Exhaustive checking with never in Typescript - Time & Space Complexity

Time Complexity: Exhaustive checking with never

O(n)

Understanding Time Complexity

We want to see how the time needed grows when using exhaustive checks with the never type in TypeScript.

How does the program behave as the number of cases to check increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

    type Shape = 'circle' | 'square' | 'triangle';

    function area(shape: Shape, size: number): number {
      switch (shape) {
        case 'circle':
          return Math.PI * size * size;
        case 'square':
          return size * size;
        case 'triangle':
          return (Math.sqrt(3) / 4) * size * size;
        default:
          const _exhaustiveCheck: never = shape;
          return _exhaustiveCheck;
      }
    }
    

This code calculates area for different shapes and uses never to ensure all cases are handled.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The switch statement checks the shape once per call.
• How many times: Exactly one check per function call; no loops or recursion.

How Execution Grows With Input

Explain the growth pattern intuitively.

Input Size (n)	Approx. Operations
3 (shapes)	Up to 3 checks per call
10 (hypothetical shapes)	Up to 10 checks per call
100 (hypothetical shapes)	Up to 100 checks per call

Pattern observation: The number of checks grows linearly with the number of shape cases.

Final Time Complexity

Time Complexity: O(n)

This means the time to check grows directly with the number of shape cases you have.

Common Mistake

[X] Wrong: "Using never makes the code run faster or skip checks."

[OK] Correct: The never type is only for compile-time checks. At runtime, the switch still checks each case one by one.

Interview Connect

Understanding how exhaustive checks affect runtime helps you write safer code and explain your reasoning clearly in interviews.

Self-Check

"What if we replaced the switch with a dictionary lookup? How would the time complexity change?"

Practice

1. What is the main purpose of using never in exhaustive checking in TypeScript?

easy

A. To declare a variable that can hold any value

B. To allow any type of value without restrictions

C. To ignore errors during compilation

D. To ensure all possible cases are handled in a switch or conditional

Solution

1. Step 1: Understand the role of never in exhaustive checks

   never is used to represent values that should never occur, helping catch unhandled cases.

2. Step 2: Connect never usage to exhaustive case handling

   By forcing a function to accept never, TypeScript ensures all cases are covered, or else a compile error occurs.

3. Final Answer:

   To ensure all possible cases are handled in a switch or conditional -> Option D

4. Quick Check:

   Exhaustive checking = catch all cases [OK]

Hint: Use never to catch missing cases in switch statements [OK]

Common Mistakes:

• Thinking never allows any value
• Using never to ignore errors
• Confusing never with unknown type

2. Which of the following is the correct syntax for a helper function that uses never to enforce exhaustive checking?

easy

A. function assertNever(x: never): never { throw new Error('Unexpected value: ' + x); }

B. function assertNever(x: any): void { console.log(x); }

C. function assertNever(x: unknown): never { return x; }

D. function assertNever(x: never): void { return; }

Solution

1. Step 1: Identify correct parameter and return types

   The helper function must accept a parameter of type never and return never because it throws an error.

2. Step 2: Check function body matches expected behavior

   The function throws an error with the unexpected value, which is the standard pattern for exhaustive checks.

3. Final Answer:

   function assertNever(x: never): never { throw new Error('Unexpected value: ' + x); } -> Option A

4. Quick Check:

   Helper function with never param and throw = correct [OK]

Hint: Helper must take never and throw error to enforce checks [OK]

Common Mistakes:

• Using any or unknown instead of never
• Not throwing an error inside the function
• Returning void instead of never

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

type Shape = 'circle' | 'square';
function area(shape: Shape) {
  switch (shape) {
    case 'circle':
      return 3.14 * 2 * 2;
    // Missing case for 'square'
    default:
      return assertNever(shape);
  }
}

function assertNever(x: never): never {
  throw new Error('Unexpected shape: ' + x);
}

console.log(area('square'));

medium

A. Returns 12.56

B. Throws Error: Unexpected shape: square

C. Returns undefined

D. Compilation error due to missing case

Solution

1. Step 1: Analyze switch cases and input

   The function handles 'circle' but not 'square', so at runtime, calling area('square') hits the default case.

2. Step 2: Understand assertNever behavior at runtime

   The assertNever function throws an error with the unexpected shape, so the program throws a runtime error.

3. Final Answer:

   Throws Error: Unexpected shape: square -> Option B

4. Quick Check:

   Missing case causes runtime error when called [OK]

Hint: Missing case triggers runtime error when called [OK]

Common Mistakes:

• Assuming missing case returns undefined
• Thinking it returns a number for all inputs
• Expecting compile error instead of runtime error

4. Identify the error in this TypeScript code using exhaustive checking:

type Direction = 'up' | 'down' | 'left';
function move(dir: Direction) {
  switch (dir) {
    case 'up':
      return 'Moving up';
    case 'down':
      return 'Moving down';
    default:
      return assertNever(dir);
  }
}

function assertNever(x: never): never {
  throw new Error('Unexpected direction: ' + x);
}

medium

A. Missing case for 'left' in switch statement

B. assertNever function has wrong parameter type

C. Switch statement should not have a default case

D. Function move should return void instead of string

Solution

1. Step 1: Check all union cases in switch

   The type Direction has 'up', 'down', and 'left', but 'left' is missing in the switch.

2. Step 2: Understand impact of missing case with assertNever

   Missing 'left' causes default to call assertNever with a string, which is not never, causing a compile error.

3. Final Answer:

   Missing case for 'left' in switch statement -> Option A

4. Quick Check:

   All union cases must be handled [OK]

Hint: Check all union cases explicitly to avoid errors [OK]

Common Mistakes:

• Ignoring missing union cases
• Thinking default case covers all safely
• Wrong assertNever parameter type

5. Given this code, how can you modify it to ensure exhaustive checking for all Status values?

type Status = 'success' | 'error' | 'loading';

function handleStatus(status: Status) {
  switch (status) {
    case 'success':
      return 'Done';
    case 'error':
      return 'Failed';
    // Missing 'loading' case
    default:
      return assertNever(status);
  }
}

function assertNever(x: never): never {
  throw new Error('Unexpected status: ' + x);
}

hard

A. Change the type Status to include only 'success' and 'error'

B. Remove the default case and rely on TypeScript errors

C. Add a case for 'loading' in the switch statement

D. Change assertNever parameter type to any

Solution

1. Step 1: Identify missing union case in switch

   The 'loading' case is missing, so the switch is not exhaustive.

2. Step 2: Add missing case to ensure all Status values are handled

   Adding case 'loading': with appropriate return ensures exhaustive checking and no runtime errors.

3. Final Answer:

   Add a case for 'loading' in the switch statement -> Option C

4. Quick Check:

   All union members must have cases [OK]

Hint: Add missing union cases to switch for full coverage [OK]

Common Mistakes:

• Removing default case without adding missing cases
• Changing type to avoid handling all cases
• Using any instead of never in assertNever