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- //#include<cstdio>
- //#include<cassert>
- //#include<iostream>
- //#include<cstring>
- //#include<algorithm>
- #include<bits/stdc++.h>
- #include<ext/pb_ds/assoc_container.hpp>
- #include<ext/pb_ds/tree_policy.hpp>
- #define MAX ((int)2e9 + 5)
- #define MAXP ((int)1e5 + 5)
- #define MAXL ((ll)1e18 + 5)
- #define MAX_X ((int)2001)
- #define MAX_Y ((int)2001)
- #define pi acos(-1)
- //#define MOD ((int)1e9 + 7)
- #define MOD ((int)998244353 + 0)
- #define BAS ((int)1e6 + 3)
- //#define BAS ((int)2e5 + 3)
- #define N ((int)2e5 + 9)
- #define err (1e-8)
- #define fastio ios_base::sync_with_stdio(false),cin.tie(NULL)
- #define logn 17
- #define endl "\n"
- #define mpp make_pair
- #define BUCK 105
- #define LEF (idx<<1)
- #define RIG ((idx<<1)|1)
- //#define int ll
- using namespace std;
- using namespace __gnu_pbds;
- typedef long long ll;
- typedef unsigned long long ull;
- /*fast io
- ios_base::sync_with_stdio(false);
- cin.tie(NULL);
- */
- typedef tree < int, null_type, less < int >, rb_tree_tag, tree_order_statistics_node_update > o_set;
- typedef tree < pair < int, int >, null_type, less < pair < int, int > >, rb_tree_tag, tree_order_statistics_node_update > o_setp;
- /// o_set s;
- /// s.order_of_key(k) : Number of items strictly smaller than k .
- /// *(s.find_by_order(k)) : K-th element in a set (counting from zero).
- typedef long double ldd;
- mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
- int my_rand(int l, int r)
- {
- return uniform_int_distribution<int>(l,r) (rng);
- }
- int main()
- {
- /// problem: https://lightoj.com/problem/triangle-partitioning
- int t, caseno = 1;
- cin>>t;
- while(t--)
- {
- double ab, ac, bc, r;
- cin>>ab>>ac>>bc>>r;
- r = r / (1 + r); /// ADE / ABC;
- double L = 0, R = ab;
- int cnt = 100;
- while(R - L > err && cnt > 0)
- {
- cnt--;
- double mid = (L+R)/2;
- double chk = mid*mid / (ab*ab);
- if(chk < r)
- {
- L = mid;
- }
- else R = mid;
- }
- cout<<setprecision(15)<<fixed;
- cout<<"Case "<<caseno++<<": "<<L<<endl;
- }
- return 0;
- }
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