36 lines
678 B
C++
36 lines
678 B
C++
#include<cstdio>
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#include<cmath>
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//C(n,m)=n!/(m!(n-m)!)
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const int maxn=200004;
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long double logF[maxn*2+1];
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inline long double logC(int n,int m)
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{
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return logF[n]-logF[m]-logF[n-m];
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}
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double solve(int n,double p)
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{
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double res=0;
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for(int i=0;i<=n;i++)
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{
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long double c=logC(n*2-i,n);
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long double v1=c+(n+1)*log(p)+(n-i)*log(1-p);
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long double v2=c+(n+1)*log(1-p)+(n-i)*log(p);
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res+=i*(exp(v1)+exp(v2));
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}
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return res;
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}
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int kase=0,n;
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double p;
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int main()
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{
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#ifdef local
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freopen("pro.in","r",stdin);
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#endif
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logF[0]=0;
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for(int i=1;i<=maxn;i++)
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logF[i]=logF[i-1]+log(i);
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while(scanf("%d%lf",&n,&p)==2)
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printf("Case %d: %.6lf\n", ++kase, solve(n, p));
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return 0;
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}
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