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  1. #include <bits/stdc++.h>
  2. using namespace std;
  3. #define int              long long int
  4. #define double           long double
  5. #define print(a)         for(auto x : a) cout << x << " "; cout << endl
  6. inline int power(int a, int b) {
  7.     int x = 1;
  8.     while (b) {
  9.         if (b & 1) x *= a;
  10.         a *= a;
  11.         b >>= 1;
  12.     }
  13.     return x;
  14. }
  15.  
  16.  
  17. const int M = 1000000007;
  18. const int N = 3e5+9;
  19. const int INF = 2e9+1;
  20. const int LINF = 2000000000000000001;
  21.  
  22. //_ ***************************** START Below *******************************
  23.  
  24. vector<pair<int,int>> a;
  25.  
  26. bool isPossible(int n, double mid){
  27.  
  28. 	double x = -1, y = -1;
  29. 	for(int i=0; i<n; i++){
  30. 		double pos = a[i].first;
  31. 		double v = a[i].second;
  32.  
  33. 		double l = pos-v*mid;
  34. 		double r = pos+v*mid;
  35.  
  36. 		if(x == -1 && y == -1){
  37. 			x = l;
  38. 			y = r;
  39. 		}
  40. 		else{
  41. 			if(y < l ) return false;
  42. 			y = min(y, r);
  43. 			x = max(x, l);
  44. 		}
  45. 	}
  46. 	return true;
  47. }
  48.  
  49. double consistency1(int n){
  50.  
  51. 	sort(begin(a), end(a));
  52.  
  53. 	double precision = 1e-7;
  54.  
  55. 	double s = 0, e = INF;
  56.  
  57. 	int iterations = 60; // 100 safer
  58.  
  59. 	for(int i=0; i<iterations; i++){
  60. 		double mid = s + (e-s)/2;
  61. 		if(isPossible(n, mid)){
  62. 			e = mid;
  63. 		}
  64. 		else s = mid;
  65. 	}
  66.  
  67. 	return e;
  68.  
  69. }
  70.  
  71.  
  72.  
  73. double consistency2(int n){
  74.  
  75. 	sort(begin(a), end(a));
  76.  
  77. 	double precision = 1e-7;
  78.  
  79. 	double s = 0, e = INF;
  80. 	double ans = INF;
  81.  
  82. 	int iterations = 60; // 100 safer
  83.  
  84. 	for(int i=0; i<iterations; i++){
  85. 		double mid = s + (e-s)/2;
  86. 		if(isPossible(n, mid)){
  87. 			ans = min(ans, mid);
  88. 			e = mid+precision;
  89. 		}
  90. 		else s = mid-precision;
  91. 	}
  92.  
  93. 	return ans;
  94.  
  95. }
  96.  
  97.  
  98.  
  99.  
  100.  
  101.  
  102.  
  103.  
  104.  
  105. void solve() {
  106.  
  107.     int n;
  108.     cin>>n;
  109.  
  110.     a.resize(n);
  111.     for(int i=0; i<n; i++){
  112.         int x , v;
  113.         cin >> x >> v;
  114.         a[i] = {x, v};
  115.     }
  116.  
  117.     cout << fixed << setprecision(7) << consistency1(n) << endl;
  118.     // cout << fixed << setprecision(7) << consistency1(n) << " " << consistency2(n) << endl;
  119.  
  120.  
  121. }
  122.  
  123.  
  124.  
  125.  
  126.  
  127. int32_t main() {
  128.     ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
  129.  
  130.     int t = 1;
  131.     while (t--) {
  132.         solve();
  133.     }
  134.  
  135.     return 0;
  136. }
Success #stdin #stdout 0s 5320KB
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stdin
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5
-1 5
10 3
4 2
7 10
8 1
stdout
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1.5000000
https://ideone.com/mlknVM
language:
C++14 (gcc 8.3)
created:
5 hours ago
visibility:
public

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