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  1. // Author: Sahil Yasar
  2.  
  3. // #include <bits/stdc++.h>
  4. #include <iostream>
  5. #include <cmath>
  6. #include <iomanip>
  7. using namespace std;
  8. #define endl '\n'
  9.  
  10. // #include <ext/pb_ds/assoc_container.hpp>
  11. // #include <ext/pb_ds/tree_policy.hpp>
  12. // using namespace __gnu_pbds;
  13. // template<class T>
  14. // using oset = tree<T, null_type, less<T>, rb_tree_tag,
  15. //              tree_order_statistics_node_update>;
  16. // template <class K, class V> using ht = gp_hash_table<K, V>;
  17.  
  18. template <class T1, class T2> ostream& operator<<(ostream& out, const pair<T1, T2> p)
  19. { return out<<'('<<p.first<<", "<<p.second<<")"; }
  20. template <class ...Args> auto &print(const Args &...args)
  21. { return ((cerr<<args<<", "), ...)<<"\b\b)"<<endl; }
  22. #define watch(...) if(true){cerr<<"("#__VA_ARGS__") = ("; print(__VA_ARGS__);}
  23.  
  24. #define all(x) x.begin(), x.end()
  25. #define rall(x) x.rbegin(), x.rend()
  26. #define sz(x) (int)x.size()
  27. #define f first
  28. #define s second
  29. #define read(arr) for(auto& x: arr) cin>>x
  30. #define write(arr) for(auto& x: arr) cout<<x<<" "; cout<<endl
  31. #define mem(x, n) memset(x, n, sizeof(x))
  32. #define getUnique(x) sort(all(x)); x.erase(unique(all(x)), x.end());
  33.  
  34. typedef long long ll;
  35. typedef long double ld;
  36. typedef unsigned long long ull;
  37. typedef pair<int, int> pii;
  38. typedef pair<ll, ll> pll;
  39.  
  40. const double PI = acos(-1);
  41.  
  42. int main(){
  43.     cin.tie(0)->sync_with_stdio(0);
  44.     cin.exceptions(cin.failbit);
  45.  
  46.     int t, nt, at, nb, ab;
  47.     double theta, alpha, beta, ans, rt, rb, x, p, c, a, len;
  48.     cout<<fixed<<setprecision(6);
  49.     cin>>t;
  50.     while(t--){
  51.         cin>>nt>>at>>nb>>ab;
  52.  
  53.         theta = 2 * PI / nb;
  54.         alpha = (PI - theta)/2;
  55.         x = sin(alpha)/sin(theta) * ab;
  56.         rb = sqrt(x*x - ab*ab/4.0); // Radius of of inscribed circle of bottom polygon
  57.         p = nb/2.0 * x*x * sin(theta); // Area of bottom polygon
  58.  
  59.         theta = 2 * PI / nt;
  60.         alpha = (PI - theta)/2;
  61.         x = sin(alpha)/sin(theta) * at;
  62.         rt = sqrt(x*x - at*at/4.0); // Radius of of inscribed circle of top polygon
  63.         c = PI*rt*rt; // Area of inscribed circle of top polygon
  64.  
  65.         a = len = 0;
  66.         if (rt > rb){
  67.             len = 2*sqrt(rt*rt - rb*rb);
  68.             if (len <= ab){
  69.                 beta = 2*acos(rb/rt);
  70.                 a = beta/2*rt*rt - rb*len/2; // For inclusion exclusion
  71.             }
  72.         }
  73.  
  74.         ans = (len > ab)? 0: p-c+nb*a;
  75.         cout<<ans<<endl;
  76.     }
  77.  
  78.     return 0;
  79. }
  80.  
Success #stdin #stdout 0.01s 5288KB
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2.820131
0.000000
515.943499
0.201572
0.171213
261798.698746
https://ideone.com/SNfGJ6
language:
C++14 (gcc 8.3)
created:
316 days ago
visibility:
secret

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