#757316 (C++23) No.1919 Many Monster Battles

提出ソース
結果

問題	No.1919 Many Monster Battles
コンテスト
ユーザー	hitonanode
提出日時	2022-04-30 00:56:17
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	359 ms / 2,000 ms
コード長	21,185 bytes
コンパイル時間	1,969 ms
コンパイル使用メモリ	196,524 KB
実行使用メモリ	35,360 KB
最終ジャッジ日時	2024-06-29 06:54:10
合計ジャッジ時間	10,003 ms
ジャッジサーバーID （参考情報）	judge5 / judge3
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
sample	AC * 3
other	AC * 32
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 <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) 0
#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>;

#ifndef ATCODER_INTERNAL_BITOP_HPP
#define ATCODER_INTERNAL_BITOP_HPP 1

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

} // namespace internal

} // namespace atcoder

#endif // ATCODER_INTERNAL_BITOP_HPP

#ifndef ATCODER_SEGTREE_HPP
#define ATCODER_SEGTREE_HPP 1

#include <algorithm>
#include <cassert>
#include <vector>

// #include "atcoder/internal_bit"

namespace atcoder {

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
public:
    segtree() : segtree(0) {}
    explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
    explicit segtree(const std::vector<S> &v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) { update(i); }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() const { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) const {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) const {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

} // namespace atcoder

#endif // ATCODER_SEGTREE_HPP

// Reference: https://atcoder.github.io/ac-library/document_ja/segtree.html
/* usage:
struct S {
    long long su;
    int nb;
};
S e() { return {0, 0}; }
S op(S l, S r) { return {l.su + r.su, l.nb + r.nb}; }
vector<S> seginit(100000, e());
atcoder::segtree<S, op, e> segtree(seginit);
*/


#include <algorithm>
#include <cassert>
#include <utility>
#include <vector>

// 逆元を要求しない領域木
template <class S, S (*op)(S, S), S (*e)(), class Coordinate> class rangetree {
    int n;
    using Pt = std::pair<Coordinate, Coordinate>;
    std::vector<Pt> _pts;
    std::vector<std::vector<Pt>> _range2yxs;
    std::vector<atcoder::segtree<S, op, e>> segtrees;
    void _set(int v, Pt p, S val) {
        auto i = std::distance(
            _range2yxs[v].begin(),
            std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{p.second, p.first}));
        segtrees[v].set(i, val);
    }
    void _add(int v, Pt p, S val) {
        auto i = std::distance(
            _range2yxs[v].begin(),
            std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{p.second, p.first}));
        segtrees[v].set(i, op(segtrees[v].get(i), val));
    }
    S _prod(int v, Coordinate yl, Coordinate yr) const {
        auto comp = [&](const Pt &l, const Pt &r) { return l.first < r.first; };
        auto il = std::distance(
            _range2yxs[v].begin(),
            std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{yl, yl}, comp));
        auto ir = std::distance(
            _range2yxs[v].begin(),
            std::lower_bound(_range2yxs[v].begin(), _range2yxs[v].end(), Pt{yr, yr}, comp));
        return segtrees[v].prod(il, ir);
    }

public:
    rangetree() = default;
    void add_point(Coordinate x, Coordinate y) noexcept { _pts.emplace_back(x, y); }
    void build() {
        std::sort(_pts.begin(), _pts.end());
        _pts.erase(std::unique(_pts.begin(), _pts.end()), _pts.end());
        n = _pts.size();

        _range2yxs.resize(n * 2);
        for (int i = 0; i < n; i++) _range2yxs[n + i] = {{_pts[i].second, _pts[i].first}};
        for (int i = n - 1; i > 0; i--) {
            auto &lch = _range2yxs[i * 2];
            auto &rch = _range2yxs[i * 2 + 1];
            std::merge(
                lch.begin(), lch.end(), rch.begin(), rch.end(), std::back_inserter(_range2yxs[i]));
            _range2yxs[i].erase(
                std::unique(_range2yxs[i].begin(), _range2yxs[i].end()), _range2yxs[i].end());
        }
        for (const auto &v : _range2yxs) segtrees.emplace_back(v.size());
    }
    void set(Coordinate x, Coordinate y, S val) {
        int i = std::distance(_pts.begin(), std::lower_bound(_pts.begin(), _pts.end(), Pt{x, y}));
        assert(i < n and _pts[i] == std::make_pair(x, y));
        for (i += n; i; i >>= 1) _set(i, {x, y}, val);
    }
    void add(Coordinate x, Coordinate y, S val) {
        int i = std::distance(_pts.begin(), std::lower_bound(_pts.begin(), _pts.end(), Pt{x, y}));
        assert(i < n and _pts[i] == std::make_pair(x, y));
        for (i += n; i; i >>= 1) _add(i, {x, y}, val);
    }
    S prod(Coordinate xl, Coordinate xr, Coordinate yl, Coordinate yr) const {
        auto comp = [](const Pt &l, const Pt &r) { return l.first < r.first; };
        int l = n + std::distance(_pts.begin(),
                                  std::lower_bound(_pts.begin(), _pts.end(), Pt{xl, yr}, comp));
        int r = n + std::distance(_pts.begin(),
                                  std::lower_bound(_pts.begin(), _pts.end(), Pt{xr, yr}, comp));
        S ret = e();
        while (l < r) {
            if (l & 1) ret = op(ret, _prod(l++, yl, yr));
            if (r & 1) ret = op(ret, _prod(--r, yl, yr));
            l >>= 1, r >>= 1;
        }
        return ret;
    }
    S get(Coordinate x, Coordinate y) const { return prod(x, x + 1, y, y + 1); }
};

struct S {
    int nv;
    mint xsum, ysum;
    mint eval1(mint x, mint y) const { return xsum + ysum - nv * (x + y); }
    mint eval2(mint x, mint y) const { return xsum - ysum - nv * (x - y); }
};
S e() { return {0, 0, 0}; }
S op(S l, S r) { return {l.nv + r.nv, l.xsum + r.xsum, l.ysum + r.ysum}; }

// 0-indexed BIT (binary indexed tree / Fenwick tree) (i : [0, len))
template <class T> struct BIT {
    int n;
    std::vector<T> data;
    BIT(int len = 0) : n(len), data(len) {}
    void reset() { std::fill(data.begin(), data.end(), T(0)); }
    void add(int pos, T v) { // a[pos] += v
        pos++;
        while (pos > 0 and pos <= n) data[pos - 1] += v, pos += pos & -pos;
    }
    T sum(int k) const { // a[0] + ... + a[k - 1]
        T res = 0;
        while (k > 0) res += data[k - 1], k -= k & -k;
        return res;
    }

    T sum(int l, int r) const { return sum(r) - sum(l); } // a[l] + ... + a[r - 1]

    template <class OStream> friend OStream &operator<<(OStream &os, const BIT &bit) {
        T prv = 0;
        os << '[';
        for (int i = 1; i <= bit.n; i++) {
            T now = bit.sum(i);
            os << now - prv << ',', prv = now;
        }
        return os << ']';
    }
};


int main() {
    int N;
    cin >> N;
    vector<lint> A(N), B(N);
    cin >> A >> B;
    vector<plint> uv;
    map<lint, vector<lint>> v2us;
    vector<lint> us;
    REP(i, N) {
        auto u = A[i] - B[i];
        auto v = A[i] + B[i];
        uv.emplace_back(u, v);
        v2us[v].push_back(u);
        us.push_back(u);
    }
    dbg(uv);
    us = sort_unique(us);
    BIT<mint> sum_x(us.size()), sum_y(us.size()), sum_1(us.size());
    // rangetree<S, op, e, lint> tree;
    // for (auto [u, v] : uv) tree.add_point(u, v);
    // tree.build();
    // for (auto [u, v] : uv) {
    //     tree.add(u, v, S{1, u, v});
    // }
    mint ret0 = 0, ret1 = 0;
    constexpr lint INF = 1LL << 60;
    for (const auto &[v, uuu] : v2us) {
        for (lint u : uuu) {
            int p = arglb(us, u);
            ret0 += sum_1.sum(0, p) * mint(u + v) - sum_x.sum(0, p) - sum_y.sum(0, p);
            ret1 += sum_1.sum(p + 1, us.size()) * mint(-u + v) + sum_x.sum(p + 1, us.size()) - sum_y.sum(p + 1, us.size());
        }
        for (lint u : uuu) {
            int p = arglb(us, u);
            sum_x.add(p, u);
            sum_y.add(p, v);
            sum_1.add(p, 1);
        }
    }
    // for (auto [u, v] : uv) {
    //     ret0 += tree.prod(u + 1, INF, v + 1, INF).eval1(u, v);
    //     ret1 += tree.prod(u + 1, INF, -INF, v).eval2(u, v);
    // }
    cout << ret0 << ' ' << ret1 << '\n';
}
yukicoder

結果

ソースコード
