Polymorphism through interfaces in Typescript - Time & Space Complexity

Time Complexity: Polymorphism through interfaces

O(n)

Understanding Time Complexity

We want to understand how the time it takes to run code changes when using polymorphism with interfaces.

Specifically, how does calling methods through interfaces affect the number of steps the program takes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

interface Shape {
  area(): number;
}

class Circle implements Shape {
  constructor(private radius: number) {}
  area() { return Math.PI * this.radius * this.radius; }
}

function totalArea(shapes: Shape[]): number {
  let sum = 0;
  for (const shape of shapes) {
    sum += shape.area();
  }
  return sum;
}
    

This code calculates the total area of many shapes by calling the area method on each shape through an interface.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through the array of shapes and calling area() on each.
• How many times: Once for each shape in the input array.

How Execution Grows With Input

Each shape requires one call to area(), so the total steps grow as the number of shapes grows.

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

Pattern observation: The number of operations grows directly with the number of shapes.

Final Time Complexity

Time Complexity: O(n)

This means the time to compute total area grows in a straight line with the number of shapes.

Common Mistake

[X] Wrong: "Calling methods through interfaces makes the code slower in a way that changes the time complexity."

[OK] Correct: Calling methods via interfaces adds a tiny fixed cost per call but does not change how the total steps grow with input size.

Interview Connect

Understanding how polymorphism affects time helps you explain your code's efficiency clearly and confidently.

Self-Check

"What if the area() method itself contained a loop over a list of points? How would the time complexity change?"

Practice

1. What does polymorphism through interfaces allow in TypeScript?

easy

A. Only one class can implement an interface

B. Different classes to be treated the same if they implement the same interface

C. Interfaces can hold data like variables

D. Classes cannot implement more than one interface

Solution

1. Step 1: Understand polymorphism concept

   Polymorphism means using different objects in the same way if they share a common interface.

2. Step 2: Apply to interfaces in TypeScript

   Interfaces define methods that classes promise to implement, allowing different classes to be used interchangeably.

3. Final Answer:

   Different classes to be treated the same if they implement the same interface -> Option B

4. Quick Check:

   Polymorphism = Same interface, different classes [OK]

Hint: Polymorphism means same interface, different class objects [OK]

Common Mistakes:

• Thinking interfaces hold data like variables
• Believing only one class can implement an interface
• Assuming classes can't implement multiple interfaces

2. Which of the following is the correct syntax for a TypeScript interface with a method speak() that returns a string?

easy

A. interface Animal { speak(): string; }

B. interface Animal { speak: string(); }

C. interface Animal { speak() => string; }

D. interface Animal { speak: () => string; }

Solution

1. Step 1: Review interface method syntax

   In TypeScript, methods in interfaces are declared as methodName(): returnType;.

2. Step 2: Check each option

   interface Animal { speak(): string; } correctly uses speak(): string;. interface Animal { speak: string(); } incorrectly places parentheses after the type. interface Animal { speak() => string; } uses arrow syntax wrongly. interface Animal { speak: () => string; } uses a function type, which is valid but less common for method declarations.

3. Final Answer:

   interface Animal { speak(): string; } -> Option A

4. Quick Check:

   Method syntax = methodName(): returnType [OK]

Hint: Method in interface uses colon after name, not arrow [OK]

Common Mistakes:

• Using arrow syntax inside interface method
• Putting parentheses after type instead of method name
• Confusing function type with method declaration

3. What will be the output of this TypeScript code?

interface Shape {
  area(): number;
}

class Square implements Shape {
  constructor(private side: number) {}
  area() { return this.side * this.side; }
}

class Circle implements Shape {
  constructor(private radius: number) {}
  area() { return Math.PI * this.radius * this.radius; }
}

function printArea(shape: Shape) {
  console.log(shape.area().toFixed(2));
}

const sq = new Square(3);
const cir = new Circle(2);
printArea(sq);
printArea(cir);

medium

A. Error: area method missing

B. 6 and 12.56

C. 9.00 and 12.57

D. 9 and 12.56

Solution

1. Step 1: Calculate area of Square

   Square side is 3, so area = 3 * 3 = 9. Output with two decimals is "9.00".

2. Step 2: Calculate area of Circle

   Circle radius is 2, area = π * 2 * 2 ≈ 12.566. Rounded to two decimals is "12.57".

3. Final Answer:

   9.00 and 12.57 -> Option C

4. Quick Check:

   Square area = 9.00, Circle area ≈ 12.57 [OK]

Hint: Calculate areas, then round to 2 decimals [OK]

Common Mistakes:

• Forgetting to round with toFixed(2)
• Using wrong formula for circle area
• Confusing radius and side length

4. Identify the error in this TypeScript code using interfaces and polymorphism:

interface Vehicle {
  move(): void;
}

class Car implements Vehicle {
  move(distance: number) {
    console.log(`Car moved ${distance} meters`);
  }
}

const myCar: Vehicle = new Car();
myCar.move();

medium

A. Missing return type in move method

B. Cannot assign new Car() to Vehicle type

C. Interface Vehicle cannot have methods

D. Method move in Car has a different signature than in Vehicle interface

Solution

1. Step 1: Compare method signatures

   Interface Vehicle defines move() with no parameters. Car's move method requires a number parameter.

2. Step 2: Understand TypeScript method compatibility

   Method signatures must match exactly for interface implementation. Car's move method does not match Vehicle's move method.

3. Final Answer:

   Method move in Car has a different signature than in Vehicle interface -> Option D

4. Quick Check:

   Method signature mismatch = Error [OK]

Hint: Method signatures must match interface exactly [OK]

Common Mistakes:

• Thinking parameter difference is allowed
• Believing assignment to interface type is invalid
• Ignoring method return type requirements

5. You have an interface Logger with a method log(message: string): void. You want to create two classes: ConsoleLogger that logs to the console, and FileLogger that stores logs in an array. How can you use polymorphism to write a function writeLog(logger: Logger, msg: string) that works with both classes? Which implementation is correct?

hard

A. function writeLog(logger: Logger, msg: string) { logger.log(msg); }

B. function writeLog(logger: Logger, msg: string) { console.log(msg); }

C. function writeLog(logger: Logger, msg: string) { logger.write(msg); }

D. function writeLog(logger: Logger, msg: string) { logger.log(); }

Solution

1. Step 1: Understand polymorphism with interfaces

   The function should accept any object implementing Logger and call its log method with the message.

2. Step 2: Check each function implementation

   function writeLog(logger: Logger, msg: string) { logger.log(msg); } calls logger.log(msg) correctly. function writeLog(logger: Logger, msg: string) { console.log(msg); } ignores the passed logger and logs directly to console. function writeLog(logger: Logger, msg: string) { logger.write(msg); } calls a non-existent method write. function writeLog(logger: Logger, msg: string) { logger.log(); } calls log without arguments, which is incorrect.

3. Final Answer:

   function writeLog(logger: Logger, msg: string) { logger.log(msg); } -> Option A

4. Quick Check:

   Call interface method with correct argument [OK]

Hint: Call the interface method with the message parameter [OK]

Common Mistakes:

• Calling wrong method name
• Not passing the message argument
• Ignoring the logger parameter