結果
| 問題 | No.1300 Sum of Inversions |
| ユーザー |
 KoD
|
| 提出日時 | 2020-11-27 21:33:00 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 206 ms / 2,000 ms |
| コード長 | 10,416 bytes |
| コンパイル時間 | 1,266 ms |
| コンパイル使用メモリ | 88,872 KB |
| 最終ジャッジ日時 | 2025-01-16 06:35:53 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 34 |
ソースコード
#line 1 "main.cpp"/*** @title Template*/#include <iostream>#include <algorithm>#include <utility>#include <numeric>#include <vector>#include <array>#include <cassert>#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/range.cpp"#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/other/range.cpp"class range {struct iter {std::size_t itr;constexpr iter(std::size_t pos) noexcept: itr(pos) { }constexpr void operator ++ () noexcept { ++itr; }constexpr bool operator != (iter other) const noexcept { return itr != other.itr; }constexpr std::size_t operator * () const noexcept { return itr; }};struct reviter {std::size_t itr;constexpr reviter(std::size_t pos) noexcept: itr(pos) { }constexpr void operator ++ () noexcept { --itr; }constexpr bool operator != (reviter other) const noexcept { return itr != other.itr; }constexpr std::size_t operator * () const noexcept { return itr; }};const iter first, last;public:constexpr range(std::size_t first, std::size_t last) noexcept: first(first), last(std::max(first, last)) { }constexpr iter begin() const noexcept { return first; }constexpr iter end() const noexcept { return last; }constexpr reviter rbegin() const noexcept { return reviter(*last - 1); }constexpr reviter rend() const noexcept { return reviter(*first - 1); }};/*** @title Range*/#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/modular.cpp"#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/mod_inv.cpp"#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/mod_inv.cpp"#include <cstdint>constexpr std::pair<int64_t, int64_t> mod_inv(int64_t a, int64_t b) {if ((a %= b) == 0) return { b, 0 };int64_t s = b, t = (a < 0 ? a + b : a);int64_t m0 = 0, m1 = 1, tmp = 0;while (t > 0) {const auto u = s / t;s -= t * u; m0 -= m1 * u;tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp;}return { s, (m0 < 0 ? m0 + b / s : m0) };}/*** @title Extended GCD*/#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/modular.cpp"#line 8 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/modular.cpp"#include <type_traits>template <class Modulus>class modular {public:using value_type = uint32_t;using cover_type = uint64_t;static constexpr uint32_t mod() { return Modulus::mod(); }template <class T>static constexpr value_type normalize(T value_) noexcept {if (value_ < 0) {value_ = -value_;value_ %= mod();if (value_ == 0) return 0;return mod() - value_;}return value_ % mod();}private:value_type value;template <bool IsPrime, std::enable_if_t<IsPrime>* = nullptr>constexpr modular inverse_helper() const noexcept { return power(*this, mod() - 2); }template <bool IsPrime, std::enable_if_t<!IsPrime>* = nullptr>constexpr modular inverse_helper() const noexcept {const auto tmp = mod_inv(value, mod());assert(tmp.first == 1);return modular(tmp.second);}public:constexpr modular() noexcept : value(0) { }template <class T>explicit constexpr modular(T value_) noexcept : value(normalize(value_)) { }template <class T>explicit constexpr operator T() const noexcept { return static_cast<T>(value); }constexpr value_type get() const noexcept { return value; }constexpr value_type &extract() noexcept { return value; }constexpr modular operator - () const noexcept { return modular(mod() - value); }constexpr modular operator ~ () const noexcept { return inverse(*this); }constexpr modular operator + (const modular &rhs) const noexcept { return modular(*this) += rhs; }constexpr modular& operator += (const modular &rhs) noexcept {if ((value += rhs.value) >= mod()) value -= mod();return *this;}constexpr modular operator - (const modular &rhs) const noexcept { return modular(*this) -= rhs; }constexpr modular& operator -= (const modular &rhs) noexcept {if ((value += mod() - rhs.value) >= mod()) value -= mod();return *this;}constexpr modular operator * (const modular &rhs) const noexcept { return modular(*this) *= rhs; }constexpr modular& operator *= (const modular &rhs) noexcept {value = (cover_type) value * rhs.value % mod();return *this;}constexpr modular operator / (const modular &rhs) const noexcept { return modular(*this) /= rhs; }constexpr modular& operator /= (const modular &rhs) noexcept { return (*this) *= inverse(rhs); }constexpr bool zero() const noexcept { return value == 0; }constexpr bool operator == (const modular &rhs) const noexcept { return value == rhs.value; }constexpr bool operator != (const modular &rhs) const noexcept { return value != rhs.value; }friend std::ostream& operator << (std::ostream &stream, const modular &rhs) { return stream << rhs.value; }friend constexpr modular inverse(const modular &val) noexcept { return val.inverse_helper<Modulus::is_prime>(); }friend constexpr modular power(modular val, cover_type exp) noexcept {modular res(1);for (; exp > 0; exp >>= 1, val *= val) if (exp & 1) res *= val;return res;}};template <uint32_t Mod, bool IsPrime = true>struct static_modulus {static constexpr uint32_t mod() noexcept { return Mod; }static constexpr bool is_prime = IsPrime;};template <uint32_t Id = 0, bool IsPrime = false>struct dynamic_modulus {static uint32_t &mod() noexcept { static uint32_t val = 0; return val; }static constexpr bool is_prime = IsPrime;};template <uint32_t Mod, bool IsPrime = true>using mint32_t = modular<static_modulus<Mod, IsPrime>>;using rmint32_t = modular<dynamic_modulus<>>;/** @title Modint*/#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/container/fenwick_tree.cpp"#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/other/bit_operation.cpp"#include <cstddef>#line 5 "/Users/kodamankod/Desktop/cpp_programming/Library/other/bit_operation.cpp"constexpr size_t bit_ppc(const uint64_t x) { return __builtin_popcountll(x); }constexpr size_t bit_ctzr(const uint64_t x) { return x == 0 ? 64 : __builtin_ctzll(x); }constexpr size_t bit_ctzl(const uint64_t x) { return x == 0 ? 64 : __builtin_clzll(x); }constexpr size_t bit_width(const uint64_t x) { return 64 - bit_ctzl(x); }constexpr uint64_t bit_msb(const uint64_t x) { return x == 0 ? 0 : uint64_t(1) << (bit_width(x) - 1); }constexpr uint64_t bit_lsb(const uint64_t x) { return x & (-x); }constexpr uint64_t bit_cover(const uint64_t x) { return x == 0 ? 0 : bit_msb(2 * x - 1); }constexpr uint64_t bit_rev(uint64_t x) {x = ((x >> 1) & 0x5555555555555555) | ((x & 0x5555555555555555) << 1);x = ((x >> 2) & 0x3333333333333333) | ((x & 0x3333333333333333) << 2);x = ((x >> 4) & 0x0F0F0F0F0F0F0F0F) | ((x & 0x0F0F0F0F0F0F0F0F) << 4);x = ((x >> 8) & 0x00FF00FF00FF00FF) | ((x & 0x00FF00FF00FF00FF) << 8);x = ((x >> 16) & 0x0000FFFF0000FFFF) | ((x & 0x0000FFFF0000FFFF) << 16);x = (x >> 32) | (x << 32);return x;}/*** @title Bit Operations*/#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/container/fenwick_tree.cpp"#line 8 "/Users/kodamankod/Desktop/cpp_programming/Library/container/fenwick_tree.cpp"#include <type_traits>template <class T>class fenwick_tree {public:using value_type = T;using size_type = size_t;private:std::vector<value_type> M_tree;public:fenwick_tree() = default;explicit fenwick_tree(size_type size) { initialize(size); }void initialize(size_type size) {M_tree.assign(size + 1, value_type { });}void add(size_type index, const value_type& x) {assert(index < size());++index;while (index <= size()) {M_tree[index] += x;index += bit_lsb(index);}}template <size_type Indexed = 1>value_type get(size_type index) const {assert(index < size());index += Indexed;value_type res{ };while (index > 0) {res += M_tree[index];index -= bit_lsb(index);}return res;}value_type fold(size_type first, size_type last) const {assert(first <= last);assert(last <= size());value_type res{};while (first < last) {res += M_tree[last];last -= bit_lsb(last);}while (last < first) {res -= M_tree[first];first -= bit_lsb(first);}return res;}template <class Func>size_type satisfies(const size_type left, Func &&func) const {assert(left <= size());if (func(value_type { })) return left;value_type val = -get<0>(left);size_type res = 0;for (size_type cur = bit_cover(size() + 1) >> 1; cur > 0; cur >>= 1) {if ((res + cur <= left) || (res + cur <= size() && !func(val + M_tree[res + cur]))) {val += M_tree[res + cur];res += cur;}}return res + 1;}void clear() {M_tree.clear();M_tree.shrink_to_fit();}size_type size() const {return M_tree.size() - 1;}};/*** @title Fenwick Tree*/#line 17 "main.cpp"using i32 = std::int32_t;using i64 = std::int64_t;using u32 = std::uint32_t;using u64 = std::uint64_t;using isize = std::ptrdiff_t;using usize = std::size_t;constexpr i32 inf32 = (i32(1) << 30) - 1;constexpr i64 inf64 = (i64(1) << 62) - 1;using Fp = mint32_t<998244353>;int main() {usize N;std::cin >> N;std::vector<u32> A(N);for (auto &x: A) {std::cin >> x;}auto cmp = A;std::sort(cmp.begin(), cmp.end());cmp.erase(std::unique(cmp.begin(), cmp.end()), cmp.end());std::vector<usize> idx(N);for (auto i: range(0, N)) {idx[i] = std::lower_bound(cmp.begin(), cmp.end(), A[i]) - cmp.begin();}fenwick_tree<Fp> lcnt(cmp.size()), rcnt(cmp.size());fenwick_tree<Fp> lsum(cmp.size()), rsum(cmp.size());for (auto i: range(0, N)) {rcnt.add(idx[i], Fp(1));rsum.add(idx[i], Fp(A[i]));}Fp ans;for (auto i: range(0, N)) {rcnt.add(idx[i], -Fp(1));rsum.add(idx[i], -Fp(A[i]));const auto L = lcnt.fold(idx[i] + 1, cmp.size());const auto R = rcnt.fold(0, idx[i]);ans += L * rsum.fold(0, idx[i]) + R * lsum.fold(idx[i] + 1, cmp.size()) + L * R * Fp(A[i]);lcnt.add(idx[i], Fp(1));lsum.add(idx[i], Fp(A[i]));}std::cout << ans << '\n';return 0;}