library

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:heavy_check_mark: verify/FZT.test.cpp

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Code

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2446"
#define ERROR "1e-6"
#include "library/template/template.cpp"
// library
#include "library/convolution/FZT.cpp"
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << setprecision(30) << fixed;
    ll n, m;
    cin >> n >> m;
    vl a(n);
    vector<ld> p(n);
    scan(a);
    rep(i, n) cin >> p[i], p[i] /= 100;
    vector<ll> f(1 << n);
    rep(s, 1, 1 << n)
    {
        ll prod = 1;
        rep(i, n)
        {
            if ((s & (1 << i)) == 0)
                continue;
            ll g = gcd(prod, a[i]);
            if ((__int128_t)prod * (a[i] / g) <= m)
                prod = prod * (a[i] / g);
            else
                prod = m + 1;
        }
        f[s] = (popcnt(s) % 2 ? 1 : -1) * (m / prod);
    }
    // FZTで包除原理
    auto g = FZT(f);
    ld ans = 0;
    // 期待値計算
    rep(s, 1 << n)
    {
        ld ps = 1;
        rep(i, n)
        {
            if ((s & (1 << i)) == 0)
                ps *= 1 - p[i];
            else
                ps *= p[i];
        }
        ans += ps * g[s];
    }
    print(ans);
}
#line 1 "verify/FZT.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2446"
#define ERROR "1e-6"
#line 2 "library/template/template.cpp"
/* #region header */
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
// types
using ll = long long;
using ull = unsigned long long;
using ld = long double;
typedef pair<ll, ll> Pl;
typedef pair<int, int> Pi;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef vector<char> vc;
template <typename T>
using mat = vector<vector<T>>;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef vector<vector<char>> vvc;
// abreviations
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep_(i, a_, b_, a, b, ...) for (ll i = (a), max_i = (b); i < max_i; i++)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define rrep_(i, a_, b_, a, b, ...) \
    for (ll i = (b - 1), min_i = (a); i >= min_i; i--)
#define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define srep(i, a, b, c) for (ll i = (a), max_i = (b); i < max_i; i += c)
#define SZ(x) ((int)(x).size())
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp make_pair
//入出力
#define print(x) cout << x << endl
template <class T>
ostream &operator<<(ostream &os, const vector<T> &v)
{
    for (auto &e : v)
        cout << e << " ";
    cout << endl;
    return os;
}
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T>
void scan(vector<T> &a)
{
    for (auto &i : a)
        scan(i);
}
#define vsum(x) accumulate(all(x), 0LL)
#define vmax(a) *max_element(all(a))
#define vmin(a) *min_element(all(a))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
// functions
// gcd(0, x) fails.
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class T>
bool chmax(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
    if (b < a)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T>
T mypow(T x, ll n)
{
    T ret = 1;
    while (n > 0)
    {
        if (n & 1)
            (ret *= x);
        (x *= x);
        n >>= 1;
    }
    return ret;
}
ll modpow(ll x, ll n, const ll mod)
{
    ll ret = 1;
    while (n > 0)
    {
        if (n & 1)
            (ret *= x);
        (x *= x);
        n >>= 1;
        x %= mod;
        ret %= mod;
    }
    return ret;
}
ll safemod(ll x, ll mod) { return (x % mod + mod) % mod; }
int popcnt(ull x) { return __builtin_popcountll(x); }
template <typename T>
vector<int> IOTA(vector<T> a)
{
    int n = a.size();
    vector<int> id(n);
    iota(all(id), 0);
    sort(all(id), [&](int i, int j)
         { return a[i] < a[j]; });
    return id;
}
long long xor64(long long range) {
    static uint64_t x = 88172645463325252ULL;
    x ^= x << 13;
    x ^= x >> 7;
    return (x ^= x << 17) % range;
}
struct Timer
{
    clock_t start_time;
    void start() { start_time = clock(); }
    int lap()
    {
        // return x ms.
        return (clock() - start_time) * 1000 / CLOCKS_PER_SEC;
    }
};
template <typename T = int>
struct Edge
{
    int from, to;
    T cost;
    int idx;

    Edge() = default;

    Edge(int from, int to, T cost = 1, int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}

    operator int() const { return to; }
};

template <typename T = int>
struct Graph
{
    vector<vector<Edge<T>>> g;
    int es;

    Graph() = default;

    explicit Graph(int n) : g(n), es(0) {}

    size_t size() const { return g.size(); }

    void add_directed_edge(int from, int to, T cost = 1)
    {
        g[from].emplace_back(from, to, cost, es++);
    }

    void add_edge(int from, int to, T cost = 1)
    {
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }

    void read(int M, int padding = -1, bool weighted = false,
              bool directed = false)
    {
        for (int i = 0; i < M; i++)
        {
            int a, b;
            cin >> a >> b;
            a += padding;
            b += padding;
            T c = T(1);
            if (weighted)
                cin >> c;
            if (directed)
                add_directed_edge(a, b, c);
            else
                add_edge(a, b, c);
        }
    }
};

/* #endregion*/
// constant
#define inf 1000000000ll
#define INF 4000000004000000000LL
#define endl '\n'
const long double eps = 0.000000000000001;
const long double PI = 3.141592653589793;
#line 4 "verify/FZT.test.cpp"
// library
#line 1 "library/convolution/FZT.cpp"
/**
 * @brief Fast Zeta Transform
 * @docs docs/FZT.md
 * @details 全ての部分集合$T_i$について$\sum_{S \subset T_i}f(S)$を計算
 */
template <typename T>
vector<T> FZT(vector<T> f)
{
    int N = 0;
    int tmp = f.size();
    while (tmp > 1)
        N++, tmp /= 2;
    for (int j = 0; j < N; j++)
    {
        for (int i = 0; i < (1 << N); i++)
        {
            if (i & (1 << j))
            {
                f[i] += f[i & ~(1 << j)];
            }
        }
    }
    return f;
}
#line 6 "verify/FZT.test.cpp"
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << setprecision(30) << fixed;
    ll n, m;
    cin >> n >> m;
    vl a(n);
    vector<ld> p(n);
    scan(a);
    rep(i, n) cin >> p[i], p[i] /= 100;
    vector<ll> f(1 << n);
    rep(s, 1, 1 << n)
    {
        ll prod = 1;
        rep(i, n)
        {
            if ((s & (1 << i)) == 0)
                continue;
            ll g = gcd(prod, a[i]);
            if ((__int128_t)prod * (a[i] / g) <= m)
                prod = prod * (a[i] / g);
            else
                prod = m + 1;
        }
        f[s] = (popcnt(s) % 2 ? 1 : -1) * (m / prod);
    }
    // FZTで包除原理
    auto g = FZT(f);
    ld ans = 0;
    // 期待値計算
    rep(s, 1 << n)
    {
        ld ps = 1;
        rep(i, n)
        {
            if ((s & (1 << i)) == 0)
                ps *= 1 - p[i];
            else
                ps *= p[i];
        }
        ans += ps * g[s];
    }
    print(ans);
}
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