题意：给定一个无穷项的分式，它的和等于π，问π的十六进制表示的小数点后第n位是多少
1 ≤ n ≤ 100000
思路：From https://blog.csdn.net/meopass/article/details/78327614
C++double写起来细节真是烦
1 #include<cstdio> 2 #include<cstring> 3 #include<string> 4 #include<cmath> 5 #include<iostream> 6 #include<algorithm> 7 #include<map> 8 #include<set> 9 #include<queue> 10 #include<vector> 11 using namespace std; 12 typedef long long ll; 13 typedef unsigned int uint; 14 typedef unsigned long long ull; 15 typedef pair<int,int> PII; 16 typedef vector<int> VI; 17 #define fi first 18 #define se second 19 #define MP make_pair 20 #define N 11000 21 #define M 41 22 #define eps 1e-8 23 #define pi acos(-1) 24 25 26 27 int read() 28 { 29 int v=0,f=1; 30 char c=getchar(); 31 while(c<48||57<c) {if(c=='-') f=-1; c=getchar();} 32 while(48<=c&&c<=57) v=(v<<3)+v+v+c-48,c=getchar(); 33 return v*f; 34 } 35 36 ll Pow(ll a,ll b,ll MOD) 37 { 38 ll ans=1; 39 while(b) 40 { 41 if(b&1) ans=ans*a%MOD; 42 a=a*a%MOD; 43 b>>=1; 44 } 45 return ans; 46 } 47 48 double BBP(int n,ll k,ll b) 49 { 50 double ans=0; 51 for(int i=0;i<=n;i++) ans+=(Pow(16,n-i,8*i+b)*1.0/(8*i+b)); 52 for(int i=n+1;i<=n+1001;i++) ans+=(powf(16,n-i)/(8*i+b)); 53 return k*ans; 54 } 55 56 int main() 57 { 58 //freopen("hdoj6217.in","r",stdin); 59 //freopen("hdoj6217.out","w",stdout); 60 int cas; 61 scanf("%d",&cas); 62 for(int v=1;v<=cas;v++) 63 { 64 int n; 65 scanf("%d",&n); 66 n--; 67 double ans=0.0; 68 ans=BBP(n,4,1)+BBP(n,-2,4)+BBP(n,-1,5)+BBP(n,-1,6); 69 ans-=int(ans); 70 if(ans<0) ans++; 71 ans*=16; 72 char ch; 73 int p=int(ans); 74 if(0<=p&&p<=9) ch=p+'0'; 75 else if(p==10) ch='A'; 76 else if(p==11) ch='B'; 77 else if(p==12) ch='C'; 78 else if(p==13) ch='D'; 79 else if(p==14) ch='E'; 80 else if(p==15) ch='F'; 81 printf("Case #%d: %d %c ",v,n+1,ch); 82 83 } 84 return 0; 85 } 86