Union vs intersection mental model in Typescript - Performance Comparison

Time Complexity: Union vs intersection mental model

O(n)

Understanding Time Complexity

When working with union and intersection types in TypeScript, it's helpful to understand how the operations scale as we combine types.

We want to see how the complexity grows when checking or combining these types.

Scenario Under Consideration

Analyze the time complexity of the following type checks using union and intersection.

type A = { a: number };
type B = { b: string };
type C = A | B; // union

type D = A & B; // intersection

function checkUnion(x: C) {
  if ('a' in x) return x.a;
  else return x.b;
}

function checkIntersection(x: D) {
  return x.a + x.b.length;
}
    

This code defines union and intersection types and shows how we access their properties.

Identify Repeating Operations

Look at how many checks or property accesses happen when using union or intersection types.

• Primary operation: Property existence checks for union, direct property access for intersection.
• How many times: For union, one check per type to decide type; for intersection, all properties accessed directly.

How Execution Grows With Input

As the number of types combined grows, the checks or accesses increase.

Input Size (number of types)	Approx. Operations
2	2 checks or accesses
5	5 checks or accesses
10	10 checks or accesses

Pattern observation: The number of operations grows linearly with the number of types combined.

Final Time Complexity

Time Complexity: O(n)

This means the time to check or access properties grows in direct proportion to the number of types involved.

Common Mistake

[X] Wrong: "Union and intersection types have constant time checks regardless of size."

[OK] Correct: Each additional type adds more properties to check or access, so the work grows with the number of types.

Interview Connect

Understanding how combining types affects checking helps you reason about code performance and type safety in real projects.

Self-Check

"What if we nested unions inside intersections? How would that affect the time complexity?"

Practice

1. Which statement best describes a union type in TypeScript?

easy

A. A value must have all combined types, like string & number.

B. A value can be one type or another, like string | number.

C. It restricts a value to only one specific type.

D. It creates a new type by excluding some properties.

Solution

1. Step 1: Understand union type meaning

   A union type means a value can be one of several types, for example, string | number means the value can be either a string or a number.

2. Step 2: Compare with intersection type

   An intersection type requires a value to have all combined types, which is different from union. So a value can be one type or another, like string | number, correctly describes union.

3. Final Answer:

   A value can be one type or another, like string | number. -> Option B

4. Quick Check:

   Union = one of multiple types [OK]

Hint: Union means one type OR another, intersection means ALL types [OK]

Common Mistakes:

• Confusing union with intersection
• Thinking union requires all types simultaneously
• Mixing up syntax symbols | and &

2. Which of the following is the correct syntax for an intersection type combining A and B?

easy

A. type C = A | B;

B. type C = A, B;

C. type C = A + B;

D. type C = A & B;

Solution

1. Step 1: Recall intersection syntax

   Intersection types use the ampersand & symbol to combine types, meaning the value must satisfy both types.

2. Step 2: Identify correct syntax

   type C = A & B; uses A & B, which is the correct syntax for intersection types in TypeScript.

3. Final Answer:

   type C = A & B; -> Option D

4. Quick Check:

   Intersection uses & symbol [OK]

Hint: Intersection uses & symbol, union uses | symbol [OK]

Common Mistakes:

• Using | instead of & for intersection
• Using invalid operators like + or comma
• Confusing type alias syntax

3. What is the type of variable value after this assignment?

type A = { name: string };
type B = { age: number };

let value: A | B = { name: "Alice", age: 30 };

medium

A. Error: value must be either A or B, not both.

B. Valid: value must have only name property.

C. Valid: value has both name and age properties.

D. Error: value must have only age property.

Solution

1. Step 1: Understand union type assignment

   The variable value is declared as A | B, meaning it can be either type A or type B.

2. Step 2: Check assigned object

   The assigned object has both name and age properties, which does not strictly satisfy either A or B alone, so it is not valid as a union type.

3. Final Answer:

   Error: value must be either A or B, not both. -> Option A

4. Quick Check:

   Union requires value to match one type exactly [OK]

Hint: Union requires value to match one type exactly [OK]

Common Mistakes:

• Thinking union allows objects with all properties combined
• Confusing union with intersection requirements
• Assuming extra properties are allowed in union

4. Identify the error in this TypeScript code:

type A = { name: string };
type B = { age: number };

let person: A & B = { name: "Bob" };

medium

A. Syntax error in type declaration.

B. Incorrect use of union instead of intersection.

C. Missing property age in the object assigned to person.

D. Extra property name not allowed.

Solution

1. Step 1: Understand intersection type requirements

   An intersection type A & B requires the value to have all properties from both types A and B.

2. Step 2: Check assigned object properties

   The object assigned has only name property but is missing age, so it does not satisfy the intersection type.

3. Final Answer:

   Missing property age in the object assigned to person. -> Option C

4. Quick Check:

   Intersection requires all properties present [OK]

Hint: Intersection needs all properties present [OK]

Common Mistakes:

• Thinking intersection allows partial properties
• Confusing union and intersection requirements
• Ignoring missing properties error

5. Given these types:

type Name = { name: string };
type Age = { age: number };
type Contact = { email: string };

// Which type correctly represents a value that must have a name and either age or email?

// Choose the correct type for Person:

hard

A. type Person = Name & (Age | Contact);

B. type Person = (Name & Age) | Contact;

C. type Person = Name | Age & Contact;

D. type Person = Name & Age & Contact;

Solution

1. Step 1: Analyze requirement

   The value must have a name property and either an age or email property.

2. Step 2: Translate to types

   This means the type must be Name AND (either Age OR Contact), which is Name & (Age | Contact).

3. Step 3: Check options

   type Person = Name & (Age | Contact); matches this exactly. Other options either change the logic or require all three properties.

4. Final Answer:

   type Person = Name & (Age | Contact); -> Option A

5. Quick Check:

   Name AND (Age OR Contact) = Name & (Age | Contact) [OK]

Hint: Use parentheses to combine union and intersection correctly [OK]

Common Mistakes:

• Ignoring parentheses changing logic
• Mixing order of union and intersection
• Choosing all properties instead of either/or