CodeM 2018 决赛
A 大力推一下式子 n * sigma i from 2 to n+1 ( C(n-1, i-2) * (i-2)! * (2n-i)! / 2^(n+1-i) ) 就没有然后了
1 /* *********************************************** 2 Author :BPM136 3 Created Time :2018/7/27 10:39:22 4 File Name :A.cpp 5 ************************************************ */ 6 7 #include<iostream> 8 #include<cstdio> 9 #include<algorithm> 10 #include<cstdlib> 11 #include<cmath> 12 #include<cstring> 13 #include<iomanip> 14 #include<bitset> 15 #include<queue> 16 #include<ctime> 17 #include<set> 18 #include<map> 19 #include<vector> 20 #include<cassert> 21 #include<functional> 22 #define pb push_back 23 #define popb pop_back 24 #define MID ((l+r)>>1) 25 #define LSON (k<<1) 26 #define RSON (k<<1|1) 27 #define get(a,i) ((a)&(1<<(i-1))) 28 #define PAU putchar(32) 29 #define ENT putchar(10) 30 #define clr(a,b) memset(a,b,sizeof(a)) 31 #define rep(_i,_a,_b) for(int _i=(_a);_i<=(_b);_i++) 32 #define down(_i,_a,_b) for(int _i=(_a);_i>=(_b);_i--) 33 #define FOR(_i,_b) for(int _i=1;_i<=(_b);_i++) 34 #define efo(_i,_a) for(int _i=last[(_a)];_i!=0;_i=e[_i].next) 35 #define Remax(a,b) if(b>a) a=b; 36 #define Remin(a,b) if(b<a) a=b; 37 #define filein(x) freopen(#x".in","r",stdin) 38 #define fileout(x) freopen(#x".out","w",stdout) 39 #define file(x) freopen(#x".in","r",stdin),freopen(#x".out","w",stdout); 40 #define mkd(x) freopen(#x".in","w",stdout); 41 #define setlargestack(x) int _SIZE=x<<20;char *_PPP=(char*)malloc(size)+_SIZE;__asm__("movl %0, %%esp\n" :: "r"(_PPP)); 42 #define END system("pause") 43 #define read2(a,b) read(a),read(b) 44 #define read3(a,b,c) read(a),read(b),read(c) 45 #define readg(_x1,_y1,_x2,_y2) read(_x1),read(_y1),read(_x2),read(_y2) 46 using namespace std; 47 48 typedef long long ll; 49 typedef double DB; 50 typedef long double LD; 51 typedef unsigned int UI; 52 typedef unsigned long long ULL; 53 typedef vector<int> VI; 54 typedef set<int> SI; 55 typedef set<int , greater<int> > SIG; 56 typedef map<int, int > MII; 57 typedef map<int, int, greater<int> > MIIG; 58 59 namespace fastIO{ 60 #define BUF_SIZE 100000 61 #define OUT_SIZE 100000 62 //fread->read 63 bool IOerror=0; 64 inline char nc(){ 65 static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE; 66 if (p1==pend){ 67 p1=buf; pend=buf+fread(buf,1,BUF_SIZE,stdin); 68 if (pend==p1){IOerror=1;return -1;} 69 //{printf("IO error!\n");system("pause");for (;;);exit(0);} 70 } 71 return *p1++; 72 } 73 inline bool blank(char ch){return ch==32||ch==10||ch==13||ch==9;} 74 inline bool enter(char ch){return ch==10||ch==13;} 75 inline void read(int &x){ 76 bool sign=0; char ch=nc(); x=0; 77 for (;blank(ch);ch=nc()); 78 if (IOerror)return; 79 if (ch==45)sign=1,ch=nc(); 80 for (;ch>=48&&ch<=57;ch=nc())x=x*10+ch-48; 81 if (sign)x=-x; 82 } 83 inline void read(ll &x){ 84 bool sign=0; char ch=nc(); x=0; 85 for (;blank(ch);ch=nc()); 86 if (IOerror)return; 87 if (ch==45)sign=1,ch=nc(); 88 for (;ch>=48&&ch<=57;ch=nc())x=x*10+ch-48; 89 if (sign)x=-x; 90 } 91 inline void read(double &x){ 92 bool sign=0; char ch=nc(); x=0; 93 for (;blank(ch);ch=nc()); 94 if (IOerror)return; 95 if (ch==45)sign=1,ch=nc(); 96 for (;ch>=48&&ch<=57;ch=nc())x=x*10+ch-48; 97 if (ch==46){ 98 double tmp=1; ch=nc(); 99 for (;ch>=48&&ch<=57;ch=nc())tmp/=10.0,x+=tmp*(ch-48); 100 } 101 if (sign)x=-x; 102 } 103 inline void read(char *s){ 104 char ch=nc(); 105 for (;blank(ch);ch=nc()); 106 if (IOerror)return; 107 for (;!blank(ch)&&!IOerror;ch=nc())*s++=ch; 108 *s=0; 109 } 110 inline void read(char *s,bool f) { 111 char ch=nc(); 112 for (;blank(ch);ch=nc()); 113 if(IOerror)return; 114 for(;!enter(ch)&&!IOerror;ch=nc())*s++=ch; 115 *s=0; 116 } 117 inline void read(char &c){ 118 for (c=nc();blank(c);c=nc()); 119 if (IOerror){c=-1;return;} 120 } 121 #undef OUT_SIZE 122 #undef BUF_SIZE 123 }; using namespace fastIO; 124 125 const int N = 2000005; 126 const ll MOD = 998244353; 127 128 ll inv[N]; 129 ll fac[N]; 130 ll fac_inv[N]; 131 ll bit2_inv[N]; 132 133 ll C(int n,int m) { 134 return fac[n]*fac_inv[m]%MOD*fac_inv[n-m]%MOD; 135 } 136 137 int main() { 138 inv[0]=fac[0]=1; inv[1]=1; 139 rep(i,1,N-1) fac[i]=fac[i-1]*i%MOD; 140 rep(i,2,N-1) inv[i]=(MOD-MOD/i)*inv[MOD%i]%MOD; 141 fac_inv[0]=1; rep(i,1,N-1) fac_inv[i]=fac_inv[i-1]*inv[i]%MOD; 142 bit2_inv[0]=1; rep(i,1,N-1) bit2_inv[i]=bit2_inv[i-1]*inv[2]%MOD; 143 ll n; 144 cin>>n; 145 ll ans=0; 146 rep(i,2,n+1) { 147 ans+=C(n-1,i-2) * fac[i-2] % MOD 148 *fac[2*n-i] % MOD * bit2_inv[n+1-i] % MOD; 149 ans%=MOD; 150 } 151 cout<<ans*n%MOD<<endl; 152 return 0; 153 }
