結果

問題 No.1193 Penguin Sequence
コンテスト
ユーザー kaage
提出日時 2020-07-31 00:11:19
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 342 ms / 2,000 ms
コード長 6,570 bytes
コンパイル時間 1,499 ms
コンパイル使用メモリ 133,240 KB
実行使用メモリ 21,376 KB
最終ジャッジ日時 2024-10-01 21:22:06
合計ジャッジ時間 10,636 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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ファイルパターン 結果
sample AC * 3
other AC * 38
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 2 "/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#pragma target("avx")
#pragma optimize("O3")
#pragma optimize("unroll-loops")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define rep(i,n) for(int i=0;i<(lint)(n);i++)
#define REP(i,n) for(int i=1;i<=(lint)(n);i++)
#define all(V) V.begin(),V.end()
typedef long long lint;
typedef unsigned long long ulint;
typedef std::pair<int, int> P;
typedef std::pair<lint, lint> LP;
constexpr int INF = INT_MAX/2;
constexpr lint LINF = LLONG_MAX/2;
constexpr double eps = DBL_EPSILON;
constexpr double PI=3.141592653589793238462643383279;
template<class T>
class prique :public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
template <class T, class U>
inline bool chmax(T& lhs, const U& rhs) {
	if (lhs < rhs) {
		lhs = rhs;
		return 1;
	}
	return 0;
}
template <class T, class U>
inline bool chmin(T& lhs, const U& rhs) {
	if (lhs > rhs) {
		lhs = rhs;
		return 1;
	}
	return 0;
}
inline lint gcd(lint a, lint b) {
	while (b) {
		lint c = a;
		a = b; b = c % b;
	}
	return a;
}
inline lint lcm(lint a, lint b) {
	return a / gcd(a, b) * b;
}
bool isprime(lint n) {
	if (n == 1)return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0)return false;
	}
	return true;
}
template<typename T>
T mypow(T a, lint b) {
	if (!b)return T(1);
	if (b & 1)return mypow(a, b - 1) * a;
	T memo = mypow(a, b >> 1);
	return memo * memo;
}
lint modpow(lint a, lint b, lint m) {
	if (!b)return 1;
	if (b & 1)return modpow(a, b - 1, m) * a % m;
	lint memo = modpow(a, b >> 1, m);
	return memo * memo % m;
}
template<typename T>
void printArray(std::vector<T>& vec) {
	rep(i, vec.size() - 1)std::cout << vec[i] << " ";
	std::cout << vec.back() << std::endl;
}
template<typename T>
void printArray(T l, T r) {
	T rprev = r;
	rprev--;
	for (T i = l; i != rprev; i++) {
		std::cout << *i << " ";
	}
	std::cout << *rprev << std::endl;
}
#line 3 "/Users/kaage/Desktop/ProgrammingWorkspace/library/algebraic/ModInt.hpp"
class ModInt {
    lint value;
public:
    static const unsigned int modulo;
    ModInt() : value(0) {}
    template<typename T>
    ModInt(T value = 0) : value(value) {
        if (value < 0)value = -(lint)(-value % modulo) + modulo;
        this->value = value % modulo;
    }
    inline operator int()const { return value; }
    inline ModInt& operator+=(const ModInt& x) {
        value += x.value;
        if (value >= modulo)value -= modulo;
        return *this;
    }
    inline ModInt& operator++() {
        if (value == modulo - 1)value = 0;
        else value++;
        return *this;
    }
    inline ModInt operator-()const {
        return ModInt(0) -= *this;
    }
    inline ModInt& operator-=(const ModInt& x) {
        value -= x.value;
        if (value < 0)value += modulo;
        return *this;
    }
    inline ModInt& operator--() {
        if (value == 0)value = modulo - 1;
        else value--;
        return *this;
    }
    inline ModInt& operator*=(const ModInt& x) {
        value = value * x.value % modulo;
        return *this;
    }
    inline ModInt& operator/=(ModInt rhs) {
        int exp = modulo - 2;
        while (exp) {
            if (exp & 1)*this *= rhs;
            rhs *= rhs;
            exp >>= 1;
        }
        return *this;
    }
    template<typename T> ModInt operator+(const T& rhs)const { return ModInt(*this) += rhs; }
    template<typename T> ModInt& operator+=(const T& rhs) { return operator+=(ModInt(rhs)); }
    template<typename T> ModInt operator-(const T& rhs)const { return ModInt(*this) -= rhs; }
    template<typename T> ModInt& operator-=(const T& rhs) { return operator-=(ModInt(rhs)); }
    template<typename T> ModInt operator*(const T& rhs)const { return ModInt(*this) *= rhs; }
    template<typename T> ModInt& operator*=(const T& rhs) { return operator*=(ModInt(rhs)); }
    template<typename T> ModInt operator/(const T& rhs)const { return ModInt(*this) /= rhs; }
    template<typename T> ModInt& operator/=(const T& rhs) { return operator/=(ModInt(rhs)); }
};
std::istream& operator>>(std::istream& ist, ModInt& x) {
    lint a;
    ist >> a;
    x = a;
    return ist;
}
#line 3 "/Users/kaage/Desktop/ProgrammingWorkspace/library/data-structure/BIT.hpp"
class BIT {
	unsigned int n;
	std::vector<lint> bit;
public:
	BIT(unsigned int n) :n(n) {
		bit.resize(n + 1, 0);
	}
	void add(int a, lint x) {
		while (a <= n) {
			bit[a] += x;
			a += a & -a;
		}
	}
	lint query(int a) {
		lint cnt = 0;
		while (a > 0) {
			cnt += bit[a];
			a -= a & -a;
		}
		return cnt;
	}
	void clear() {
		bit.assign(n + 1, 0);
	}
	unsigned int lower_bound(int x){
		int p=0,k=1;
		while(k*2<=n)k*=2;
		while(k>0){
			if(p+k<=n&&bit[p+k]<x){
				x-=bit[p+k];
				p+=k;
			}
			k/=2;
		}
		return p+1;
	}
	unsigned int upper_bound(int x){
		int p=0,k=1;
		while(k*2<=n)k*=2;
		while(k>0){
			if(p+k<=n&&bit[p+k]<=x){
				x-=bit[p+k];
				p+=k;
			}
			k/=2;
		}
		return p+1;
	}
};
#line 4 "main.cpp"
const unsigned int ModInt::modulo=998244353;
int n,a[200010];
std::map<int,P> mp;
ModInt fact[200010],inv[200010];
ModInt comb(int a,int b){
    return fact[a]*inv[a-b]*inv[b];
}
int main(){
    assert(scanf("%d",&n));
    assert(1<=n&&n<=200000);
    rep(i,n){
        assert(scanf("%d",a+i));
        assert(1<=a[i]&&a[i]<=1000000000);
        mp[a[i]].second++;
    }
    int count=1;
    for(auto& i:mp)i.second.first=count++;
    rep(i,n)a[i]=mp[a[i]].first;

    fact[0]=1;
    REP(i,n)fact[i]=fact[i-1]*i;
    inv[n]=ModInt(1)/fact[n];
    for(int i=n-1;i>=0;i--)inv[i]=inv[i+1]*(i+1);

    BIT bit(mp.size()+1);
    ModInt swaps=0;
    rep(i,n){
        swaps+=bit.query(mp.size())-bit.query(a[i]);
        bit.add(a[i],1);
    }

    ModInt r=1;
    rep(i,n)r*=comb(n,i);

    ModInt ans=0;
    for(int i=2;i<=n;i++)ans+=ModInt(i)*(i-1)/n/(n-1);
    ans*=swaps*r;

    ModInt cnt=-ModInt(1)/4*n*n*(n-1)*(n-1)-ModInt(1)/6*n*(n-1)*(2*n-1)+ModInt(1)/2*n*n*(n-1)*(n+1);
    cnt/=ModInt(2)*n*n;
    ModInt p=ModInt(n)*(n-1)/2;
    for(const auto& i:mp)p-=ModInt(i.second.second)*(i.second.second-1)/2;
    ans+=cnt*r*p;

    printf("%d\n",ans);
}
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