#include #pragma GCC optimize("O3") #pragma GCC target("tune=native") // #pragma GCC target("avx") #pragma GCC target("avx2") #pragma GCC optimize("unroll-loops") using namespace std; using i64 = int64_t; const i64 MOD = 1e9+7; const i64 INF = 1e18+7; // pythonのrangeのような範囲for文用のclass for(const auto& i : Range<>(10)) のように書く template struct Range{ struct iterator{ T value; const T step, last; const T& operator*(){return value;} iterator(T value, T step, T last) : value(step < static_cast(0) ? max(last, value) : min(last, value)), step(step), last(last) { } iterator operator++(){value = step < static_cast(0) ? max(value + step, last) : min(value + step, last); return *this;} bool operator!=(const iterator& x){return value != x.value;} }; const T start, last, step; Range(const T start, const T last, const T step = static_cast(1)) : start(start), last(last), step(step) { } Range(const T last) : start(0), last(last), step(1) { } iterator begin(){return iterator(start, step, last);} iterator end(){return iterator(last, step, last);} }; // lambda式を用いた再帰 template struct FixPoint{ const F _f; FixPoint(F&& f) : _f(forward(f)){} template decltype(auto) operator()(Types&&... args) const{ return _f(*this, forward(args)...); } }; template static decltype(auto) makeRec(F&& f){ return FixPoint(forward(f)); } // 多次元vectorの一斉初期化 makeVector(a, b, ...)のように書く template vector makeVector(size_t x){ return vector(x, T(Value)); } template auto makeVector(size_t x, Types... args){ return vector(args...))>(x, makeVector(args...)); } // 最大値を更新し、更新できた時にはtrueを返す template bool chmax(T& a, T b){ if(a < b){ a = b; return true; } return false; } // 同様に最小値を更新する template bool chmin(T& a, T b){ if(a > b){ a = b; return true; } return false; } // 行数と変数名、値をclogに表示するデバッグ用print #define dump(x) fprintf(stderr, "line =%4d, name =%7s , ", __LINE__, #x); clog << "value = " << x << endl; // 同様の配列向けデバッグ用print #define vecdump(x) fprintf(stderr, "line =%4d, name =%7s\n", __LINE__, #x); _dump_macro(x); void _dump(int, string& x){ clog << x << endl; } template void _dump(bool, T& x){ clog << x << " "; } template void _dump(int, T& x){ for(auto& elm : x) _dump(0, elm); clog << endl; } template void _dump_macro(T& x){ _dump(0, x); } // input用の関数群 void _input(int, string& x){ cin >> x; } template void _input(bool, T& x){ cin >> x; } template void _input(int, T& x){ for(auto& elm : x) _input(0, elm); } template void input_single(T& x){ _input(0, x); } auto input(){} template void input(T& value, Types&&... args){ input_single(value); input(forward(args)...); }; void _pararell_input(size_t){} template void _pararell_input(size_t index, T& value, Types&&... args){ input(value[index]); _pararell_input(index, forward(args)...); } template void pararell_input(size_t count, Types&&... args){ for(const auto& i : Range<>(count)) _pararell_input(i, forward(args)...); } struct r{ unsigned long x = 123456789, y = 362436069, z = 521288629, w; double call(){ unsigned long t = (x ^ (x << 11)); x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); // 剰余をとっている都合上正確な分布にはならないが、64bitの範囲で均等に取られているので誤差の範囲内 return (long double)(1.0) * w / numeric_limits::max(); } }; signed main(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); r ra; int n; long double p, q; input(n, p, q); auto f = [n, p, q, &ra]{ int po = 0; int m = 1; for(const auto& _ : Range<>(2e3)){ po += m; if(!(0 < po && po < n)) break; double va = ra.call(); if(va < p){ m *= -1; }else if(va < p + q){ ; }else{ return 0.0; } } if(po == 0) return 1.0; if(po == n) return 0.0; return 0.5; }; double ans = 0; int cnt = 0; for(const auto& i : Range<>(2e6)){ auto t = f(); if(t < 0) continue; ++cnt; ans += t; } cout << ans / cnt << endl; }