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  1. /*
  2.  * Bisection Method.
  3.  * x^2 - a = 0
  4.  */
  5. #include <iostream>
  6.  
  7. using namespace std;
  8.  
  9. double EPS = 0.00001;
  10.  
  11. double f(double x, int a) {
  12.  
  13.        return x * x - a;
  14. }
  15.  
  16. double divideEtImpera(double lo, double hi, int a) {
  17.  
  18.     if(hi - lo <= EPS) return (lo + hi) / 2;
  19.  
  20.     else {
  21.  
  22.          double m = (lo + hi) / 2;
  23.          //cout<<m<<endl;
  24.          if(f(lo,a) * f(m,a) < 0) {
  25.  
  26.             return divideEtImpera(lo, m, a);
  27.  
  28.          } else {
  29.  
  30.             return divideEtImpera(m, hi, a);
  31.          }
  32.     }
  33. }
  34.  
  35. //Bisection method using iteration
  36. void bisection(double lo, double hi, double a) {
  37.  
  38.      double m;
  39.  
  40.      while((hi - lo) >= EPS) {
  41.  
  42.           m = (lo + hi) / 2;
  43.  
  44.           if(f(lo, a) * f(m, a) < 0) {
  45.  
  46.                hi = m;
  47.  
  48.           } else {
  49.  
  50.                lo = m;
  51.           }
  52.  
  53.           cout<<m<<endl;
  54.      }
  55.  
  56.      cout<<m<<endl;
  57. }
  58.  
  59.  
  60. //Bisection method using iteration - version 2
  61. void bisection2(double lo, double hi, double a) {
  62.  
  63.      double m, y_x, y_m;
  64.  
  65.      while((hi - lo) >= EPS) {
  66.  
  67.           m = (lo + hi) / 2;
  68.  
  69.           y_x = lo * lo - a;
  70.           y_m = m * m - a;
  71.  
  72.           if( (y_x > 0 && y_m < 0) || (y_x < 0 && y_m > 0)) {
  73.  
  74.                hi = m;
  75.  
  76.           } else {
  77.  
  78.                lo = m;
  79.           }
  80.  
  81.           cout<<m<<endl;
  82.      }
  83.  
  84.      cout<<m<<endl;
  85. }
  86.  
  87. int main(int argc, char const *argv[]) {
  88.   int a;
  89.   cin>>a;
  90.   cout<<divideEtImpera(0, a + 5, a)<<endl;
  91.   bisection(0, a + 5, a);
  92.   bisection2(0, a + 5, a);
  93.   return 0;
  94. }
Success #stdin #stdout 0.01s 5408KB
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stdin
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49
stdout
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7
27
13.5
6.75
10.125
8.4375
7.59375
7.17188
6.96094
7.06641
7.01367
6.9873
7.00049
6.9939
6.99719
6.99884
6.99966
7.00008
6.99987
6.99997
7.00002
7
7.00001
7.00001
7.00001
27
13.5
6.75
10.125
8.4375
7.59375
7.17188
6.96094
7.06641
7.01367
6.9873
7.00049
6.9939
6.99719
6.99884
6.99966
7.00008
6.99987
6.99997
7.00002
7
7.00001
7.00001
7.00001
https://ideone.com/cAFUqI
Finding SQRT using Bisection Method
language:
C++ (gcc 8.3)
created:
3 years ago
visibility:
secret

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