DIV1 250pt

题意：小球从一段折线斜坡上滚下来，告诉所用时间，求重力加速度。

解法：二分答案模拟即可。

tag:二分，simulation

1 // BEGIN CUT HERE  2 /*  3  * Author:  plum rain  4  * score :  5  */  6 /*  7   8  */  9 // END CUT HERE 10 #line 11 "IncredibleMachine.cpp" 11 #include 
      
        12 #include 
       
         13 #include 
        
          14 #include 
         
           15 #include 
          
            16 #include 
           
             17 #include 
            
              18 #include 
             
               19 #include 
              
                20 #include 
               
                 21 #include 
                
                  22 #include 
                 
                   23 #include 
                  
                    24 #include 
                   
                     25 #include 
                    
                      26 #include 
                     
                       27 #include 
                      
                        28 #include 
                       
                         29 #include 
                        
                          30 #include 
                         
                           31 #include 
                          

vi; 49 typedef vector

vs; 50 typedef vector

vd; 51 typedef pair

pii; 52 typedef long long int64; 53 54 const double eps = 1e-8; 55 const double PI = atan(1.0)*4; 56 const int inf = 2139062143 / 2; 57 58 class IncredibleMachine 59 { 60 public: 61 vi x, y; 62 double gao(double g) 63 { 64 int n = sz(x); 65 double v = 0, sum = 0; 66 for (int i = 0; i < n-1; ++ i){ 67 double d = sqrt((y[i]-y[i+1])*(y[i]-y[i+1]) + (x[i]-x[i+1])*(x[i]-x[i+1])); 68 double a = g * (y[i] - y[i+1]) / d; 69 double t = (-v + sqrt(v*v+2*a*d)) / a; 70 sum += t; v += a*t; 71 } 72 return sum; 73 } 74 75 double gravitationalAcceleration(vector

X, vector

Y, int T){ 76 x = X; y = Y; 77 int cnt = 0; 78 double l = 0, r = inf; 79 while (cnt <= 1000){ 80 double mid = (l + r) / 2; 81 if (gao(mid) < T) r = mid; 82 else l = mid; 83 ++ cnt; 84 } 85 return l; 86 } 87 88 // BEGIN CUT HERE 89 public: 90 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(); } 91 private: 92 template

string print_array(const vector

&V) { ostringstream os; os << "{ "; for (typename vector

::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); } 93 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; } } 94 void test_case_0() { int Arr0[] = { 0,6}; vector

Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = { 100,22}; vector

Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arg2 = 4; double Arg3 = 9.807692307692307; verify_case(0, Arg3, gravitationalAcceleration(Arg0, Arg1, Arg2)); } 95 void test_case_1() { int Arr0[] = { 0,26,100}; vector

Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = { 50,26,24}; vector

Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arg2 = 4; double Arg3 = 26.743031720603582; verify_case(1, Arg3, gravitationalAcceleration(Arg0, Arg1, Arg2)); } 96 void test_case_2() { int Arr0[] = { 0,7,8}; vector

Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = { 10,6,0}; vector

Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[0]))); int Arg2 = 7; double Arg3 = 1.1076837407708007; verify_case(2, Arg3, gravitationalAcceleration(Arg0, Arg1, Arg2)); } 97 98 // END CUT HERE 99 100 };101 102 // BEGIN CUT HERE103 int main()104 {105 // freopen( "a.out" , "w" , stdout ); 106 IncredibleMachine ___test;107 ___test.run_test(-1);108 return 0;109 }110 // END CUT HERE