結果

問題 No.1840 Random Painting
コンテスト
ユーザー hitonanode
提出日時 2021-12-12 23:43:37
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 10,518 bytes
コンパイル時間 9,224 ms
コンパイル使用メモリ 404,280 KB
実行使用メモリ 11,904 KB
最終ジャッジ日時 2024-06-27 15:56:59
合計ジャッジ時間 13,554 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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 * 7 TLE * 1 -- * 24
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 # 

#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

__int128 str2i128(std::string str) {
    __int128 ret = 0;
    bool minus = false;
    for (auto c : str) {
        if (c == '-')
            minus = true;
        else
            ret = ret * 10 + c - '0';
    }
    return minus ? -ret : ret;
}
std::istream &operator>>(std::istream &is, __int128 &x) {
    std::string s;
    return is >> s, x = str2i128(s), is;
}
std::ostream &operator<<(std::ostream &os, const __int128 &x) {
    __int128 tmp = x;
    if (tmp == 0) return os << 0;
    std::vector<int> ds;
    if (tmp < 0) {
        os << '-';
        while (tmp) {
            int d = tmp % 10;
            if (d > 0) d -= 10;
            ds.emplace_back(-d), tmp = (tmp - d) / 10;
        }
    } else {
        while (tmp) ds.emplace_back(tmp % 10), tmp /= 10;
    }
    std::reverse(ds.begin(), ds.end());
    for (auto i : ds) os << i;
    return os;
}

#include <boost/multiprecision/cpp_int.hpp>
using mpint = boost::multiprecision::cpp_int;

// Rational number + {infinity(1 / 0), -infiity(-1 / 0)} （有理数）
struct Rational {
    using Int = mpint;
    Int num, den;
    static Int my_gcd(Int a, Int b) {
        // return __gcd(a, b);
        if (a < 0) a = -a;
        if (b < 0) b = -b;
        while (a and b) {
            if (a > b)
                a %= b;
            else
                b %= a;
        }
        return a + b;
    }
    Rational(Int num = 0, Int den = 1) : num(num), den(den) { normalize(); }
    void normalize() { // reduction and making denominator nonnegative
        Int g = my_gcd(num, den);
        num /= g, den /= g;
        if (den < 0) num = -num, den = -den;
    }
    Rational operator+(const Rational &r) const { return Rational(num * r.den + den * r.num, den * r.den); }
    Rational operator-(const Rational &r) const { return Rational(num * r.den - den * r.num, den * r.den); }
    Rational operator*(const Rational &r) const { return Rational(num * r.num, den * r.den); }
    Rational operator/(const Rational &r) const { return Rational(num * r.den, den * r.num); }
    Rational &operator+=(const Rational &r) { return *this = *this + r; }
    Rational &operator-=(const Rational &r) { return *this = *this - r; }
    Rational &operator*=(const Rational &r) { return *this = *this * r; }
    Rational &operator/=(const Rational &r) { return *this = *this / r; }
    Rational operator-() const { return Rational(-num, den); }
    Rational abs() const { return Rational(num > 0 ? num : -num, den); }
    bool operator==(const Rational &r) const { return num == r.num and den == r.den; }
    bool operator!=(const Rational &r) const { return num != r.num or den != r.den; }
    bool operator<(const Rational &r) const {
        if (den == 0 and r.den == 0)
            return num < r.num;
        else if (den == 0)
            return num < 0;
        else if (r.den == 0)
            return r.num > 0;
        else
            return num * r.den < den * r.num;
    }
    bool operator<=(const Rational &r) const { return (*this == r) or (*this < r); }
    bool operator>(const Rational &r) const { return r < *this; }
    bool operator>=(const Rational &r) const { return (r == *this) or (r < *this); }
    explicit operator double() const { return (double)num / (double)den; }
    explicit operator long double() const { return (long double)num / (long double)den; }
    friend std::ostream &operator<<(std::ostream &os, const Rational &x) { return os << x.num << '/' << x.den; }
};

struct rand_int_ {
    using lint = long long;
    mt19937 mt;
    rand_int_() : mt(chrono::steady_clock::now().time_since_epoch().count()) {}
    lint operator()(lint x) { return this->operator()(0, x); } // [0, x)
    lint operator()(lint l, lint r) {
        uniform_int_distribution<lint> d(l, r - 1);
        return d(mt);
    }
} rnd;

__int128 A107984(__int128 n, __int128 k) {
    return (k + 1) * (n + 2) * (2 * n - k + 3) * (n - k + 1) / 6;
}

// 右に r ステップ進むより左に l ステップ進む方が先の確率 * （そのようなときにそれを達成するまでの時間の条件付き期待値）
Rational solve(int l, int r) {
    __int128 N = l + r;
    return Rational(A107984(N - 2, l - 1) * 2, N * N);
}

int main() {
    int N;
    string S;
    cin >> N >> S;
    while (S.size() < N) S.push_back('0' + rnd(3) != 0);
    vector<int> zeropos;
    for (int i = 0; i < N; i++) {
        if (S[i] == '1') continue;
        zeropos.push_back(i);
    }
    Rational ret(0, 1);

    REP(t, 2) {
        ret += solve(N - zeropos[0], zeropos[0]);
        for (auto &x : zeropos) x = N - x;
        reverse(zeropos.begin(), zeropos.end());
    }

    mpint denmax;
    FOR(i, 1, zeropos.size()) {
        int a = zeropos[i - 1], b = zeropos[i];
        REP(t, 2) {
            Rational e1 = solve(a, N - b);
            Rational e2 = solve(N - (b - a), b - a);
            ret += e1 * Rational(b - a, N) + e2 * Rational(N - b, N - b + a);
            swap(a, b);
            a = N - a;
            b = N - b;
            chmax(denmax, ret.den);
        }
    }
    assert(ret.den == 1);
    cout << ret.num << '\n';
}
0