Discriminated unions in Typescript - Time & Space Complexity

Time Complexity: Discriminated unions

O(n)

Understanding Time Complexity

We want to understand how the time it takes to check and use discriminated unions grows as the input changes.

Specifically, how does the program's work change when it looks at different union types?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

    type Shape =
      | { kind: 'circle'; radius: number }
      | { kind: 'square'; size: number };

    function area(shape: Shape): number {
      switch (shape.kind) {
        case 'circle':
          return Math.PI * shape.radius ** 2;
        case 'square':
          return shape.size * shape.size;
      }
    }
    

This code checks the kind of shape and calculates its area accordingly.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: A single switch-case check on the shape's kind.
• How many times: Exactly once per function call, no loops or recursion.

How Execution Grows With Input

Since the function only checks one property once, the work stays the same no matter how many shapes we have.

Input Size (n)	Approx. Operations
10	10 checks
100	100 checks
1000	1000 checks

Pattern observation: The work grows linearly (O(n)) with the number of shapes processed.

Final Time Complexity

Time Complexity: O(n)

This means checking the kind and calculating area takes time proportional to the number of shapes processed.

Common Mistake

[X] Wrong: "Checking the kind property takes longer if there are more union types."

[OK] Correct: The check is a simple property read and switch, which does not get slower with more types because it happens once per call.

Interview Connect

Understanding how discriminated unions work helps you write clear and efficient code that is easy to reason about, a skill valued in many coding tasks.

Self-Check

"What if the function had to check multiple properties or nested discriminated unions? How would the time complexity change?"

Practice

1.

What is the main purpose of a discriminated union in TypeScript?

easy

A. To automatically convert types at runtime

B. To create a union of unrelated primitive types

C. To enforce a single type for all variables

D. To distinguish between different object types using a common property

Solution

1. Step 1: Understand discriminated unions

   Discriminated unions use a shared property (called the discriminant) to identify which type an object belongs to.

2. Step 2: Purpose of discriminated unions

   This helps TypeScript safely narrow types in code by checking that property.

3. Final Answer:

   To distinguish between different object types using a common property -> Option D

4. Quick Check:

   Discriminated union = common property to tell types apart [OK]

Hint: Look for a shared property that identifies each type [OK]

Common Mistakes:

• Thinking discriminated unions convert types automatically
• Confusing with simple unions of primitives
• Believing they enforce one single type only

2.

Which of the following is the correct syntax to define a discriminated union type in TypeScript?

type Shape = ?

easy

A. type Shape = { kind: 'circle'; radius: number } | { kind: 'square'; side: number }

B. type Shape = { radius: number } & { side: number }

C. type Shape = { kind: string; radius?: number; side?: number }

D. type Shape = { circle: number } | { square: number }

Solution

1. Step 1: Identify discriminant property

   type Shape = { kind: 'circle'; radius: number } | { kind: 'square'; side: number } uses a common property kind with literal types ('circle' or 'square') to discriminate.

2. Step 2: Check union structure

   type Shape = { kind: 'circle'; radius: number } | { kind: 'square'; side: number } correctly uses a union of two object types distinguished by kind.

3. Final Answer:

   type Shape = { kind: 'circle'; radius: number } | { kind: 'square'; side: number } -> Option A

4. Quick Check:

   Discriminated union = union with common literal property [OK]

Hint: Look for union with a shared literal property for discrimination [OK]

Common Mistakes:

• Using intersection (&) instead of union (|)
• Missing literal type for discriminant property
• Using optional properties without discriminant

3.

What will be the output of the following TypeScript code?

type Animal =
  | { type: 'dog'; barkVolume: number }
  | { type: 'cat'; livesLeft: number };

function describe(animal: Animal) {
  switch (animal.type) {
    case 'dog':
      return `Dog barks at volume ${animal.barkVolume}`;
    case 'cat':
      return `Cat has ${animal.livesLeft} lives left`;
  }
}

console.log(describe({ type: 'cat', livesLeft: 7 }));

medium

A. Cat has 7 lives left

B. Dog barks at volume undefined

C. TypeError at runtime

D. Cat has undefined lives left

Solution

1. Step 1: Analyze the input object

   The input is { type: 'cat', livesLeft: 7 }, so the type is 'cat'.

2. Step 2: Follow the switch case

   The switch matches 'cat' case and returns `Cat has ${animal.livesLeft} lives left`, which becomes 'Cat has 7 lives left'.

3. Final Answer:

   Cat has 7 lives left -> Option A

4. Quick Check:

   Switch on discriminant returns correct string [OK]

Hint: Match the discriminant property in switch to get output [OK]

Common Mistakes:

• Confusing 'dog' and 'cat' cases
• Expecting runtime error due to union
• Ignoring the discriminant property

4.

Identify the error in this TypeScript code using discriminated unions:

type Vehicle =
  | { kind: 'car'; wheels: number }
  | { kind: 'bike'; pedals: number };

function getWheels(vehicle: Vehicle) {
  if (vehicle.kind === 'car') {
    return vehicle.wheels;
  } else {
    return vehicle.wheels;
  }
}

medium

A. Function should use switch instead of if

B. Property 'wheels' does not exist on type 'bike' object

C. Incorrect discriminant property name

D. Missing return type annotation on function

Solution

1. Step 1: Check property access in else branch

   In the else branch, the code accesses vehicle.wheels, but bike type has no wheels property.

2. Step 2: Understand TypeScript error

   This causes a type error because wheels is not defined for { kind: 'bike'; pedals: number }.

3. Final Answer:

   Property 'wheels' does not exist on type 'bike' object -> Option B

4. Quick Check:

   Accessing wrong property on union member causes error [OK]

Hint: Check property exists on all union members before access [OK]

Common Mistakes:

• Assuming all union members share same properties
• Ignoring TypeScript error messages
• Thinking switch is mandatory over if

5.

Given the following discriminated union, how can you safely add a new shape type rectangle with width and height properties and update the area function accordingly?

type Shape =
  | { kind: 'circle'; radius: number }
  | { kind: 'square'; side: number };

function area(shape: Shape): number {
  switch (shape.kind) {
    case 'circle':
      return Math.PI * shape.radius ** 2;
    case 'square':
      return shape.side ** 2;
  }
}

hard

A. Add { kind: 'rectangle'; width: number; height: number } to Shape union and replace switch with if-else

B. Add { kind: 'rectangle'; width: number; height: number } to Shape union but no change needed in area function

C. Add { kind: 'rectangle'; width: number; height: number } to Shape union and add case 'rectangle' in switch returning width * height

D. Add { kind: 'rectangle'; width: number; height: number } to Shape union and remove existing cases

Solution

1. Step 1: Extend the union type

   Add the new shape type with discriminant kind: 'rectangle' and properties width and height to the Shape union.

2. Step 2: Update the area function

   Add a new case in the switch for 'rectangle' that returns shape.width * shape.height to correctly calculate the area.

3. Final Answer:

   Add { kind: 'rectangle'; width: number; height: number } to Shape union and add case 'rectangle' in switch returning width * height -> Option C

4. Quick Check:

   Extend union and handle new case in switch [OK]

Hint: Add new type to union and handle it in switch [OK]

Common Mistakes:

• Forgetting to update the function for new type
• Removing existing cases accidentally
• Not using discriminant property in new type