Abstract classes in C++ - Time & Space Complexity

Time Complexity: Abstract classes

O(n)

Understanding Time Complexity

When using abstract classes, we want to know how the program's running time changes as we create and use objects from these classes.

We ask: How does the time to run methods from abstract classes grow with the number of objects?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class Shape {
public:
    virtual void draw() = 0; // abstract method
};

class Circle : public Shape {
public:
    void draw() override {
        // drawing circle code
    }
};

void drawShapes(std::vector<Shape *> &shapes) {
    for (auto shape : shapes) {
        shape->draw();
    }
}
    

This code defines an abstract class Shape with a pure virtual method draw. It then draws all shapes in a list by calling draw on each.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Calling the draw() method on each shape object.
• How many times: Once for each shape in the vector, so as many times as the number of shapes.

How Execution Grows With Input

As the number of shapes increases, the total time to draw all shapes grows directly with that number.

Input Size (n)	Approx. Operations
10	10 draw calls
100	100 draw calls
1000	1000 draw calls

Pattern observation: The time grows in a straight line with the number of shapes.

Final Time Complexity

Time Complexity: O(n)

This means the time to draw all shapes grows directly with how many shapes there are.

Common Mistake

[X] Wrong: "Using abstract classes makes the program slower because of extra overhead in method calls."

[OK] Correct: The main time cost comes from how many times methods run, not from the abstract class itself. Calling virtual methods has a small fixed cost, but the total time depends mostly on how many objects you process.

Interview Connect

Understanding how abstract classes affect time helps you explain design choices clearly and shows you know how code structure relates to performance.

Self-Check

"What if we added nested loops inside the draw() method? How would the time complexity change?"

Practice

1. What is true about an abstract class in C++?

easy

A. It can be instantiated like any other class.

B. It cannot be instantiated directly.

C. It must have no member functions.

D. It cannot have any data members.

Solution

1. Step 1: Understand abstract class instantiation rules

   Abstract classes have at least one pure virtual function, so they cannot create objects directly.

2. Step 2: Check other options

   The other options are incorrect because abstract classes can have member functions and data members.

3. Final Answer:

   It cannot be instantiated directly. -> Option B

4. Quick Check:

   Abstract class = no direct objects [OK]

Hint: Abstract classes always have pure virtual functions [OK]

Common Mistakes:

• Thinking abstract classes can create objects
• Believing abstract classes cannot have data members
• Confusing abstract classes with interfaces

2. Which of the following is the correct way to declare a pure virtual function in a C++ abstract class?

easy

A. virtual void func() = 0;

B. void func() = 0;

C. virtual void func();

D. void func() {};

Solution

1. Step 1: Recall pure virtual function syntax

   Pure virtual functions are declared with 'virtual' keyword and '= 0' at the end.

2. Step 2: Analyze options

   virtual void func() = 0; matches the correct syntax. void func() = 0; misses 'virtual'. virtual void func(); is a normal virtual function. void func() {}; is a normal function with a body.

3. Final Answer:

   virtual void func() = 0; -> Option A

4. Quick Check:

   Pure virtual = virtual + '= 0' [OK]

Hint: Pure virtual always ends with '= 0;' [OK]

Common Mistakes:

• Omitting 'virtual' keyword
• Adding function body to pure virtual
• Confusing normal virtual with pure virtual

3. What will be the output of the following C++ code?

#include <iostream>
class Base {
public:
    virtual void show() = 0;
};
class Derived : public Base {
public:
    void show() { std::cout << "Hello"; }
};
int main() {
    Derived d;
    d.show();
    return 0;
}

medium

A. No output

B. Compilation error

C. Hello

D. Runtime error

Solution

1. Step 1: Check abstract class and derived implementation

   Base has a pure virtual function 'show'. Derived overrides it with a concrete implementation.

2. Step 2: Analyze main function output

   Derived object 'd' calls 'show()', which prints "Hello".

3. Final Answer:

   Hello -> Option C

4. Quick Check:

   Derived implements pure virtual, so prints output [OK]

Hint: Derived must implement pure virtual to avoid errors [OK]

Common Mistakes:

• Expecting compilation error without implementation
• Thinking pure virtual functions run by themselves
• Confusing output with no output

4. Identify the error in this code snippet:

#include <iostream>
class Abstract {
public:
    virtual void display() = 0;
};

class Concrete : public Abstract {
public:
    void display() { std::cout << "Hi"; }
};

int main() {
    Abstract a;
    Concrete c;
    c.display();
    return 0;
}

medium

A. Cannot instantiate abstract class 'Abstract' directly.

B. Missing implementation of display() in Concrete.

C. Syntax error in class declaration.

D. No error, code runs fine.

Solution

1. Step 1: Check instantiation of abstract class

   Abstract class 'Abstract' has a pure virtual function, so cannot create object 'a'.

2. Step 2: Verify other parts

   Concrete implements display(), so no error there. Syntax is correct.

3. Final Answer:

   Cannot instantiate abstract class 'Abstract' directly. -> Option A

4. Quick Check:

   Abstract objects not allowed [OK]

Hint: Never create objects of abstract classes [OK]

Common Mistakes:

• Trying to instantiate abstract class
• Ignoring pure virtual function rules
• Assuming implementation missing in derived

5. You want to design a shape system where every shape must provide its area calculation. Which is the best way to enforce this using abstract classes in C++?

hard

A. Create a class Shape with no functions and add area() only in derived classes.

B. Create a class Shape with a normal function double area() that returns 0, and override it in derived classes.

C. Create a class Shape with a virtual function double area() with empty body.

D. Create an abstract class Shape with a pure virtual function double area() = 0; and derive specific shapes implementing area().

Solution

1. Step 1: Understand requirement for enforcing area() implementation

   Using a pure virtual function in an abstract class forces all derived classes to implement area().

2. Step 2: Evaluate options

   Create an abstract class Shape with a pure virtual function double area() = 0; and derive specific shapes implementing area(). uses pure virtual function, which is the best way. Create a class Shape with a normal function double area() that returns 0, and override it in derived classes. returns 0 by default, which may hide missing implementations. Create a class Shape with no functions and add area() only in derived classes. does not enforce area() in base. Create a class Shape with a virtual function double area() with empty body. has virtual but not pure, so no enforcement.

3. Final Answer:

   Create an abstract class Shape with a pure virtual function double area() = 0; and derive specific shapes implementing area(). -> Option D

4. Quick Check:

   Pure virtual enforces implementation [OK]

Hint: Use pure virtual to force derived class methods [OK]

Common Mistakes:

• Using normal virtual instead of pure virtual
• Not enforcing method in base class
• Returning default values hiding missing overrides