/** * author: otera **/ #include using namespace std; using ll = long long; using ld = long double; using ull = unsigned long long; using uint = unsigned; const int inf=1e9+7; const ll INF=1LL<<60; #define rep(i, n) for(int i = 0; i < n; ++ i) #define per(i,n) for(int i=n-1;i>=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) typedef pair P; typedef pair LP; #define pb push_back #define eb emplace_back #define fr first #define sc second #define all(c) c.begin(),c.end() #define lb(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define ub(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define Sort(a) sort(all(a)) #define Rev(a) reverse(all(a)) #define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a)) #define si(c) (int)(c).size() inline ll popcnt(ull a){ return __builtin_popcountll(a); } #define tpow(n) (1LL<<(n)) #define unless(A) if(!(A)) ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;in(__VA_ARGS__) #define vec(type,name,...) vectorname(__VA_ARGS__) #define VEC(type,name,size) vectorname(size);in(name) #define vv(type,name,h,...) vector>name(h,vector(__VA_ARGS__)) #define VV(type,name,h,w) vector>name(h,vector(w));in(name) #define vvv(type,name,h,w,...) vector>>name(h,vector>(w,vector(__VA_ARGS__))) template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; template void scan(T& a){ cin >> a; } template void scan(vector& a){ for(auto&& i : a) scan(i); } void in(){} template void in(Head& head, Tail&... tail){ scan(head); in(tail...); } void print(){ cout << ' '; } template void print(const T& a){ cout << a; } template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout << ' '; print(*i); } } int out(){ cout << '\n'; return 0; } template int out(const T& t){ print(t); cout << '\n'; return 0; } template int out(const Head& head, const Tail&... tail){ print(head); cout << ' '; out(tail...); return 0; } #define CHOOSE(a) CHOOSE2 a #define CHOOSE2(a0,a1,a2,a3,a4,x,...) x #define debug_1(x1) cout<<#x1<<": "< x(n), y(n), r(n), v(n), a(n); rep(i, n - 1) { in(x[i], y[i], r[i], v[i], a[i]); } x[n - 1] = y[n - 1] = r[n - 1] = v[n - 1] = a[n - 1] = 0; auto xi = [&](int i, ld t) -> ld { ld s = (ld)v[i] * t + (ld)a[i]; s *= pi / 180.0; return (ld)x[i] + (ld)r[i] * cos(s); }; auto yi = [&](int i, ld t) -> ld { ld s = (ld)v[i] * t + (ld)a[i]; s *= pi / 180.0; return (ld)y[i] + (ld)r[i] * sin(s); }; auto dist = [&](int i, int j, ld t1, ld t2) -> ld { return sqrt(pow(xi(i, t1) - xi(j, t2), 2.0) + pow(yi(i, t1) - yi(j, t2), 2.0)); }; rep(i, (1<<13)) rep(j, 13) dp[i][j] = inf; dp[tpow(n - 1)][n - 1] = 0.0; rep(bit, (1< inf - 1.0) continue; if(bit & tpow(i) and !(bit & tpow(j))) { ld ti = dp[bit][i]; // ld s = (ld)v[j] * ti + (ld)a[j] - ((ld)v[i] * ti + (ld)a[i]); // s *= pi / 180.0; ld ok = 1000.0, ng = 0.0; rep(_, 40) { ld mid = (ok + ng) / 2.0; // ld ss = s + (ld)v[j] * mid * pi / 180.0; // ld di = pow((ld)r[i], 2.0) + pow((ld)r[j], 2.0) - 2.0 * (ld)r[i] * (ld)r[j] * cos(ss); if((ld)w * mid >= dist(i, j, ti, ti + mid)) ok = mid; else ng = mid; } chmin(dp[bit | tpow(j)][j], dp[bit][i] + ok); } } } } ld ans = inf; rep(i, n) chmin(ans, dp[(1<