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KiK0S

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Mar 20th, 2019
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C++ 2.06 KB | None | 0 0
  1. #include <iostream>
  2. #include <vector>
  3. #include <map>
  4. #include <set>
  5. #include <queue>
  6. #include <algorithm>
  7. #include <string>
  8. #include <cmath>
  9. #include <cstdio>
  10. #include <iomanip>
  11. #include <fstream>
  12. #include <cassert>
  13. #include <cstring>
  14. #include <unordered_set>
  15. #include <unordered_map>
  16. #include <numeric>
  17. #include <ctime>
  18. #include <bitset>
  19. #include <complex>
  20. #include <random>
  21. using namespace std;
  22.  
  23. typedef long long ll;
  24. typedef unsigned long long ull;
  25.  
  26. #ifdef DEBUG
  27.     const int MAXN = 10;
  28.     const int MAXLOG = 4;
  29.     const int MAXSQRT = 4;
  30. #else
  31.     const int MAXN = 3e5;
  32.     const int MAXLOG = 20;
  33.     const int MAXSQRT = 400;
  34.     #define cerr if (false) cerr
  35. #endif
  36.  
  37. mt19937 rng(time(0));
  38. #define double long double
  39. const int INF = 1e9;
  40. const int MOD = 1e9 + 7;
  41.  
  42. int n, a, b;
  43. int x[MAXN];
  44. double v[MAXN];
  45. double can[MAXN];
  46.  
  47. inline void init() {
  48.  
  49. }
  50.  
  51. inline void solve() {
  52.     init();
  53.     for (int i = 0; i < n; i++) {
  54.         cin >> x[i] >> v[i];
  55.     }
  56.     can[n - 1] = v[n - 1];
  57.     for (int i = n - 2; i >= 0; i--) {
  58.         double s = x[i + 1] - x[i];
  59.         double t = (-can[i + 1] + sqrtl(can[i + 1] * can[i + 1] + 2 * b * s)) / b;
  60.         can[i] = min(v[i], can[i + 1] + b * t);
  61.     }
  62.     double ans = 0;
  63.     double cur = 0;
  64.     for (int i = 0; i < n - 1; i++) {
  65.         double f = can[i + 1];
  66.         double s = x[i + 1] - x[i];
  67.         {
  68.             double t1 = (-cur + sqrtl(cur * cur + 2 * a * s)) / a;
  69.             if (cur + t1 * a <= f) {
  70.                 cur += t1 * a;
  71.                 ans += t1;
  72.                 continue;
  73.             }
  74.         }
  75.         double A = a * a + a * b;
  76.         double B = 2 * cur * (a + b);
  77.         double C = -f * f - 2 * b * s - cur * cur;
  78.         double d1 = (-B + sqrtl(B * B - 4 * A * C)) / 2 * A;
  79.         double d2 = (-B - sqrtl(B * B - 4 * A * C)) / 2 * A;
  80.         double d;
  81.         if (d2 < 0) {
  82.             d = d1;
  83.         }  
  84.         else {
  85.             d = d2;
  86.         }
  87.         double t = (cur - f + a * d) / b;
  88.         ans += t + d;
  89.         cur = can[i + 1];
  90.     }
  91.     cout << ans << '\n';
  92. }
  93.  
  94. signed main() {
  95.     #ifdef DEBUG
  96.         freopen("A.in", "r", stdin);
  97.         freopen("A.out", "w", stdout);
  98.     #else
  99.    
  100.     #endif
  101.     ios_base::sync_with_stdio(0);
  102.     cin.tie(0);
  103.     cout.tie(0);
  104.     while (cin >> n >> a >> b)
  105.         solve();
  106.     return 0;
  107. }
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