From f306f7f50eabfa5f646ccab18bb2a8ca3a48ccd7 Mon Sep 17 00:00:00 2001
From: Disha <cs21b1033@iiitr.ac.in>
Date: Tue, 10 Oct 2023 23:40:45 +0530
Subject: [PATCH] added a new file named bisection.cpp in the math folder

---
 math/bisection.cpp | 66 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 66 insertions(+)
 create mode 100644 math/bisection.cpp

diff --git a/math/bisection.cpp b/math/bisection.cpp
new file mode 100644
index 000000000..90c64998b
--- /dev/null
+++ b/math/bisection.cpp
@@ -0,0 +1,66 @@
+#include <iostream>
+#include <cmath>
+#include <cassert>
+# define maxIterations 1000 // Maximum number of iterations to avoid infinite loops during the computation
+
+// Define the function for which you want to find the root
+// In case you want to compute bisection for some different function, you can just make changes in the return value of this function "f"
+double f(double x) {
+    return x * x - 4; // Here, solving for sqrt(4) = 2
+}
+
+// Bisection method
+double bisection(double a, double b, double tolerance) {
+    if (f(a) * f(b) >= 0) {
+        std::cout << "Error: Function has the same sign at endpoints." << std::endl;
+        return NAN; // Not-a-number to indicate an error
+    }
+
+    double c;
+
+    for (int i = 0; i < maxIterations; ++i) {
+        // Calculate the midpoint
+        c = (a + b) / 2;
+
+        // Check if the root has been found with the desired tolerance
+        if (fabs(f(c)) < tolerance) {
+            return c;
+        }
+
+        // Update the interval [a, b] based on the sign of f(c)
+        if (f(c) * f(a) < 0) {
+            b = c;
+        } else {
+            a = c;
+        }
+    }
+
+    std::cout << "Warning: Maximum number of iterations reached." << std::endl;
+    return c; // Return the best approximation found so far
+}
+
+void test() {
+    // Test cases with known solutions
+    double tolerance = 1e-6;
+    
+    // Test case 1: Finding the square root of 4
+    double root1 = bisection(0.0, 5.0, tolerance);
+    assert(std::abs(root1 - 2.0) < tolerance);   //you will have to change the parameter accordindly in case of channge in the above "f" function
+
+}
+
+int main() {
+    double tolerance = 1e-6;
+    double root = bisection(0.0, 5.0, tolerance);
+
+    if (!std::isnan(root)) {
+        std::cout << "Approximate root: " << root << std::endl;
+    } else {
+        std::cout << "Unable to find a root within the specified tolerance." << std::endl;
+    }
+
+    // Run the tests
+    test();
+
+    return 0;
+}