Binary Search in C: Find Equation Roots

The binary search method is a commonly used numerical computation approach that can be used to find the roots of an equation. Here is an example code in C language for implementing the binary search method to find the roots of an equation.

#include <stdio.h>
#include <math.h>

// 定义方程的函数
double f(double x) {
    return x*x - 2;
}

// 二分法求解方程的根
double bisection(double a, double b, double epsilon) {
    double c;
    
    while ((b - a) > epsilon) {
        c = (a + b) / 2;
        
        if (f(c) == 0) {
            return c;
        } else if (f(c)*f(a) < 0) {
            b = c;
        } else {
            a = c;
        }
    }
    
    return (a + b) / 2;
}

int main() {
    double a = 1.0;
    double b = 2.0;
    double epsilon = 0.0001;
    double root;
    
    root = bisection(a, b, epsilon);
    
    printf("The root of the equation is: %f\n", root);
    
    return 0;
}

The function f in the given code defines the equation that needs to be solved for its roots, and the bisection function implements the algorithm for finding roots using the bisection method. In the main function, we define the initial interval a and b for the equation, as well as the precision epsilon, and then call the bisection function to solve for the root of the equation and output the result.

You can modify the definition and initial interval of the equation as needed, run the code to solve the roots of different equations.