結果

問題 No.1084 積の積
ユーザー kcvlex
提出日時 2020-06-19 22:05:41
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 145 ms / 2,000 ms
コード長 9,002 bytes
コンパイル時間 1,668 ms
コンパイル使用メモリ 159,680 KB
最終ジャッジ日時 2025-01-11 06:25:19
ジャッジサーバーID
(参考情報)
judge1 / 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 * 5
other AC * 27
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 #
プレゼンテーションモードにする

#define CPP17
#include <limits>
#include <initializer_list>
#include <utility>
#include <bitset>
#include <tuple>
#include <type_traits>
#include <functional>
#include <string>
#include <array>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <unordered_map>
#include <unordered_set>
#include <iterator>
#include <algorithm>
#include <complex>
#include <random>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <regex>
#include <cassert>
#include <cstddef>
#ifdef CPP17
#include <variant>
#endif
// Yay!!
#define endl codeforces
// macros for iterator
#define ALL(v) std::begin(v), std::end(v)
#define ALLR(v) std::rbegin(v), std::rend(v)
// alias
using ll = std::int64_t;
using ull = std::uint64_t;
using pii = std::pair<int, int>;
using tii = std::tuple<int, int, int>;
using pll = std::pair<ll, ll>;
using tll = std::tuple<ll, ll, ll>;
template <typename T> using vec = std::vector<T>;
template <typename T> using vvec = vec<vec<T>>;
// variadic min/max
template <typename T> const T& var_min(const T &t) { return t; }
template <typename T> const T& var_max(const T &t) { return t; }
template <typename T, typename... Tail> const T& var_min(const T &t, const Tail&... tail) { return std::min(t, var_min(tail...)); }
template <typename T, typename... Tail> const T& var_max(const T &t, const Tail&... tail) { return std::max(t, var_max(tail...)); }
// variadic chmin/chmax
template <typename T, typename... Tail> void chmin(T &t, const Tail&... tail) { t = var_min(t, tail...); }
template <typename T, typename... Tail> void chmax(T &t, const Tail&... tail) { t = var_max(t, tail...); }
// multi demension array
template <typename T, std::size_t Head, std::size_t... Tail> struct multi_dim_array { using type = std::array<typename multi_dim_array<T, Tail
    ...>::type, Head>; };
template <typename T, std::size_t Head> struct multi_dim_array<T, Head> { using type = std::array<T, Head>; };
template <typename T, std::size_t... Args> using mdarray = typename multi_dim_array<T, Args...>::type;
#ifdef CPP17
// fill container
template <typename T, typename F, typename... Args>
void fill_seq(T &t, F f, Args... args) { if constexpr (std::is_invocable<F, Args...>::value) { t = f(args...); } else { for (ssize_t i = 0; i < t
    .size(); i++) fill_seq(t[i], f, args..., i); } }
#endif
// make multi dimension vector
template <typename T> vec<T> make_v(ssize_t sz) { return vec<T>(sz); }
template <typename T, typename... Tail> auto make_v(ssize_t hs, Tail&&... ts) { auto v = std::move(make_v<T>(std::forward<Tail>(ts)...)); return vec
    <decltype(v)>(hs, v); }
// init
namespace init__ {
struct InitIO { InitIO() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << std::fixed << std::setprecision(30); } }
    init_io;
}
namespace math {
template <typename T>
constexpr T pow(const T &n, ll k) {
T ret = n.mul_id_ele();
T cur = n;
while (k) {
if (k & 1) ret *= cur;
cur *= cur;
k /= 2;
}
return ret;
}
}
namespace math {
template <ll Mod>
struct Modint {
constexpr Modint(ll x) noexcept : x((Mod + x % Mod) % Mod) { }
constexpr Modint() noexcept : Modint(0) { }
constexpr Modint<Mod> add_id_ele() const noexcept {
return Modint<Mod>(0);
}
constexpr Modint<Mod> mul_id_ele() const noexcept {
return Modint<Mod>(1);
}
constexpr ll& value() noexcept {
return x;
}
constexpr ll value() const noexcept {
return x;
}
constexpr Modint& operator +=(const Modint &oth) noexcept {
x += oth.value();
if (Mod <= x) x -= Mod;
return *this;
}
constexpr Modint& operator -=(const Modint &oth) noexcept {
x += Mod - oth.value();
if (Mod <= x) x -= Mod;
return *this;
}
constexpr Modint& operator *=(const Modint &oth) noexcept {
x *= oth.value();
x %= Mod;
return *this;
}
constexpr Modint& operator /=(const Modint &oth) noexcept {
x *= oth.inv().value();
x %= Mod;
return *this;
}
constexpr Modint operator +(const Modint &oth) const noexcept {
return Modint(x) += oth;
}
constexpr Modint operator -(const Modint &oth) const noexcept {
return Modint(x) -= oth;
}
constexpr Modint operator *(const Modint &oth) const noexcept {
return Modint(x) *= oth;
}
constexpr Modint operator /(const Modint &oth) const noexcept {
return Modint(x) /= oth;
}
constexpr Modint operator -() const noexcept {
return Modint((x != 0) * (Mod - x));
}
template <typename T>
constexpr typename std::enable_if<std::is_integral<T>::value, const Modint&>::type
operator =(T t) noexcept {
(*this) = Modint(std::forward<T>(t));
return *this;
}
constexpr Modint inv() const noexcept {
return ::math::pow(*this, Mod - 2);
}
constexpr ll mod() const noexcept {
return Mod;
}
private:
ll x;
};
}
ssize_t ceil_pow2(ssize_t s) {
ssize_t ret = 1;
while (ret < s) ret *= 2;
return ret;
}
namespace segtree {
template <typename T, typename Op>
struct SegmentTree {
vec<T> nodes;
Op op;
T id_ele;
auto get_children_idx(ssize_t idx) const -> std::pair<ssize_t, ssize_t> {
return std::make_pair(2 * idx + 1, 2 * idx + 2);
}
T get_merged(ssize_t idx) const {
ssize_t a, b;
std::tie(a, b) = get_children_idx(idx);
return op(nodes[a], nodes[b]);
}
public:
SegmentTree(const vec<T> &init_v, Op op, T id_ele)
: op(op), id_ele(id_ele)
{
build(init_v);
}
void build(const vec<T> &v) {
nodes.resize(ceil_pow2(v.size()) * 2 - 1, id_ele);
ssize_t sz = size();
std::copy(ALL(v), nodes.begin() + sz - 1);
build_parents();
}
void build_parents() {
ssize_t sz = size();
for (ssize_t i = sz - 2; 0 <= i; i--) nodes[i] = get_merged(i);
}
ssize_t size() const {
return (nodes.size() + 1) / 2;
}
const T& operator [](ll idx) const {
return nodes[idx + size() - 1];
}
T get_query(ll ql, ll qr) const {
return get_query(ql, qr, id_ele);
}
T get_query(ll ql, ll qr, T init) const {
T ret = init;
ssize_t lnode = ql + size(), rnode = qr + size();
while (lnode < rnode) {
if (lnode & 1) {
ret = std::move(op(nodes[lnode - 1], ret));
lnode++;
}
if (rnode & 1) {
rnode--;
ret = std::move(op(ret, nodes[rnode - 1]));
}
lnode /= 2;
rnode /= 2;
}
return ret;
}
void update_query(ll idx, T val) {
idx += size() - 1;
nodes[idx] = val;
while (idx) {
ll pidx = (idx - 1) / 2;
nodes[pidx] = get_merged(pidx);
idx = pidx;
}
}
template <typename F>
ssize_t lower_bound(F f) const {
T sum = id_ele;
ssize_t l = 0, r = size(), idx = 0, bidx = 0;
if (!f(nodes[0])) return -1;
while (true) {
if (r - l == 1) {
if (!f(sum)) bidx++;
break;
}
auto lidx = 2 * idx + 1;
auto ridx = lidx + 1;
T nsum = op(sum, nodes[lidx]);
ssize_t m = (l + r) / 2;
if (f(nsum)) {
r = m;
idx = lidx;
} else {
l = m;
idx = ridx;
bidx = m;
sum = std::move(nsum);
}
}
return bidx;
}
};
}
const ll mod = 1e9 + 7;
using mint = math::Modint<mod>;
mint solve() {
ll n;
std::cin >> n;
vec<ll> av(n);
for (ll &e : av) {
std::cin >> e;
if (e == 0) return mint(0);
}
vec<mint> sum_m(n + 1), sum(n + 1);
sum_m[0] = 1;
sum[0] = 1;
for (ll i = 0; i < n; i++) sum_m[i + 1] = sum_m[i] * av[i];
for (ll i = 0; i < n; i++) sum[i + 1] = sum[i] * sum_m[i + 1];
const ll maxv = 1e9;
auto merge = [&](ll a, ll b) { return std::min(maxv, a * b); };
segtree::SegmentTree<ll, decltype(merge)> seg(av, merge, maxv);
mint ans = 1;
for (ll i = 0; i < n; i++) {
{
auto tmp = seg.get_query(i, n, 1);
if (tmp < maxv) {
ans *= (sum[n] / sum[i]) / pow(sum_m[i], n - i);
continue;
}
}
ll ok = i + 1, ng = n;
while (1 < std::abs(ok - ng)) {
ll mid = (ok + ng) / 2;
(seg.get_query(i, mid, 1) < maxv ? ok : ng) = mid;
}
ans *= (sum[ok] / sum[i]) / pow(sum_m[i], ok - i);
}
return ans;
}
int main() {
std::cout << solve().value() << "\n";
return 0;
}
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