#851348 (C++17) No.1333 Squared Sum

提出ソース
結果

問題	No.1333 Squared Sum
コンテスト
ユーザー	minato
提出日時	2023-03-20 23:12:45
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	267 ms / 2,000 ms
コード長	18,993 bytes
コンパイル時間	2,382 ms
コンパイル使用メモリ	215,536 KB
最終ジャッジ日時	2025-02-11 15:41:32
ジャッジサーバーID （参考情報）	judge4 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン	結果
other	AC * 44
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
#line 1 "library-cpp/other/template.hpp"
// clang-format off
#include <bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using i128 = __int128_t;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using maxheap = priority_queue<T>;
template <class T> using minheap = priority_queue<T, vector<T>, greater<T>>;
template <class T> using vec = vector<T>;
template <class T> using vvec = vector<vector<T>>;
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP0(n) for (auto minato = decay_t<decltype(n)>{}; minato < (n); ++minato)
#define REP1(i, n) for (auto i = decay_t<decltype(n)>{}; (i) < (n); (i)++)
#define REP2(i, l, r) for (auto i = (l); (i) < (r); (i)++)
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1, REP0)(__VA_ARGS__)
#define OVERLOAD_RREP(_1, _2, _3, name, ...) name
#define RREP1(i, n) for (auto i = (n) - 1; (i) >= decay_t<decltype(n)>{}; (i)--)
#define RREP2(i, l, r) for (auto i = (r) - 1; (i) >= (l); (i)--)
#define rrep(...) OVERLOAD_RREP(__VA_ARGS__, RREP2, RREP1)(__VA_ARGS__)
#define all(x) begin(x), end(x)
template <class Container> int SZ(const Container& v) { return int(v.size()); }
template <class T> void UNIQUE(vector<T>& v) { v.erase(unique(v.begin(), v.end()), v.end()); }
template <class T> T MAX(const vector<T>& v) { return *max_element(v.begin(), v.end()); }
template <class T> T MIN(const vector<T>& v) { return *min_element(v.begin(), v.end()); }
template <class T> T SUM(const vector<T>& v) { return accumulate(v.begin(), v.end(), T(0)); }
template <class T> T ABS(T x) { return max(x, -x); }
template <class T1, class T2> bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; }
template <class T1, class T2> bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; }
int topbit(ull x) { return x == 0 ? -1 : 63 - __builtin_clzll(x); }
int botbit(ull x) { return x == 0 ? 64 : __builtin_ctzll(x); }
int popcount(ull x) { return __builtin_popcountll(x); }
int kthbit(ull x, int k) { return (x >> k) & 1; }
constexpr long long TEN(int x) { return x == 0 ? 1 : TEN(x - 1) * 10; }
template <typename S> void rearrange(const vector<S>& id) { (void)id; }
template <typename S, typename T> void rearrange_exec(const vector<S>& id, vector<T>& v) { vector<T> w(v.size()); for (size_t i = 0; i < id.size(); i++) { w[i] = v[id[i]]; } v.swap(w); }
template <typename S, typename Head, typename... Tail> void rearrange(const vector<S>& id, Head& a, Tail& ...tail) { rearrange_exec(id, a); rearrange(id, tail...); }
istream& operator>>(istream& is, __int128_t& x) {
    x = 0;
    string s;
    is >> s;
    int n = int(s.size()), it = 0;
    if (s[0] == '-') it++;
    for (; it < n; it++) x = (x * 10 + s[it] - '0');
    if (s[0] == '-') x = -x;
    return is;
}
ostream& operator<<(ostream& os, __int128_t x) {
    if (x == 0) return os << 0;
    if (x < 0) os << '-', x = -x;
    deque<int> deq;
    while (x) deq.emplace_front(x % 10), x /= 10;
    for (int e : deq) os << e;
    return os;
}
template <class T> vector<T> &operator++(vector<T>& v) { for (auto& e : v) { e++; } return v;} 
template <class T> vector<T> operator++(vector<T>& v, int) { auto res = v; for (auto& e : v) { e++; } return res; }
template <class T> vector<T> &operator--(vector<T>& v) { for (auto& e : v) { e--; } return v; }
template <class T> vector<T> operator--(vector<T>& v, int) { auto res = v; for (auto& e : v) { e--; } return res; }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x) { return pair<T1, T2>(-x.first, -x.second); }
template <class T1, class T2> pair<T1, T2> operator-(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first - y.first, x.second - y.second); }
template <class T1, class T2> pair<T1, T2> operator+(const pair<T1, T2>& x, const pair<T1, T2>& y) { return pair<T1, T2>(x.first + y.first, x.second + y.second); }
template <class T1, class T2> pair<T1, T2> operator+=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l + r; }
template <class T1, class T2> pair<T1, T2> operator-=(pair<T1, T2>& l, const pair<T1, T2>& r) { return l = l - r; }
constexpr char ln = '\n';
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
void YES(bool t = true) { cout << YESNO[t] << "\n"; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = true) { cout << YesNo[t] << "\n"; }
void No(bool t = 1) { Yes(!t); }
template <class T> void drop(T x) { cout << x << "\n"; exit(0); }
#define INT(...)     \
    int __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LL(...)     \
    ll __VA_ARGS__; \
    IN(__VA_ARGS__)
#define STR(...)        \
    string __VA_ARGS__; \
    IN(__VA_ARGS__)
#define CHR(...)      \
    char __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LDB(...)             \
    long double __VA_ARGS__; \
    IN(__VA_ARGS__)
#define VEC(type, name, size) \
    vector<type> name(size);  \
    IN(name)
#define VEC2(type, name1, name2, size)     \
    vector<type> name1(size), name2(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i])
#define VEC3(type, name1, name2, name3, size)           \
    vector<type> name1(size), name2(size), name3(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])
#define VEC4(type, name1, name2, name3, name4, size)                 \
    vector<type> name1(size), name2(size), name3(size), name4(size); \
    for (int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]);
#define VV(type, name, N, M)                       \
    vector<vector<type>> name(N, vector<type>(M)); \
    IN(name)
template <class T> void scan(T& a) { cin >> a; }
template <class T> void scan(vector<T>& a) { for (auto& i : a) scan(i); }
void IN() {}
template <class Head, class... Tail> void IN(Head& head, Tail&... tail) { scan(head); IN(tail...); }
void print() { cout << "\n"; }
template <class T> void print(const vector<T>& v) { for (auto it = v.begin(); it != v.end(); ++it) { if (it != v.begin()) { cout << " "; } cout << *it; } print(); }
template <class T, class... Args> void print(const T& x, const Args& ... args) { cout << x; if (sizeof...(Args)) cout << " "; print(args...); }
#ifdef MINATO_LOCAL
template <class T1, class T2> ostream& operator<<(ostream& os, pair<T1, T2> p) { return os << "(" << p.first << ", " << p.second << ")"; }
template <size_t N, class TUPLE> void debug_tuple(ostream& os, TUPLE _) { (void)os; (void)_; }
template <size_t N, class TUPLE, class T, class ...Args> void debug_tuple(ostream &os, TUPLE t) { os << (N == 0 ? "" : ", ") << get<N>(t); debug_tuple<N + 1, TUPLE, Args...>(os, t); }
template <class ...Args> ostream& operator<<(ostream& os, tuple<Args...> t) { os << "("; debug_tuple<0, tuple<Args...>, Args...>(os, t); return os << ")"; }
string debug_delim(int& i) { return i++ == 0 ? "" : ", "; }
#define debug_embrace(x) { int i = 0; os << "{";  { x } return os << "}"; }
template <class T> ostream& operator<<(ostream& os, vector<T> v) { debug_embrace( for (T e : v) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> ostream& operator<<(ostream& os, array<T, N> a) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class T, size_t N> enable_if_t<!is_same_v<char, remove_cv_t<T>>, ostream>& operator<<(ostream& os, T(&a)[N]) { debug_embrace( for (T e : a) { os << debug_delim(i) << e; } ) }
template <class Key> ostream& operator<<(ostream& os, set<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class Key, class T> ostream& operator<<(ostream& os, map<Key, T> mp) { debug_embrace( for (auto e : mp) { os << debug_delim(i) << e; }) }
template <class Key> ostream& operator<<(ostream& os, multiset<Key> s) { debug_embrace( for (Key e : s) { os << debug_delim(i) << e; }) }
template <class T> ostream& operator<<(ostream& os, queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.front(); } ) }
template <class T> ostream& operator<<(ostream& os, deque<T> q) { debug_embrace( for (T e : q) { os << debug_delim(i) << e; } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
template <class T> ostream& operator<<(ostream& os, priority_queue<T, vector<T>, greater<T>> q) { debug_embrace( for (; !q.empty(); q.pop()) { os << debug_delim(i) << q.top(); } ) }
void debug_out() { cerr << endl; }
template <class T, class... Args> void debug_out(const T& x, const Args& ... args) { cerr << " " << x; debug_out(args...); }
#define debug(...) cerr << __LINE__ << " : [" << #__VA_ARGS__ << "] =", debug_out(__VA_ARGS__)
#else
#define debug(...) (void(0))
#endif
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// clang-format on
#line 2 "library-cpp/tree/Rerooting.hpp"

/**
 * @brief 全方位木 DP
 * @param n int 頂点数
 * @param op (EdgeValue a, EdgeValue b) -> EdgeValue : dp の値の演算
 * @param vtoe (VertexValue a, auto(Edge) e) -> EdgeValue : 頂点の dp
 * の値をから辺の dp の値を計算する
 * @param etov (EdgeValue a, int v) -> VertexValue : 辺の dp の値から頂点の dp
 * の値を計算する
 * @param id EdgeValue 単位元
 */
template <class EdgeValue,
          class VertexValue,
          class Weight,
          class F,
          class G,
          class H>
struct Rerooting {
    struct Edge {
        int from;
        int to;
        Weight weight;
        Edge(int from, int to, const Weight& weight)
            : from(from), to(to), weight(weight) {
        }
    };
    int n;
    vector<vector<Edge>> g;
    vector<VertexValue> subdp, dp;
    F op;
    G vtoe;
    H etov;
    EdgeValue id;

    Rerooting() {
    }
    Rerooting(int n,
              const F& op,
              const G& vtoe,
              const H& etov,
              const EdgeValue& id)
        : n(n), g(n), subdp(n), dp(n), op(op), vtoe(vtoe), etov(etov), id(id) {
    }

    void add_edge(int u, int v, const Weight& weight = Weight()) {
        g[u].emplace_back(u, v, weight);
        g[v].emplace_back(v, u, weight);
    }

    void build() {
        dfs_sub(0, -1);
        dfs_all(0, -1, VertexValue());
        return;
    }

    VertexValue operator[](int i) const {
        return dp[i];
    }

#ifdef MINATO_LOCAL
    friend ostream& operator<<(ostream& os, const Rerooting& r) {
        os << "\nsubdp = " << r.subdp;
        os << "\ndp = " << r.dp;
        return os;
    }
#endif

  private:
    void dfs_sub(int v, int pv) {
        EdgeValue merge_value = id;
        for (const Edge& edge : g[v]) {
            if (edge.to == pv) continue;
            dfs_sub(edge.to, v);
            merge_value = op(merge_value, vtoe(subdp[edge.to], edge));
        }
        subdp[v] = etov(merge_value, v);
        return;
    }

    void dfs_all(int v, int pv, const VertexValue& top) {
        dp[v] = calc_dp(v, pv, top);

        vector<EdgeValue> prefix_sum = get_prefix_sum(v, pv, top);
        EdgeValue merge_value = id;
        for (int i = int(g[v].size()) - 1; i >= 0; i--) {
            if (g[v][i].to != pv) {
                dfs_all(g[v][i].to, v, etov(op(merge_value, prefix_sum[i]), v));
                merge_value = op(merge_value, vtoe(subdp[g[v][i].to], g[v][i]));
            } else {
                merge_value = op(merge_value, vtoe(top, g[v][i]));
            }
        }
        return;
    }

    VertexValue calc_dp(int v, int pv, const VertexValue& top) const {
        EdgeValue merge_value = id;
        for (const Edge& edge : g[v]) {
            if (edge.to == pv) {
                merge_value = op(merge_value, vtoe(top, edge));
            } else {
                merge_value = op(merge_value, vtoe(subdp[edge.to], edge));
            }
        }
        return etov(merge_value, v);
    }

    vector<EdgeValue> get_prefix_sum(int v,
                                     int pv,
                                     const VertexValue& top) const {
        vector<EdgeValue> prefix_sum(g[v].size(), id);
        for (int i = 0; i < int(g[v].size()) - 1; i++) {
            if (g[v][i].to == pv) {
                prefix_sum[i + 1] = op(prefix_sum[i], vtoe(top, g[v][i]));
            } else {
                prefix_sum[i + 1] =
                    op(prefix_sum[i], vtoe(subdp[g[v][i].to], g[v][i]));
            }
        }
        return prefix_sum;
    }
};
#line 1 "library-cpp/mod/ModInt.hpp"
template <int m> struct ModInt {
  public:
    static constexpr int mod() {
        return m;
    }
    static ModInt raw(int v) {
        ModInt x;
        x._v = v;
        return x;
    }

    ModInt() : _v(0) {
    }
    ModInt(long long v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }

    unsigned int val() const {
        return _v;
    }

    ModInt& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    ModInt& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    ModInt operator++(int) {
        ModInt result = *this;
        ++*this;
        return result;
    }
    ModInt operator--(int) {
        ModInt result = *this;
        --*this;
        return result;
    }

    ModInt& operator+=(const ModInt& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    ModInt& operator-=(const ModInt& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    ModInt& operator*=(const ModInt& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    ModInt& operator^=(long long n) {
        ModInt x = *this;
        *this = 1;
        if (n < 0) x = x.inv(), n = -n;
        while (n) {
            if (n & 1) *this *= x;
            x *= x;
            n >>= 1;
        }
        return *this;
    }
    ModInt& operator/=(const ModInt& rhs) {
        return *this = *this * rhs.inv();
    }

    ModInt operator+() const {
        return *this;
    }
    ModInt operator-() const {
        return ModInt() - *this;
    }
    explicit operator bool() const {
        return _v != 0;
    }

    ModInt pow(long long n) const {
        ModInt r = *this;
        r ^= n;
        return r;
    }
    ModInt inv() const {
        int a = _v, b = umod(), y = 1, z = 0, t;
        for (;;) {
            t = a / b;
            a -= t * b;
            if (a == 0) {
                assert(b == 1 || b == -1);
                return ModInt(b * z);
            }
            y -= t * z;
            t = b / a;
            b -= t * a;
            if (b == 0) {
                assert(a == 1 || a == -1);
                return ModInt(a * y);
            }
            z -= t * y;
        }
    }

    friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) += rhs;
    }
    friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) -= rhs;
    }
    friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) *= rhs;
    }
    friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) /= rhs;
    }
    friend ModInt operator^(const ModInt& lhs, long long rhs) {
        return ModInt(lhs) ^= rhs;
    }
    friend bool operator==(const ModInt& lhs, const ModInt& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const ModInt& lhs, const ModInt& rhs) {
        return lhs._v != rhs._v;
    }
    friend ModInt operator+(long long lhs, const ModInt& rhs) {
        return (ModInt(lhs) += rhs);
    }
    friend ModInt operator-(long long lhs, const ModInt& rhs) {
        return (ModInt(lhs) -= rhs);
    }
    friend ModInt operator*(long long lhs, const ModInt& rhs) {
        return (ModInt(lhs) *= rhs);
    }
    friend ostream& operator<<(ostream& os, const ModInt& M) {
        return os << M._v;
    }
    friend istream& operator>>(istream& is, ModInt& M) {
        long long x;
        is >> x;
        M = x;
        return is;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() {
        return m;
    }
};
#line 1 "library-cpp/mod/ModCombination.hpp"
template <class M> struct ModCombination {
  public:
    ModCombination() {
    }
    ModCombination(int n) : n_(n), fac_(n + 1), facinv_(n + 1) {
        assert(1 <= n);
        fac_[0] = 1;
        for (int i = 1; i <= n; i++) fac_[i] = fac_[i - 1] * i;
        facinv_[n] = M(1) / fac_[n];
        for (int i = n; i >= 1; i--) facinv_[i - 1] = facinv_[i] * i;
    }

    M fac(int k) const {
        assert(0 <= k and k <= n_);
        return fac_[k];
    }
    M facinv(int k) const {
        assert(0 <= k and k <= n_);
        return facinv_[k];
    }
    M inv(int k) const {
        assert(1 <= k and k <= n_);
        return facinv_[k] * fac_[k - 1];
    }

    M P(int n, int k) const {
        if (k < 0 or k > n) return M(0);
        assert(n <= n_);
        return fac_[n] * facinv_[n - k];
    }
    M C(int n, int k) const {
        if (k < 0 or k > n) return M(0);
        assert(n <= n_);
        return fac_[n] * facinv_[n - k] * facinv_[k];
    }
    M H(int n, int k) const {
        if (n == 0 and k == 0) return M(1);
        return C(n + k - 1, n);
    }
    M catalan(int n) const {
        if (n == 0) return M(1);
        return C(2 * n, n) - C(2 * n, n - 1);
    }

  private:
    int n_;
    vector<M> fac_, facinv_;
};
#line 5 "A.cpp"
// using mint = ModInt<998244353>;
using mint = ModInt<1000000007>;
using Tu = tuple<mint, mint, mint>;
void solve() {
    INT(N);
    auto op = [](Tu a, Tu b) {
        auto [a0, a1, a2] = a;
        auto [b0, b1, b2] = b;
        return Tu(a0 + b0, a1 + b1, a2 + b2);
    };
    auto etov = [](Tu a, auto e) {
        auto [a0, a1, a2] = a;
        return Tu(a0 + a1 * e.weight * 2 + e.weight * e.weight * a2,
                  a1 + e.weight * a2, a2);
    };
    auto vtoe = [](Tu a, int v) {
        (void)v;
        auto [a0, a1, a2] = a;
        return Tu(a0, a1, a2 + 1);
    };
    const Tu e = Tu(0, 0, 0);
    Rerooting<Tu, Tu, mint, decltype(op), decltype(etov), decltype(vtoe)> r(
        N, op, etov, vtoe, e);
    rep(N - 1) {
        INT(a, b, c);
        a--;
        b--;
        r.add_edge(a, b, c);
    }
    r.build();
    mint ans = 0;
    rep(i, N) {
        ans += get<0>(r[i]);
    }
    ans /= 2;
    print(ans);
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
    cerr << fixed << setprecision(7);

    int T = 1;
    // cin >> T;
    for (int test_case = 1; test_case <= T; test_case++) {
        // debug(test_case);
        solve();
    }
}
yukicoder

結果

ソースコード
