結果

問題 No.1300 Sum of Inversions
ユーザー tkmst201tkmst201
提出日時 2020-11-27 21:49:19
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 154 ms / 2,000 ms
コード長 5,895 bytes
コンパイル時間 2,395 ms
コンパイル使用メモリ 211,836 KB
最終ジャッジ日時 2025-01-16 06:54:51
ジャッジサーバーID
（参考情報） 		judge3 / 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 * 34
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function ‘int main()’:
main.cpp:132:24: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
  132 |         REP(i, N) scanf("%d", &A[i]);
      |                   ~~~~~^~~~~~~~~~~~~

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) begin(v),end(v)
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
using ll = long long;
using pii = pair<int, int>;
constexpr ll INF = 1ll<<30;
constexpr ll longINF = 1ll<<60;
constexpr ll MOD = 998244353;
constexpr bool debug = false;
//---------------------------------//

template<int M>
struct ModInt {
	static_assert(M > 0);
	
public:
	using value_type = int;
	using calc_type = std::int_fast64_t;
	
private:
	value_type val_;
	
public:
	constexpr ModInt(calc_type val = 0) : val_(val < 0 ? (val % M + M) % M : val % M) {}
	constexpr const value_type & val() const noexcept { return val_; }
	constexpr static decltype(M) mod() noexcept { return M; }
	
	explicit constexpr operator bool() const noexcept { return val_; }
	constexpr bool operator !() const noexcept { return !static_cast<bool>(*this); }
	constexpr ModInt operator +() const noexcept { return ModInt(*this); }
	constexpr ModInt operator -() const noexcept { return ModInt(-val_); }
	constexpr ModInt operator ++(int) noexcept { ModInt res = *this; ++*this; return res; }
	constexpr ModInt operator --(int) noexcept { ModInt res = *this; --*this; return res; }
	constexpr ModInt & operator ++() noexcept { val_ = val_ + 1 == M ? 0 : val_ + 1; return *this; }
	constexpr ModInt & operator --() noexcept { val_ = val_ == 0 ? M - 1 : val_ - 1; return *this; }
	constexpr ModInt & operator +=(const ModInt & rhs) noexcept { val_ += val_ < M - rhs.val_ ? rhs.val_ : rhs.val_ - M; return *this; }
	constexpr ModInt & operator -=(const ModInt & rhs) noexcept { val_ += val_ >= rhs.val_ ? -rhs.val_ : M - rhs.val_; return *this; }
	constexpr ModInt & operator *=(const ModInt & rhs) noexcept { val_ = static_cast<calc_type>(val_) * rhs.val_ % M; return *this; }
	constexpr ModInt & operator /=(const ModInt & rhs) noexcept { return *this *= rhs.inv(); }
	friend constexpr ModInt operator +(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) += rhs; }
	friend constexpr ModInt operator -(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) -= rhs; }
	friend constexpr ModInt operator *(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) *= rhs; }
	friend constexpr ModInt operator /(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) /= rhs; }
	friend constexpr bool operator ==(const ModInt & lhs, const ModInt & rhs) noexcept { return lhs.val_ == rhs.val_; }
	friend constexpr bool operator !=(const ModInt & lhs, const ModInt & rhs) noexcept { return !(lhs == rhs); }
	friend std::ostream & operator <<(std::ostream & os, const ModInt & rhs) { return os << rhs.val_; }
	friend std::istream & operator >>(std::istream & is, ModInt & rhs) { calc_type x; is >> x; rhs = ModInt(x); return is; }
	
	constexpr ModInt pow(calc_type n) const noexcept {
		ModInt res = 1, x = val_;
		if (n < 0) { x = x.inv(); n = -n; }
		while (n) { if (n & 1) res *= x; x *= x; n >>= 1; }
		return res;
	}
	
	constexpr ModInt inv() const noexcept {
		value_type a = val_, a1 = 1, a2 = 0, b = M, b1 = 0, b2 = 1;
		while (b > 0) {
			value_type q = a / b, r = a % b;
			value_type nb1 = a1 - q * b1, nb2 = a2 - q * b2;
			a = b; b = r;
			a1 = b1; b1 = nb1;
			a2 = b2; b2 = nb2;
		}
		assert(a == 1);
		return a1;
	}
};
using mint = ModInt<MOD>;

template<typename T>
struct BinaryIndexedTree {
	using value_type = T;
	using const_reference = const value_type &;
	using F = std::function<value_type(const_reference, const_reference)>;
	using size_type = std::size_t;
	
	BinaryIndexedTree(size_type n, const F & f, const_reference id_elem) : n(n), f(f), id_elem(id_elem) {
		node.resize(n + 1, id_elem);
	}
	
	size_type size() const noexcept {
		return n;
	}
	
	void add(size_type i, const_reference x) {
		assert(i < size());
		++i;
		for (; i <= size(); i += i & -i) node[i] = f(node[i], x);
	}
	
	// [0, i)
	value_type sum(size_type i) const {
		assert(i <= size());
		value_type res = id_elem;
		for (; i > 0; i -= i & -i) res = f(res, node[i]);
		return res;
	}
	
	// sum[0, r] <= x を満たす最小の r を返す (存在しなければ size())
	size_type lower_bound(const_reference x) const {
		size_type res = 0;
		size_type s = id_elem, w = 1;
		while (w < size()) w <<= 1;
		for (; w > 0; w >>= 1) {
			if (res + w <= size()) {
				value_type cur = f(s, node[res + w]);
				if (cur < x) {
					res += w;
					s = cur;
				}
			}
		}
		return res;
	}
	
private:
	size_type n;
	F f;
	value_type id_elem;
	std::vector<value_type> node;
};

int main() {
	int N;
	cin >> N;
	vector<int> A(N);
	REP(i, N) scanf("%d", &A[i]);
	
	vector<int> cx;
	auto compress = [](auto &&v, auto &&cv) -> void {
		for (auto &&u : v) cv.emplace_back(u);
		cv.emplace_back(INF);
		cv.emplace_back(-INF);
		std::sort(std::begin(cv), std::end(cv));
		cv.erase(std::unique(std::begin(cv), std::end(cv)), std::end(cv));
		for (auto &&u : v) u = std::lower_bound(std::begin(cv), std::end(cv), u) - std::begin(cv);
	};
	compress(A, cx);
	
	using P = pair<mint, mint>;
	BinaryIndexedTree<P> rbit(cx.size(), [](const P & x, const P & y) { return P{x.first + y.first, x.second + y.second}; }, P{0, 0});
	auto lbit = rbit;
	
	FOR(i, 2, N) rbit.add(A[i], P{1, cx[A[i]]});
	lbit.add(A[0], P{1, cx[A[0]]});
	
	mint ans = 0;
	FOR(i, 1, N - 1) {
		auto l1 = lbit.sum(cx.size()), l2 = lbit.sum(A[i] + 1);
		auto r1 = rbit.sum(A[i]);
		
		ans += (l1.second - l2.second) * r1.first;
		ans += (l1.first - l2.first) * r1.second;
		ans += (l1.first - l2.first) * r1.first * cx[A[i]];
		lbit.add(A[i], {1, cx[A[i]]});
		rbit.add(A[i + 1], {-1, -cx[A[i + 1]]});
	}
	cout << ans << endl;
}
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