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| // Bisection method for root finding | |
| // Bracketing method with guaranteed convergence | |
| // Test function: x^3 - 2*x - 5 (root near 2.09) | |
| double f1(double x) { | |
| return x * x * x - 2.0 * x - 5.0; | |
| } | |
| // Test function: cos(x) - x (root near 0.739) | |
| double f2(double x) { | |
| return cos(x) - x; | |
| } | |
| // Test function: e^x - 3*x^2 (multiple roots) | |
| double f3(double x) { | |
| return exp(x) - 3.0 * x * x; | |
| } | |
| double bisection(double (*f)(double), double a, double b, double tol, int max_iter) { | |
| if (f(a) * f(b) >= 0) { | |
| return NAN; // No root or multiple roots in interval | |
| } | |
| double c = a; | |
| for (int i = 0; i < max_iter; i++) { | |
| c = (a + b) / 2.0; | |
| double fc = f(c); | |
| if (fabs(fc) < tol || fabs(b - a) < tol) { | |
| return c; | |
| } | |
| if (f(a) * fc < 0) { | |
| b = c; | |
| } else { | |
| a = c; | |
| } | |
| } | |
| return c; | |
| } | |
| int main() { | |
| clock_t start = clock(); | |
| double sum = 0.0; | |
| int found = 0; | |
| for (int iter = 0; iter < NUM_TRIALS; iter++) { | |
| double root; | |
| // Find different roots | |
| if (iter % 3 == 0) { | |
| root = bisection(f1, 2.0, 3.0, TOL, MAX_ITER); | |
| } else if (iter % 3 == 1) { | |
| root = bisection(f2, 0.0, 1.0, TOL, MAX_ITER); | |
| } else { | |
| root = bisection(f3, 0.0, 1.0, TOL, MAX_ITER); | |
| } | |
| if (!isnan(root)) { | |
| sum += root; | |
| found++; | |
| } | |
| } | |
| clock_t end = clock(); | |
| double time_spent = (double)(end - start) / CLOCKS_PER_SEC; | |
| printf("Bisection method: %d trials, %.6f seconds\n", | |
| NUM_TRIALS, time_spent); | |
| printf("Found %d roots, average: %.10f\n", found, sum / found); | |
| return 0; | |
| } | |