結果

問題 No.1300 Sum of Inversions
ユーザー Imperi_NightImperi_Night
提出日時 2020-11-27 21:52:10
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,296 ms / 2,000 ms
コード長 8,374 bytes
コンパイル時間 1,960 ms
コンパイル使用メモリ 144,180 KB
実行使用メモリ 258,612 KB
最終ジャッジ日時 2023-10-01 05:27:26
合計ジャッジ時間 32,406 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge15
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
4,380 KB
testcase_01 AC 2 ms
4,376 KB
testcase_02 AC 1 ms
4,376 KB
testcase_03 AC 988 ms
208,196 KB
testcase_04 AC 966 ms
202,832 KB
testcase_05 AC 787 ms
172,204 KB
testcase_06 AC 1,118 ms
229,780 KB
testcase_07 AC 1,069 ms
221,364 KB
testcase_08 AC 1,192 ms
241,224 KB
testcase_09 AC 1,196 ms
240,128 KB
testcase_10 AC 680 ms
146,456 KB
testcase_11 AC 685 ms
147,712 KB
testcase_12 AC 975 ms
204,376 KB
testcase_13 AC 955 ms
199,720 KB
testcase_14 AC 1,296 ms
258,612 KB
testcase_15 AC 1,190 ms
238,540 KB
testcase_16 AC 1,024 ms
212,332 KB
testcase_17 AC 647 ms
142,180 KB
testcase_18 AC 744 ms
160,176 KB
testcase_19 AC 900 ms
183,876 KB
testcase_20 AC 901 ms
187,592 KB
testcase_21 AC 887 ms
186,840 KB
testcase_22 AC 803 ms
171,944 KB
testcase_23 AC 1,126 ms
229,492 KB
testcase_24 AC 838 ms
177,036 KB
testcase_25 AC 728 ms
155,312 KB
testcase_26 AC 706 ms
153,224 KB
testcase_27 AC 785 ms
167,796 KB
testcase_28 AC 1,213 ms
246,152 KB
testcase_29 AC 888 ms
185,784 KB
testcase_30 AC 1,195 ms
239,640 KB
testcase_31 AC 821 ms
173,812 KB
testcase_32 AC 857 ms
178,536 KB
testcase_33 AC 116 ms
11,040 KB
testcase_34 AC 147 ms
11,192 KB
testcase_35 AC 267 ms
48,672 KB
testcase_36 AC 267 ms
48,464 KB
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 # 

#line 1 "main.cpp"
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdint>
#include <cstdlib>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <type_traits>
#include <unordered_map>
#include <utility>
#include <vector>

/* template start */

using i64 = std::int_fast64_t;
using u64 = std::uint_fast64_t;

i64 operator"" _i64(unsigned long long num){
  return i64(num);
}
 
u64 operator"" _u64(unsigned long long num){
  return u64(num);
}

#define rep(i, a, b) for (i64 i = (a); (i) < (b); (i)++)
#define all(i) i.begin(), i.end()

#ifdef LOCAL
#define debug(...)                                                    \
  std::cerr << "LINE: " << __LINE__ << "  [" << #__VA_ARGS__ << "]:", \
      debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

void debug_out() { std::cerr << std::endl; }

template <typename Head, typename... Tail>
void debug_out(Head h, Tail... t) {
  std::cerr << " " << h;
  if (sizeof...(t) > 0) std::cout << " :";
  debug_out(t...);
}

template <typename T1, typename T2>
std::ostream& operator<<(std::ostream& os, std::pair<T1, T2> pa) {
  return os << pa.first << " " << pa.second;
}

template <typename T>
std::ostream& operator<<(std::ostream& os, std::vector<T> vec) {
  for (std::size_t i = 0; i < vec.size(); i++)
    os << vec[i] << (i + 1 == vec.size() ? "" : " ");
  return os;
}

template <typename T1, typename T2>
inline bool chmax(T1& a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1& a, T2 b) {
  return a > b && (a = b, true);
}

template <typename Num>
constexpr Num mypow(Num a, u64 b, Num id = 1) {
  if (b == 0) return id;
  Num x = id;
  while (b > 0) {
    if (b & 1) x *= a;
    a *= a;
    b >>= 1;
  }
  return x;
}

/* template end */

#line 2 "/home/imperi/cp-library/lib/utility/modint.hpp"

/*
  author:noshi91
  reference:https://noshi91.hatenablog.com/entry/2019/03/31/174006
            https://github.com/noshi91/Library/blob/master/other/modint.cpp

  1つめのmodintにoperator==,!=を追加したものです

  thx @noshi91!!
*/

#line 14 "/home/imperi/cp-library/lib/utility/modint.hpp"

template <std::uint_fast64_t Modulus>
class modint {
  using u64 = std::uint_fast64_t;

 public:
  u64 a;

  constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr bool operator==(const modint rhs) const noexcept {
    return a == rhs.a;
  }
  constexpr bool operator!=(const modint rhs) const noexcept {
    return !(*this == rhs);
  }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint &operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }
  constexpr modint &operator-=(const modint rhs) noexcept {
    if (a < rhs.a) {
      a += Modulus;
    }
    a -= rhs.a;
    return *this;
  }
  constexpr modint &operator*=(const modint rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
};
#line 100 "main.cpp"

constexpr u64 MOD = 998244353;

using mint = modint<MOD>;

struct Monoid{
  using value_t = std::pair<mint,mint>;
  static constexpr value_t id = {0,0};
  static constexpr value_t op(value_t a,value_t b){
    return {a.first+b.first,a.second+b.second};
  }
};

#line 2 "/home/imperi/cp-library/lib/SegmentTree/DynamicSegmentTree.hpp"

#line 5 "/home/imperi/cp-library/lib/SegmentTree/DynamicSegmentTree.hpp"

// Monoid
// type value_t
// static var id
// static (value_t,value_t)->value_t op

template <typename Monoid>
class DynamicSegmentTree {
 public:
  using value_t = typename Monoid::value_t;
  using size_t = std::size_t;

 private:
  struct Node {
    value_t val;
    Node *left, *right, *par;
    Node(Node* par_ = nullptr) : val(Monoid::id), left(), right(), par(par_) {}
    ~Node() {
      if (left) delete left;
      if (right) delete right;
      left = nullptr;
      right = nullptr;
      par = nullptr;
    }
  };

  using node_ptr = Node*;

  size_t n, n0;
  node_ptr root;

  value_t fold(size_t a, size_t b, const node_ptr& now, size_t l, size_t r) {
    if (a <= l && r <= b) return now->val;
    if (b <= l || r <= a) return Monoid::id;
    value_t lval =
        (now->left) ? fold(a, b, now->left, l, l + (r - l) / 2) : Monoid::id;
    value_t rval =
        (now->right) ? fold(a, b, now->right, l + (r - l) / 2, r) : Monoid::id;
    return Monoid::op(lval, rval);
  }

  void copy_dfs(node_ptr& node, const node_ptr& from) {
    node->val = from->val;
    if (from->left) {
      node->left = new Node(node);
      copy_dfs(node->left, from->left);
    }
    if (from->right) {
      node->right = new Node(node);
      copy_dfs(node->right, from->right);
    }
  }

 public:
  DynamicSegmentTree(size_t n_ = 0) : n(n_), root(nullptr) {
    n0 = 1;
    while (n0 < n) n0 <<= 1;
  }
  DynamicSegmentTree(const DynamicSegmentTree& from) {
    n = from.n;
    n0 = from.n0;
    root = nullptr;
    if (from.root) {
      root = new Node();
      copy_dfs(root, from.root);
    }
  }
  DynamicSegmentTree& operator=(const DynamicSegmentTree& from) {
    n = from.n;
    n0 = from.n0;
    root = nullptr;
    if (from.root) {
      root = new Node();
      copy_dfs(root, from.root);
    }
  }
  DynamicSegmentTree(DynamicSegmentTree&&) = default;
  DynamicSegmentTree& operator=(DynamicSegmentTree&&) = default;
  ~DynamicSegmentTree() {
    if (root) delete root;
    root = nullptr;
  }

  void update(size_t i, value_t val, bool change) {
    assert(0 <= i && i < n);
    if (!root) root = new Node();
    node_ptr now = root;
    size_t l = 0, r = n0;
    while (r - l > 1) {
      size_t mid = l + (r - l) / 2;
      if (i < mid) {
        if (!now->left) now->left = new Node(now);
        now = now->left;
        r = mid;
      } else {
        if (!now->right) now->right = new Node(now);
        now = now->right;
        l = mid;
      }
    }
    if (change)
      now->val = val;
    else
      now->val = Monoid::op(now->val, val);

    while (now->par) {
      now = now->par;
      now->val = Monoid::op((now->left) ? now->left->val : Monoid::id,
                            (now->right) ? now->right->val : Monoid::id);
    }
  }

  value_t fold(size_t a, size_t b) {
    assert(0 <= a && a <= b && b <= n);
    if (!root) return Monoid::id;
    return fold(a, b, root, 0, n0);
  }
};
#line 114 "main.cpp"

int main() {
  std::cin.tie(nullptr);
  std::ios::sync_with_stdio(false);

  i64 n;
  std::cin>>n;

  std::vector<i64> a(n);
  for(auto&& e:a)std::cin>>e;

  std::reverse(all(a));

  constexpr i64 INF = 1e10;

  DynamicSegmentTree<Monoid> seg1(INF),seg2(INF);

  std::vector<mint> left_sum(n,0),right_sum(n,0);
  std::vector<mint> left_cnt(n,1),right_cnt(n,1);

  rep(i,0,n){
    auto tmp = seg1.fold(0,a[i]);
    left_sum[i] = tmp.first;
    left_cnt[i] = tmp.second;
    seg1.update(a[i],Monoid::value_t(a[i],1),false);
  }

  for(i64 i = n-1;i>=0;i--){
    auto tmp = seg2.fold(a[i]+1,INF);
    right_sum[i] = tmp.first;
    right_cnt[i] = tmp.second;
    seg2.update(a[i],Monoid::value_t(a[i],1),false);
  }

  mint ans = 0;

  rep(i,0,n){
    ans += left_sum[i] * right_cnt[i];
    ans += right_sum[i] * left_cnt[i];
    ans += left_cnt[i] * right_cnt[i] * a[i];
  }

  rep(i,0,n){
    debug(i,left_sum[i].value(),left_cnt[i].value());
  }
  for(i64 i = n-1;i>=0;i--){
    debug(i,right_sum[i].value(),right_cnt[i].value());
  }

  std::cout<<ans.value()<<"\n";

  return 0;
}
0