TopCoder SRM 559 Div 1 - Problem 900 CircusTents

  1 #include <cmath>
  2 #include <cstdio>
  3 #include <string>
  4 #include <vector>
  5 #include <cstring>
  6 #include <iostream>
  7 #include <algorithm>
  8 using namespace std;
  9 #define _CLASSNAME_ CircusTents
 10 #define _METHODNAME_ findMaximumDistance
 11 #define _RC_ double
 12 #define _METHODPARMS_ vector <int> x, vector <int> y, vector <int> r
 13 #define ref(i,x,y)for(int i=x;i<=y;++i)
 14 #define def(i,x,y)for(int i=x;i>=y;--i)
 15 typedef long double LD;
 16 const int N = 51;
 17 const LD pi = acos(-1);
 18 int n;
 19 struct xint { int x, y, r; }s[N];
 20 struct yint { LD op, ed; }S[N];
 21 bool cmp(yint a, yint b) { return a.op < b.op; }
 22 bool check(LD ss) {
 23     ref(i, 2, n) {
 24         LD _min = sqrt(s[i].x*s[i].x + s[i].y*s[i].y) - s[1].r;
 25         LD _max = sqrt(s[i].x*s[i].x + s[i].y*s[i].y - s[1].r*s[1].r);
 26         LD _dis = s[i].r + ss;
 27         if (_dis < _min) {
 28             S[i].op = 0, S[i].ed = 0; continue;
 29         }
 30         LD b = atan2(s[i].y, s[i].x); if (b < 0)b = 2 * pi + b;
 31         if (_dis > _max) {
 32             LD a = (_dis - _max) / s[1].r + acos(s[1].r / sqrt(s[i].x*s[i].x + s[i].y*s[i].y));
 33             if (a > pi)S[i].op = 0, S[i].ed = 2 * pi;
 34             else S[i].op = b - a, S[i].ed = b + a;
 35         }
 36         else {
 37             LD dis2 = s[i].x*s[i].x + s[i].y*s[i].y;
 38             //s[1].r*s[1].r + dis2 - 2 * s[1].r*sqrt(dis2)* cos(alpha) = _dis*_dis;
 39             LD a = acos((s[1].r*s[1].r + dis2 - _dis*_dis) / 2 / s[1].r / sqrt(dis2));
 40             S[i].op = b - a, S[i].ed = b + a;
 41         }
 42         if (S[i].ed > 2 * pi)S[i].op -= 2 * pi, S[i].ed -= 2 * pi;
 43     }
 44     LD LL = 0, RR = 2 * pi;
 45     sort(S + 2, S + n + 1, cmp);
 46     ref(i, 2, n) {
 47         if (S[i].op < 0)LL = max(LL, S[i].ed), RR = min(RR, S[i].op + 2 * pi);
 48         else {
 49             if (LL < S[i].op)return 1;
 50             if (S[i].ed > LL)LL = S[i].ed;
 51         }
 52         if (LL >= RR)return 0;
 53     }
 54     return 1;
 55 }
 56 LD work() {
 57     LD L = -1e6, R = 1e6;
 58     ref(times, 1, 50) {
 59         LD mid = (L + R) / 2;
 60         if (check(mid))L = mid; else R = mid;
 61     }
 62     return L;
 63 }
 64 class _CLASSNAME_ {
 65 public:
 66     _RC_ _METHODNAME_(_METHODPARMS_)
 67     {
 68         n = x.size();
 69         ref(i, 1, n)s[i].x = x[i - 1], s[i].y = y[i - 1], s[i].r = r[i - 1];
 70         ref(i, 2, n)s[i].x -= s[1].x, s[i].y -= s[1].y; s[1].x = s[1].y = 0;
 71         return _RC_(work());
 72     }
 73 
 74     // BEGIN CUT HERE
 75 public:
 76     void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) test_case_3(); if ((Case == -1) || (Case == 4)) test_case_4(); }
 77 private:
 78     template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << ‘\"‘ << *iter << "\","; os << " }"; return os.str(); }
 79     void verify_case(int Case, const double &Expected, const double &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: \"" << Expected << ‘\"‘ << endl; cerr << "\tReceived: \"" << Received << ‘\"‘ << endl; } }
 80     void test_case_0() { int Arr0[] = { 0,3 }; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = { 0,0 }; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = { 1,1 }; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); double Arg3 = 3.7390603609952078; verify_case(0, Arg3, findMaximumDistance(Arg0, Arg1, Arg2)); }
 81     void test_case_1() { int Arr0[] = { 0,3,-3,3,-3 }; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = { 0,3,3,-3,-3 }; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = { 1,1,1,1,1 }; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); double Arg3 = 2.6055512754639887; verify_case(1, Arg3, findMaximumDistance(Arg0, Arg1, Arg2)); }
 82     void test_case_2() { int Arr0[] = { 3,7,7,7,3 }; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = { 4,6,1,-3,0 }; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = { 2,2,2,1,1 }; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); double Arg3 = 4.3264459099620725; verify_case(2, Arg3, findMaximumDistance(Arg0, Arg1, Arg2)); }
 83     void test_case_3() { int Arr0[] = { 10,-1 }; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = { 0,0 }; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = { 8,2 }; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); double Arg3 = 24.63092458664212; verify_case(3, Arg3, findMaximumDistance(Arg0, Arg1, Arg2)); }
 84     void test_case_4() { int Arr0[] = { 0,4,-4 }; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = { 0,4,-4 }; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arr2[] = { 1,1,1 }; vector <int> Arg2(Arr2, Arr2 + (sizeof(Arr2) / sizeof(Arr2[0]))); double Arg3 = 4.745474963675133; verify_case(4, Arg3, findMaximumDistance(Arg0, Arg1, Arg2)); }
 85     // END CUT HERE
 86 
 87 };
 88 
 89 // BEGIN CUT HERE
 90 int main()
 91 {
 92     /*
 93     {3, 7, 7, 7, 3}
 94     {4, 6, 1, -3, 0}
 95     {2, 2, 2, 1, 1}
 96     */
 97     CircusTents ___test;
 98     ___test.run_test(-1);
 99     getchar();
100     return 0;
101 }
102 // END CUT HERE