Exercise 9

Added Exercise 9 to repository

Informatik_I/Exercise_9/Task_1/README.org

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+#+title: Task 1: Complex Numbers
+
+#+author: JirR02
+* Task
+:PROPERTIES:
+:CUSTOM_ID: task
+:END:
+Create your own data type for complex numbers that can be used as a
+drop-in replacement for double. The definition of the data type and the
+forward declarations of operators must be in file =complex.h=, while the
+implementation of operators must be in file =complex.cpp=.
+
+1. Define a struct named =Complex= that represents a complex number in
+   the cartesian form. As data type use floating point numbers with
+   =double= precision.
+
+2. Implement input and output =(>>, <<)= operators for reading and
+   writing of complex numbers.
+
+A complex number \((x pm yi)\) is represented in the format =[x,y]=,
+where =x= and =y= follows the format of floating point numbers with
+=double= precision.
+
+E.g., =[-2,5]= represents \((-2 + 5i)\) . *Important: No spaces*.
+
+*Note*: You can assume that your input value is a well-formatted complex
+number.
+
+3. [@3] Implement arithmetic operators for addition, subtraction,
+   multiplication, and division \((+,-,*,/)\) of complex numbers. For
+   the division, you may assume that the squared modulus of the divisor
+   is not zero, even after rounding it to a floating point number.
+   Finally, you do not need to treat the case of division by zero.
+
+4. Implement the negation operator \((-)\) of complex numbers.
+
+5. Implement comparison operators for equality and inequality
+   \((==,!=)\) of complex numbers.
+
+*Hint*: recall from Exercise 5 how to correctly compare floating point
+numbers.
+
+* Solution
+:PROPERTIES:
+:CUSTOM_ID: solution
+:END:
+** =complex.h=
+:PROPERTIES:
+:CUSTOM_ID: complex.h
+:END:
+#+begin_src cpp
+#pragma once
+
+#include <cmath>
+#include <iostream>
+
+struct Complex {
+  double a;
+  double b;
+};
+
+// arithmetic operators
+Complex operator+(const Complex &cn1, const Complex &cn2);
+Complex operator-(const Complex &cn1, const Complex &cn2);
+Complex operator*(const Complex &cn1, const Complex &cn2);
+Complex operator/(const Complex &cn1, const Complex &cn2);
+
+// negation operator
+
+Complex operator-(const Complex &cn1);
+
+// equality and inequality operators
+
+bool operator==(const Complex &cn1, const Complex &cn2);
+bool operator!=(const Complex &cn1, const Complex &cn2);
+
+// reads a complex number from input
+std::istream &operator>>(std::istream &in, Complex &a);
+std::ostream &operator<<(std::ostream &out, const Complex &a);
+#+end_src
+
+** =complex.cpp=
+:PROPERTIES:
+:CUSTOM_ID: complex.cpp
+:END:
+#+begin_src cpp
+#include "complex.h"
+#include <cstdlib>
+
+std::istream &operator>>(std::istream &in, Complex &a) {
+  char open;
+  char comma;
+  char close;
+  double aa;
+  double ab;
+  in >> open;
+  if (open == '[') {
+    in >> aa >> comma >> ab >> close;
+    if (comma == ',' && close == ']') {
+      a.a = aa;
+      a.b = ab;
+    } else {
+      std::cerr << "Invalid Input!";
+  }
+  } else {
+    std::cerr << "Invalid Input!";
+  }
+  return in;
+}
+
+std::ostream &operator<<(std::ostream &out, const Complex &a) {
+  return out << "[" << a.a << "," << a.b << "]";
+}
+
+Complex operator+(const Complex &cn1, const Complex &cn2) {
+  Complex res;
+  double a = cn1.a + cn2.a;
+  double b = cn1.b + cn2.b;
+  res.a = a;
+  res.b = b;
+  return res;
+}
+
+Complex operator-(const Complex &cn1, const Complex &cn2) {
+  Complex res;
+  double a = cn1.a - cn2.a;
+  double b = cn1.b - cn2.b;
+  res.a = a;
+  res.b = b;
+  return res;
+}
+
+Complex operator*(const Complex &cn1, const Complex &cn2) {
+  Complex res;
+  double a = (cn1.a * cn2.a) - (cn1.b * cn2.b);
+  double b = (cn1.a * cn2.b) + (cn1.b * cn2.a);
+  res.a = a;
+  res.b = b;
+  return res;
+}
+
+Complex operator/(const Complex &cn1, const Complex &cn2) {
+  Complex res;
+  double a = (cn1.a * cn2.a + cn1.b * cn2.b) / (cn2.a * cn2.a + cn2.b * cn2.b);
+  double b = (cn1.b * cn2.a - cn1.a * cn2.b) / (cn2.a * cn2.a + cn2.b * cn2.b);
+  res.a = a;
+  res.b = b;
+  return res;
+}
+
+Complex operator-(const Complex &cn1) {
+  Complex res;
+  double a = -cn1.a;
+  double b = -cn1.b;
+  res.a = a;
+  res.b = b;
+  return res;
+}
+
+bool operator==(const Complex &cn1, const Complex &cn2) {
+  double epsilon = 0.1;
+  return (std::abs(cn1.a - cn2.a) < epsilon) &&
+  (std::abs(cn1.b - cn2.b) < epsilon);
+}
+
+bool operator!=(const Complex &cn1, const Complex &cn2) {
+  double epsilon = 0.1;
+  return (std::abs(cn1.a - cn2.a) > epsilon) ||
+  (std::abs(cn1.b - cn2.b) > epsilon);
+}
+#+end_src
+
+--------------
+
+Made by JirR02 in Switzerland 🇨🇭