#include #define _overload(_1,_2,_3,name,...) name #define _rep(i,n) _range(i,0,n) #define _range(i,a,b) for(int i=int(a);i=int(b);--i) #define rrep(...) _overload(__VA_ARGS__,_rrange,_rrep,)(__VA_ARGS__) #define _all(arg) begin(arg),end(arg) #define uniq(arg) sort(_all(arg)),(arg).erase(unique(_all(arg)),end(arg)) #define getidx(ary,key) lower_bound(_all(ary),key)-begin(ary) #define clr(a,b) memset((a),(b),sizeof(a)) #define bit(n) (1LL<<(n)) #define popcount(n) (__builtin_popcountll(n)) using namespace std; templatebool chmax(T &a, const T &b) { return (abool chmin(T &a, const T &b) { return (bEPS=1e-8 [-10000,10000]->EPS=1e-7 inline int sgn(const R& r){return(r > EPS)-(r < -EPS);} inline R sq(R x){return sqrt(max(x,0.0));} const int dx[8]={1,0,-1,0,1,-1,-1,1}; const int dy[8]={0,1,0,-1,1,1,-1,-1}; // Problem Specific Parameter: using vec=valarray; using mat=valarray; const R eps=1e-10; vec gauss_jordan(mat &a){ const int n=a.size(),m=a[0].size(); rep(i,n){ int pivot=i; rep(j,i,n) if(abs(a[j][i])>abs(a[pivot][i])) pivot=j; swap(a[i],a[pivot]); if(abs(a[i][i])> p >> q; mat a(vec(0.0,102),101); rep(i,101) a[i][i]=1.0; rep(i,101){ int up=min(i+q,100),down=max(i-q,0); if(up==i){ const R coef=1.0/(1.0-1.0*(100-i)/100.0/3.0); a[i][down]-=coef*i/100.0/2.0; a[i][101]+=coef*(i/100.0/2.0+1.0*(100-i)/100.0/3.0); }else if(down==i){ const R coef=1.0/(1.0-1.0*i/100.0/2.0); a[i][up]-=coef*(100.0-i)/100.0/3.0; a[i][101]+=coef*(i/100.0/2.0+1.0*(100-i)/100.0/3.0); }else{ const R coef=1.0; a[i][down]-=coef*i/100.0/2.0; a[i][up]-=coef*(100.0-i)/100.0/3.0; a[i][101]+=coef*(i/100.0/2.0+1.0*(100.0-i)/100.0/3.0); } } vec x=gauss_jordan(a); cout.precision(20); cout << fixed << 1.0/3.0*(1.0+x[p]) << endl; return 0; }