Bisection method using Recursion

標題：使用遞迴函式計算二分法

使用遞迴
VC++ (recursion.cpp)：

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

//Chapter 3 - Recursion #include <iostream> using namespace std; const int No = 1000; const double tolerance = 0.00001; const double minimal = 0; const double maximal = 1; double equation(double); double determine(double, double, double=equation(minimal), int=0); int main(void) { cout << "Best: " << scientific << determine(minimal, maximal) << endl; system("pause"); return 0; } double determine(double a, double b, double fa, int n) { double p = 0, fp = 0; p = a+(b-a)/2; fp = equation(p); //cout << dec << n << '\t' << scientific << p << endl; if(( fp==0 || (b-a)/2 < tolerance ) || n >= No) return p; return (fa*fp>0) ? determine(p, b, fp, n+1) : determine(a, p, fa, n+1); } double equation(double x) { return x - 1/pow(2.0, x); } /*double equation(double x) { return pow(x, 4)-2*pow(x, 3)-4*pow(x, 2)-4*x+4; }*/

不使用遞迴
VC++ (bisectionMethod.cpp)：

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

//Chapter 3 - Bisection Method #include <iostream> using namespace std; const int No = 1000; const double tolerance = 0.00001; const double minimal = 0; const double maximal = 1; double equation(double); int main(void) { int i=0; double x=0, y=0, fa=0, fp=0, p=0, a=0, b=0; a = minimal; b = maximal; fa = equation(a); while(i<No) { p = a+(b-a)/2; fp = equation(p); if(fp==0 || (b-a)/2 < tolerance) { break; } if(fa*fp>0) { a = p; fa = fp; } else { b = p; } i++; } cout << scientific << p << endl; system("pause"); return 0; } /* double equation(double x) { return pow(x, 4)-2*pow(x, 3)-4*pow(x, 2)-4*x+4; } */ double equation(double x) { return x - 1/pow(2.0, x); }

說明：
比較遞迴與不遞迴方式計算二分法。