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Apr 24th, 2016
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  1. #include <bits/stdc++.h>
  2.  
  3. using namespace std;
  4.  
  5. const int MAXN = 500000;
  6. double Pref[MAXN], Suff[MAXN];
  7. double PA[MAXN], PB[MAXN];
  8.  
  9. bool bad(int i) {
  10. double a = PA[i] - PA[i - 1];
  11. double b = PB[i] - PB[i - 1];
  12.  
  13. double rez = Pref[i - 1] + a * PB[i - 1] + b * PA[i - 1] + a * b;
  14. if(fabs(rez - Pref[i]) < 1e-9)
  15. return false;
  16. return true;
  17. }
  18.  
  19. void getSols(int i) {
  20. double prod = Pref[i];
  21. double b = Suff[i + 1];
  22.  
  23. //b = 1 - (sum) + (prod)
  24. double sum = 1 - b + prod;
  25.  
  26. //Stim suma si produsul -> profit
  27. double disc = sqrt(fabs(sum * sum - 4 * prod));
  28. PA[i] = (sum + disc) / 2;
  29. PB[i] = (sum - disc) / 2;
  30.  
  31. if(bad(i)) swap(PA[i], PB[i]);
  32. }
  33.  
  34. int main() {
  35. int n;
  36. cin >> n;
  37.  
  38. for(int i = 1; i <= n; ++i) {
  39. cin >> Pref[i];
  40. Pref[i] += Pref[i - 1];
  41. }
  42. for(int i = 1; i <= n; ++i) {
  43. cin >> Suff[i];
  44. }
  45. for(int i = n; i >= 1; --i) {
  46. Suff[i] += Suff[i + 1];
  47. }
  48.  
  49. for(int i = 1; i <= n; ++i) {
  50. getSols(i);
  51. }
  52.  
  53. cout << fixed << setprecision(12);
  54. for(int i = 1; i <= n; ++i) {
  55. cout << PA[i] - PA[i - 1] << " ";
  56. }
  57. cout << endl;
  58. for(int i = 1; i <= n; ++i) {
  59. cout << PB[i] - PB[i - 1] << " ";
  60. }
  61. cout << endl;
  62.  
  63. return 0;
  64. }
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