SRM 440(1-250pt, 1-500pt)

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

 // BEGIN CUT HERE
 /*
  * Author:  plum rain
  * score :
  */
 /*

  */
 // END CUT HERE
 #line 11 "IncredibleMachine.cpp"
 #include <sstream>
 #include <stdexcept>
 #include <functional>
 #include <iomanip>
 #include <numeric>
 #include <fstream>
 #include <cctype>
 #include <iostream>
 #include <cstdio>
 #include <vector>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 #include <cstdlib>
 #include <set>
 #include <queue>
 #include <bitset>
 #include <list>
 #include <string>
 #include <utility>
 #include <map>
 #include <ctime>
 #include <stack>

 using namespace std;

 #define clr0(x) memset(x, 0, sizeof(x))
 #define clr1(x) memset(x, -1, sizeof(x))
 #define pb push_back
 #define sz(v) ((int)(v).size())
 #define all(t) t.begin(),t.end()
 #define zero(x) (((x)>0?(x):-(x))<eps)
 #define out(x) cout<<#x<<":"<<(x)<<endl
 #define tst(a) cout<<a<<" "
 #define tst1(a) cout<<#a<<endl
 #define CINBEQUICKER std::ios::sync_with_stdio(false)

 typedef vector<int> vi;
 typedef vector<string> vs;
 typedef vector<double> vd;
 typedef pair<int, int> pii;
 typedef long long int64;

 const double eps = 1e-;
 const double PI = atan(1.0)*;
 const int inf =  / ;

 class IncredibleMachine
 {
     public:
         vi x, y;
         double gao(double g)
         {
             int n = sz(x);
             double v = , sum = ;
             for (int i = ; i < n-; ++ i){
                 double d = sqrt((y[i]-y[i+])*(y[i]-y[i+]) + (x[i]-x[i+])*(x[i]-x[i+]));
                 double a = g * (y[i] - y[i+]) / d;
                 double t = (-v + sqrt(v*v+*a*d)) / a;
                 sum += t; v += a*t;
             }
             return sum;
         }

         double gravitationalAcceleration(vector <int> X, vector <int> Y, int T){
             x = X; y = Y;
             int cnt = ;
             double l = , r = inf;
             while (cnt <= ){
                 double mid = (l + r) / ;
                 if (gao(mid) < T) r = mid;
                 else l = mid;
                 ++ cnt;
             }
             return l;
         }

 // BEGIN CUT HERE
     public:
     void run_test(int Case) { if ((Case == -) || (Case == )) test_case_0(); if ((Case == -) || (Case == )) test_case_1(); if ((Case == -) || (Case == )) test_case_2(); }
     private:
     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(); }
     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; } }
     void test_case_0() { int Arr0[] = {,}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arr1[] = {,}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); int Arg2 = ; double Arg3 = 9.807692307692307; verify_case(, Arg3, gravitationalAcceleration(Arg0, Arg1, Arg2)); }
     void test_case_1() { int Arr0[] = {,,}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arr1[] = {,,}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); int Arg2 = ; double Arg3 = 26.743031720603582; verify_case(, Arg3, gravitationalAcceleration(Arg0, Arg1, Arg2)); }
     void test_case_2() { int Arr0[] = {,,}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[]))); int Arr1[] = {,,}; vector <int> Arg1(Arr1, Arr1 + (sizeof(Arr1) / sizeof(Arr1[]))); int Arg2 = ; double Arg3 = 1.1076837407708007; verify_case(, Arg3, gravitationalAcceleration(Arg0, Arg1, Arg2)); }

 // END CUT HERE

 };

 // BEGIN CUT HERE
 int main()
 {
 //    freopen( "a.out" , "w" , stdout );
     IncredibleMachine ___test;
     ___test.run_test(-);
        return ;
 }
 // END CUT HERE

DIV1 500pt

裸的高斯消元求解概率dp。。。。。。