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;
}