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 <sstream> 12 #include <stdexcept> 13 #include <functional> 14 #include <iomanip> 15 #include <numeric> 16 #include <fstream> 17 #include <cctype> 18 #include <iostream> 19 #include <cstdio> 20 #include <vector> 21 #include <cstring> 22 #include <cmath> 23 #include <algorithm> 24 #include <cstdlib> 25 #include <set> 26 #include <queue> 27 #include <bitset> 28 #include <list> 29 #include <string> 30 #include <utility> 31 #include <map> 32 #include <ctime> 33 #include <stack> 34 35 using namespace std; 36 37 #define clr0(x) memset(x, 0, sizeof(x)) 38 #define clr1(x) memset(x, -1, sizeof(x)) 39 #define pb push_back 40 #define sz(v) ((int)(v).size()) 41 #define all(t) t.begin(),t.end() 42 #define zero(x) (((x)>0?(x):-(x))<eps) 43 #define out(x) cout<<#x<<":"<<(x)<<endl 44 #define tst(a) cout<<a<<" " 45 #define tst1(a) cout<<#a<<endl 46 #define CINBEQUICKER std::ios::sync_with_stdio(false) 47 48 typedef vector<int> vi; 49 typedef vector<string> vs; 50 typedef vector<double> vd; 51 typedef pair<int, int> 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 <int> X, vector <int> 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 <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(); } 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 << " Expected: "" << Expected << '"' << endl; cerr << " Received: "" << Received << '"' << endl; } } 94 void test_case_0() { int Arr0[] = {0,6}; vector <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {100,22}; vector <int> 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 <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {50,26,24}; vector <int> 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 <int> Arg0(Arr0, Arr0 + (sizeof(Arr0) / sizeof(Arr0[0]))); int Arr1[] = {10,6,0}; vector <int> 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 HERE 103 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
DIV1 500pt
裸的高斯消元求解概率dp。。。。。。