C++ beta, betaf and betal實例講解

beta(),betaf()和betal()是C++ STL中的內置函數,用于計算兩個正實數值的beta函數。該函數將兩個變量x和y作為輸入,并返回x和y的beta函數。 x和y的Beta函數(也稱為第一類Euler積分)可以定義為:

用法

double beta(double x, double y)or long double betal(long double x, long double y)or float betaf(float x, float y)

參數:該函數接受兩個強制性參數x和y,它們指定浮點或整數類型的值。參數可以是double,double或float,float或long double,long double數據類型。

返回值:該函數返回x和y的beta函數的值。返回類型取決于傳遞的參數。與參數相同。

注意:該函數在C++ 17(7.1)及更高版本中運行。

以下示例程序旨在說明beta(),betaf()和betal()函數:

// C++ program to illustrate the three functions // Being a special function, beta is only guaranteed // to be in cmath if the user defines //? __STDCPP_WANT_MATH_SPEC_FUNCS__ before including // any standard library headers. #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1 #include <bits/stdc++.h> using namespace std; ??int main() { ????// Computes the beta function of 5 and 4 and print it ????// If provided arguments are not of type double ????// they are implicitly type-casted to the higher type. ??????// first example of beta() ????cout << beta(5, 4) << "\n"; ??????// second example of betaf() ????cout << betaf(10.0, 4.0) << "\n"; ??????// third example of betal() ????cout << betal(10.0, 6.7) << "\n"; ????return 0; }

輸出:

0.003571430.000349651.65804e-005

Beta函數的應用:用于計算二項式系數。以beta函數表示的二項式系數可以表示為:

以上關系可用于計算二項式系數。圖示如下:

// C++ program to print the pascal triangle // Being a special function, beta is only guaranteed // to be in cmath if the user defines //? __STDCPP_WANT_MATH_SPEC_FUNCS__ before including // any standard library headers. #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1 #include <bits/stdc++.h> #include <cmath> using namespace std; ??// Function to return the value of binomial Coefficient double binomialCoefficient(int n, int k) { ????// Calculate the value of nCr using above formula. ????double ans = 1 / ((n + 1) * beta(n - k + 1, k + 1)); ????return ans; } // Driver Code int main() { ????// Print the binomial Coefficient nCr where n=5 and r=2 ????cout << binomialCoefficient(5, 2) << "\n"; ??????return 0; }

輸出:

10