmp.top();
                pq.push(np);
                tmp.pop();
            }
        }
        while (pq.size()) {
            auto[_, to] = pq.top();
            if (in[u] <= in[to] and in[to] < out[u]) pq.pop();
            else break;
        }
        if (pq.size()) mn[u] = pq.top().first;
    };
    PQ pq;
    dfs(dfs, 0, -1, pq);
    INT(q);
    auto dist = [&](int x, int y) {
        int l = lca(x, y);
        return dep[x] + dep[y] - dep[l] * 2;
    };
    rep(_, q) {
        INT(x, y, z);
        x--, y--, z--;
        if (!used[z]) {
            print(dist(x, y));
            continue;
        }
        int l = lca(x, y);
        int d = lca.dist(x, l);
        int d1 = lca.dist(x, a[z]) + lca.dist(b[z], l) + 1;
        int d2 = lca.dist(x, b[z]) + lca.dist(a[z], l) + 1;
        if (d1 == d or d2 == d) {
            if (d2 == d) swap(a[z], b[z]);
            if (mn[a[z]] == inf) print(-1);
            else {
                int s = a[mn[a[z]]];
                int t = b[mn[a[z]]];
                if (in[s] < in[a[z]] or out[a[z]] <= in[s]) swap(s, t);
                assert(in[a[z]] <= in[s] and in[s] < out[a[z]]);
                print(dist(x, s) + dist(t, y) + mint(2).pow(mn[a[z]] + 1));
            }
            continue;
        }
        d = lca.dist(y, l);
        d1 = lca.dist(y, a[z]) + lca.dist(b[z], l) + 1;
        d2 = lca.dist(y, b[z]) + lca.dist(a[z], l) + 1;
        if (d1 == d or d2 == d) {
            if (d2 == d) swap(a[z], b[z]);
            if (mn[a[z]] == inf) print(-1);
            else {
                int s = a[mn[a[z]]];
                int t = b[mn[a[z]]];
                if (in[s] < in[a[z]] or out[a[z]] <= in[s]) swap(s, t);
                assert(in[a[z]] <= in[s] and in[s] < out[a[z]]);
                print(dist(y, s) + dist(t, x) + mint(2).pow(mn[a[z]] + 1));
            }
            continue;
        }
        print(dist(x, y));
    }
}
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結果

ソースコード
