結果

問題 No.2949 Product on Tree
ユーザー noya2noya2
提出日時 2024-11-01 22:12:05
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 373 ms / 2,000 ms
コード長 18,018 bytes
コンパイル時間 4,665 ms
コンパイル使用メモリ 276,272 KB
実行使用メモリ 72,792 KB
最終ジャッジ日時 2024-11-01 22:12:32
合計ジャッジ時間 20,824 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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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
6,816 KB
testcase_01 AC 4 ms
6,820 KB
testcase_02 AC 3 ms
6,820 KB
testcase_03 AC 246 ms
44,544 KB
testcase_04 AC 199 ms
43,776 KB
testcase_05 AC 213 ms
44,876 KB
testcase_06 AC 220 ms
45,056 KB
testcase_07 AC 208 ms
43,976 KB
testcase_08 AC 246 ms
45,432 KB
testcase_09 AC 207 ms
45,964 KB
testcase_10 AC 212 ms
46,760 KB
testcase_11 AC 219 ms
47,948 KB
testcase_12 AC 223 ms
52,276 KB
testcase_13 AC 251 ms
52,992 KB
testcase_14 AC 230 ms
55,960 KB
testcase_15 AC 242 ms
60,436 KB
testcase_16 AC 239 ms
57,232 KB
testcase_17 AC 234 ms
58,572 KB
testcase_18 AC 245 ms
58,432 KB
testcase_19 AC 274 ms
62,352 KB
testcase_20 AC 246 ms
61,480 KB
testcase_21 AC 248 ms
62,296 KB
testcase_22 AC 240 ms
63,468 KB
testcase_23 AC 211 ms
45,552 KB
testcase_24 AC 239 ms
45,688 KB
testcase_25 AC 216 ms
45,592 KB
testcase_26 AC 216 ms
45,724 KB
testcase_27 AC 215 ms
45,908 KB
testcase_28 AC 217 ms
46,008 KB
testcase_29 AC 265 ms
46,444 KB
testcase_30 AC 244 ms
47,524 KB
testcase_31 AC 228 ms
49,788 KB
testcase_32 AC 229 ms
50,320 KB
testcase_33 AC 242 ms
57,056 KB
testcase_34 AC 250 ms
65,128 KB
testcase_35 AC 287 ms
60,056 KB
testcase_36 AC 260 ms
68,528 KB
testcase_37 AC 269 ms
69,104 KB
testcase_38 AC 373 ms
63,560 KB
testcase_39 AC 290 ms
64,420 KB
testcase_40 AC 273 ms
71,980 KB
testcase_41 AC 263 ms
67,228 KB
testcase_42 AC 321 ms
72,792 KB
testcase_43 AC 81 ms
33,508 KB
testcase_44 AC 83 ms
33,976 KB
testcase_45 AC 111 ms
42,880 KB
testcase_46 AC 95 ms
38,664 KB
testcase_47 AC 71 ms
29,160 KB
testcase_48 AC 98 ms
39,820 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 # 

#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v){
    int s = (int)v.size();
    for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u){
    cin >> t;
    in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u){
    cout << t;
    if (sizeof...(u)) cout << sep;
    out(u...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/tree/rerootingdp.hpp"

#line 5 "/Users/noya2/Desktop/Noya2_library/tree/rerootingdp.hpp"
#include <ranges>

namespace noya2 {

// g[from] contains outgoing edges (to, edgeid(from, to))
// (E, op, e) is commutative monoid
// ~edgeid(from, to) == edgeid(to, from)
// return calculator of dp(r, v)
template<class V, class E>
auto rerootingdp(auto op, E e, auto put_edge, auto put_vertex, const std::vector<std::vector<std::pair<int, int>>> &g, int root = 0){
    struct dp {
        // dp(r, v) : root is r, dp of subtree v
        // ans[v]  = dp(v, v)
        // from[v] = dp(v, par(v))
        // to[v]   = dp(par(v), v)
        // from[root] and to[root] is undefined
        std::vector<V> ans, from, to;
        std::vector<int> down, up;
        std::vector<std::vector<int>> childs;
        bool is_in_subtree(int r, int v){
            return down[r] < down[v] && up[v] <= up[r];
        }
        V operator()(int r, int v){
            if (r == v) return ans[v];
            if (!is_in_subtree(v, r)) return to[v];
            int le = 0, ri = childs[v].size();
            while (ri - le > 1){
                int md = (le + ri) / 2;
                if (down[childs[v][md]] <= down[r]){
                    le = md;
                }
                else {
                    ri = md;
                }
            }
            return from[childs[v][le]];
        }
    };
    int n = g.size();
    std::vector<E> from(n, e), to(n, e);
    std::vector<V> dp_to(n);
    std::vector<std::vector<int>> childs(n);
    std::vector<int> down(n), up(n);
    int t = 0;
    auto dfs = [&](auto sfs, int v, int f) -> void {
        down[v] = t++;
        childs[v].reserve(g[v].size());
        for (auto [c, eid] : g[v]){
            if (c == f) continue;
            childs[v].emplace_back(c);
            sfs(sfs, c, v);
            dp_to[c] = put_vertex(to[c], c);
            to[c] = put_edge(dp_to[c], eid);
            to[v] = op(to[v], to[c]);
        }
        up[v] = t;
    };
    dfs(dfs, root, -1);
    std::vector<V> dp_ans(n), dp_from(n);
    std::vector<E> inner(n);
    auto bfs = [&](auto sfs, int v, int f) -> void {
        int sz = g[v].size();
        inner[sz] = e;
        int i = sz-1;
        for (auto [c, eid] : g[v] | std::views::reverse){
            if (c == f) continue;
            inner[i] = op(inner[i+1], to[c]);
            i--;
        }
        dp_ans[v] = put_vertex(op(inner[++i], from[v]), v);
        E rui = e;
        for (auto [c, eid] : g[v]){
            if (c == f) continue;
            dp_from[c] = put_vertex(op(op(rui, inner[++i]), from[v]), v);
            from[c] = put_edge(dp_from[c], ~eid);
            rui = op(rui, to[c]);
        }
        for (auto [c, eid] : g[v]){
            if (c == f) continue;
            sfs(sfs, c, v);
        }
    };
    bfs(bfs, root, -1);
    return dp{dp_ans, dp_from, dp_to, down, up, childs};
}

}  // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"

#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"

#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"
namespace noya2 {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;
    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u; 
        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);

// constexpr long long primitive_root_constexpr(long long m){
//     if (m == (1LL << 47) - (1LL << 24) + 1) return 3;
//     return primitive_root_constexpr(static_cast<int>(m));
// }

} // namespace noya2
#line 6 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"

namespace noya2{

struct barrett {
    unsigned int _m;
    unsigned long long im;
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
    unsigned int umod() const { return _m; }
    unsigned int mul(unsigned int a, unsigned int b) const {
        unsigned long long z = a;
        z *= b;
        unsigned long long x = (unsigned long long)((__uint128_t(z) * im) >> 64);
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

template <int m>
struct static_modint {
    using mint = static_modint;
  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }
    constexpr static_modint() : _v(0) {}
    template<std::signed_integral T>
    constexpr static_modint(T v){
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template<std::unsigned_integral T>
    constexpr static_modint(T v){
        _v = (unsigned int)(v % umod());
    }
    constexpr unsigned int val() const { return _v; }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    constexpr mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    constexpr mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    constexpr mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (uint)(z % umod());
        return *this;
    }
    constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    constexpr mint operator+() const { return *this; }
    constexpr mint operator-() const { return mint() - *this; }
    constexpr mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    constexpr mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend constexpr mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend constexpr mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend constexpr mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend constexpr bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = is_prime_flag<m>;
};


template <int id> struct dynamic_modint {
    using mint = dynamic_modint;
  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template<std::signed_integral T>
    dynamic_modint(T v){
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template<std::unsigned_integral T>
    dynamic_modint(T v){
        _v = (unsigned int)(v % umod());
    }
    uint val() const { return _v; }
    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }
    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = noya2::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }
    friend std::ostream &operator<<(std::ostream &os, const mint& p) {
        return os << p.val();
    }
    friend std::istream &operator>>(std::istream &is, mint &a) {
        long long t; is >> t;
        a = mint(t);
        return (is);
    }

  private:
    unsigned int _v;
    static barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

template<typename T>
concept Modint = requires (T &a){
    T::mod();
    a.inv();
    a.val();
    a.pow(declval<int>());
};

} // namespace noya2
#line 5 "c.cpp"
using mint = modint998244353;

void solve(){
    int n; in(n);
    vector<mint> a(n); in(a);
    vector<vector<pii>> g(n);
    rep(i,n-1){
        int u, v; in(u,v); u--, v--;
        g[u].emplace_back(v,i);
        g[v].emplace_back(u,~i);
    }
    auto op = [&](mint l, mint r){
        return l + r;
    };
    auto pute = [&](mint v, int){
        return v;
    };
    auto putv = [&](mint e, int v){
        return e * a[v] + a[v];
    };
    auto dp = rerootingdp<mint,mint>(op,mint(0),pute,putv,g);
    mint ans = 0;
    rep(i,n){
        ans += dp(i,i);
        ans -= a[i];
    }
    ans /= 2;
    out(ans);
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}
0