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Jul 16th, 2021
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  1. //#include<cstdio>
  2. //#include<cassert>
  3. //#include<iostream>
  4. //#include<cstring>
  5. //#include<algorithm>
  6. #include<bits/stdc++.h>
  7. #include<ext/pb_ds/assoc_container.hpp>
  8. #include<ext/pb_ds/tree_policy.hpp>
  9. #define MAX ((int)2e9 + 5)
  10. #define MAXP ((int)1e5 + 5)
  11. #define MAXL ((ll)1e18 + 5)
  12. #define MAX_X ((int)2001)
  13. #define MAX_Y ((int)2001)
  14. #define pi acos(-1)
  15. //#define MOD ((int)1e9 + 7)
  16. #define MOD ((int)998244353 + 0)
  17. #define BAS ((int)1e6 + 3)
  18. //#define BAS ((int)2e5 + 3)
  19. #define N ((int)2e5 + 9)
  20. #define err (1e-8)
  21. #define fastio ios_base::sync_with_stdio(false),cin.tie(NULL)
  22. #define logn 17
  23. #define endl "\n"
  24. #define mpp make_pair
  25. #define BUCK 105
  26. #define LEF (idx<<1)
  27. #define RIG ((idx<<1)|1)
  28. //#define int ll
  29.  
  30.  
  31. using namespace std;
  32. using namespace __gnu_pbds;
  33.  
  34. typedef long long ll;
  35. typedef unsigned long long ull;
  36.  
  37. /*fast io
  38. ios_base::sync_with_stdio(false);
  39. cin.tie(NULL);
  40. */
  41.  
  42.  
  43.  
  44.  
  45. typedef tree < int,  null_type,  less < int >,  rb_tree_tag,  tree_order_statistics_node_update > o_set;
  46. typedef tree < pair < int, int >,  null_type,  less < pair < int, int > >,  rb_tree_tag,  tree_order_statistics_node_update > o_setp;
  47. /// o_set s;
  48. /// s.order_of_key(k) : Number of items strictly smaller than k .
  49. /// *(s.find_by_order(k)) : K-th element in a set (counting from zero).
  50.  
  51. typedef long double ldd;
  52.  
  53. mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
  54.  
  55. int my_rand(int l, int r)
  56. {
  57.     return uniform_int_distribution<int>(l,r) (rng);
  58. }
  59.  
  60.  
  61.  
  62.  
  63. int main()
  64. {
  65.     /// problem: https://lightoj.com/problem/triangle-partitioning
  66.     int t, caseno = 1;
  67.     cin>>t;
  68.     while(t--)
  69.     {
  70.         double ab, ac, bc, r;
  71.         cin>>ab>>ac>>bc>>r;
  72.         r = r / (1 + r); /// ADE / ABC;
  73.         double L = 0, R = ab;
  74.         int cnt = 100;
  75.         while(R - L > err && cnt > 0)
  76.         {
  77.             cnt--;
  78.             double mid = (L+R)/2;
  79.             double chk = mid*mid / (ab*ab);
  80.             if(chk < r)
  81.             {
  82.                 L = mid;
  83.             }
  84.             else R = mid;
  85.         }
  86.         cout<<setprecision(15)<<fixed;
  87.         cout<<"Case "<<caseno++<<": "<<L<<endl;
  88.     }
  89.     return 0;
  90. }
  91.  
  92.  
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