Luogu5367 【模板】康托展开（康拓展开）

\(n^2\)暴力

#include <iostream>

#include <cstdio>

#include <cstring>

#include <algorithm>

#include <cmath>

#define R(a,b,c) for(register int  a = (b); a <= (c); ++ a)

#define nR(a,b,c) for(register int  a = (b); a >= (c); -- a)

#define Max(a,b) ((a) > (b) ? (a) : (b))

#define Min(a,b) ((a) < (b) ? (a) : (b))

#define Fill(a,b) memset(a, b, sizeof(a))

#define Abs(a) ((a) < 0 ? -(a) : (a))

#define Swap(a,b) a^=b^=a^=b

#define ll long long

#define ON_DEBUG

#ifdef ON_DEBUG

#define D_e_Line printf("\n\n----------\n\n")

#define D_e(x)  cout << #x << " = " << x << endl

#define Pause() system("pause")

#define FileOpen() freopen("in.txt","r",stdin);

#else

#define D_e_Line ;

#define D_e(x)  ;

#define Pause() ;

#define FileOpen() ;

#endif

struct ios{

    template<typename ATP>ios& operator >> (ATP &x){

        x = 0; int f = 1; char c;

        for(c = getchar(); c < '0' || c > '9'; c = getchar()) if(c == '-')  f = -1;

        while(c >= '0' && c <= '9') x = x * 10 + (c ^ '0'), c = getchar();

        x*= f;

        return *this;

    }

}io;

using namespace std;

const int mod = 998244353;

int fac[1000007];

int n;

inline int Cantor(int *a, int n){

	int ans = 1, sum = 0;

	R(i,1,n){

		R(j,i+1,n){

			sum += (a[i] > a[j]);

			if(sum > mod) sum -= mod;

		}

		ans = (ans + 1ll * sum * fac[n - i] % mod) % mod;

		sum = 0;

	}

	return ans;

}

int a[1000007];

int main(){

    int n;

    io >> n;

    fac[0] = 1;

    R(i,1,n){

		io >> a[i];

		fac[i] = 1ll * fac[i - 1] * i % mod;

	}

	printf("%d", Cantor(a, n));

    return 0;

}

BIT优化

#include <iostream>

#include <cstdio>

#include <cstring>

#include <algorithm>

#include <cmath>

#define R(a,b,c) for(register int  a = (b); a <= (c); ++ a)

#define nR(a,b,c) for(register int  a = (b); a >= (c); -- a)

#define Max(a,b) ((a) > (b) ? (a) : (b))

#define Min(a,b) ((a) < (b) ? (a) : (b))

#define Fill(a,b) memset(a, b, sizeof(a))

#define Abs(a) ((a) < 0 ? -(a) : (a))

#define Swap(a,b) a^=b^=a^=b

#define ll long long

#define ON_DEBUG

#ifdef ON_DEBUG

#define D_e_Line printf("\n\n----------\n\n")

#define D_e(x)  cout << #x << " = " << x << endl

#define Pause() system("pause")

#define FileOpen() freopen("in.txt","r",stdin);

#else

#define D_e_Line ;

#define D_e(x)  ;

#define Pause() ;

#define FileOpen() ;

#endif

struct ios{

    template<typename ATP>ios& operator >> (ATP &x){

        x = 0; int f = 1; char c;

        for(c = getchar(); c < '0' || c > '9'; c = getchar()) if(c == '-')  f = -1;

        while(c >= '0' && c <= '9') x = x * 10 + (c ^ '0'), c = getchar();

        x*= f;

        return *this;

    }

}io;

using namespace std;

const int N = 1000007;

const int mod = 998244353;

int n;

int t[N];

inline void Updata(int x, int w){

	for(; x <= n; x += x&-x) t[x] += w;

}

inline int Query(int x){

	int sum = 0;

	for(; x; x -= x&-x) sum += t[x];

	return sum;

}

int a[N];

int main(){

	//FileOpen();

    io >> n;

	int fac = 1;

    nR(i,n,1){

    	io >> a[i];

    }

    int ans = 0;

    R(i,1,n){

    	int sum = Query(a[i]);

        ans = (ans + 1ll * fac * sum % mod) % mod;

		fac = 1ll * fac * i % mod;

        Updata(a[i], 1);

    }

	printf("%d\n", ans + 1);

    return 0;

}

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Luogu5367 【模板】康托展开（康拓展开）

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巴特西

Luogu5367 【模板】康托展开 （康拓展开）

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Luogu5367 【模板】康托展开（康拓展开）