[ADD] bisection_method.cpp

This commit adds a new file for implementing bisection method.

math/bisection_method.cpp

@@ -0,0 +1,43 @@
+#include <iostream>
+#include <math.h>
+using namespace std;
+
+double f(double x) {//can add your own function
+    return cos(x) - x*exp(x);
+}
+
+void bisection(double x, double y, double error = 0.00001) {
+    static bool flag = false;//to make sure the 'invalid interval' message is printed correctly
+    if(f(x)*f(y) >= 0) {
+        if(flag == false) cout << "The interval [a,b] provided is not valid" << endl;
+        return;
+    }
+
+    flag = true;
+    double z = (x+y)/2;
+    if(abs(x-y) <= error) {
+        cout << "The approximate root is : " << z << endl;
+        return;
+    }
+
+    if(f(z) == 0.0) {
+        cout << "The root is : " << z << endl;
+        return;
+    }
+    else {
+        if(f(x)*f(z) < 0) bisection(x, z, error);
+        else if(f(z)*f(y) < 0) bisection(y, z, error);
+        else {
+            cout << "The given function does not follow the required assumtions" << endl;
+            return;
+        }
+    }
+}
+
+int main(void) {
+    double a, b;
+    cout << "Enter the two guesses : " << endl;
+    cin >> a;
+    cin >> b;
+    bisection(a, b);
+}