Numeric literal formats in Swift - Time & Space Complexity

Time Complexity: Numeric literal formats

O(n)

Understanding Time Complexity

Let's see how the time it takes to read and use different numeric literals changes as the numbers get bigger.

We want to know how the program's work grows when using various numeric formats.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

let decimal = 12345
let binary = 0b11000000111001
let octal = 0o30071
let hexadecimal = 0x3039

print(decimal)
print(binary)
print(octal)
print(hexadecimal)
    

This code defines numbers in different formats and prints them.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Converting each numeric literal from its format to a usable number.
• How many times: Once per literal, four times total here.

How Execution Grows With Input

As the number of digits in the literal grows, the work to convert it grows too.

Input Size (digits)	Approx. Operations
5	5 steps to read digits
10	10 steps to read digits
20	20 steps to read digits

Pattern observation: The work grows directly with the number of digits in the number.

Final Time Complexity

Time Complexity: O(n)

This means the time to process a numeric literal grows in a straight line with the number of digits it has.

Common Mistake

[X] Wrong: "All numeric literals take the same time to process no matter their size or format."

[OK] Correct: Larger numbers or different formats need more steps to read each digit, so they take more time.

Interview Connect

Understanding how numeric literals are processed helps you explain how programs handle data efficiently, a useful skill in many coding situations.

Self-Check

"What if we changed the numeric literals to include underscores for readability? How would the time complexity change?"

Practice

1. Which of the following is a valid binary numeric literal in Swift?

easy

A. 0b1010

B. 0x1010

C. 1010b

D. 0o1010

Solution

1. Step 1: Understand binary literal format in Swift

   Binary literals start with 0b followed by 0s and 1s.

2. Step 2: Check each option

   0b1010 uses 0b prefix correctly. 0x1010 is hexadecimal, C is invalid, A is octal.

3. Final Answer:

   0b1010 -> Option A

4. Quick Check:

   Binary literals start with 0b = D [OK]

Hint: Binary literals always start with 0b prefix [OK]

Common Mistakes:

• Confusing binary (0b) with hexadecimal (0x)
• Placing the b suffix after the number
• Using octal prefix 0o for binary

2. Which of the following is the correct way to write the number one million using underscores in Swift?

easy

A. 1_00_0000

B. 1000_000

C. 10_00_000

D. 1_000_000

Solution

1. Step 1: Understand underscore usage in numeric literals

   Underscores can be placed anywhere between digits to improve readability.

2. Step 2: Check each option for correct grouping

   1_000_000 groups digits in thousands correctly. Others have irregular grouping which is allowed but uncommon and confusing.

3. Final Answer:

   1_000_000 -> Option D

4. Quick Check:

   Use underscores to separate thousands = A [OK]

Hint: Use underscores every three digits for clarity [OK]

Common Mistakes:

• Placing underscores at the start or end of number
• Using inconsistent grouping that confuses readers
• Thinking underscores change the value

3. What is the output of the following Swift code?

let number = 1.5e2
print(number)

medium

A. 150.0

B. 1.5e2

C. 15.0

D. SyntaxError

Solution

1. Step 1: Understand scientific notation in Swift

   1.5e2 means 1.5 x 10², which equals 150.0.

2. Step 2: Evaluate the print output

   Printing the number shows the decimal value 150.0, not the literal string.

3. Final Answer:

   150.0 -> Option A

4. Quick Check:

   1.5e2 = 150.0 [OK]

Hint: e2 means multiply by 10 squared [OK]

Common Mistakes:

• Thinking print shows the literal string '1.5e2'
• Confusing e2 with e-2 (which divides)
• Assuming integer output instead of floating-point

4. Identify the error in this Swift numeric literal:

let value = 0b1021

medium

A. Should use 0x prefix for binary

B. Binary literals cannot contain digits other than 0 or 1

C. Missing underscore for readability

D. Floating-point literals cannot use binary format

Solution

1. Step 1: Check digits allowed in binary literals

   Binary literals only allow digits 0 and 1 after the 0b prefix.

2. Step 2: Analyze the given literal

   The literal contains digit 2, which is invalid for binary (only 0s and 1s allowed).

3. Final Answer:

   Binary literals cannot contain digits other than 0 or 1 -> Option B

4. Quick Check:

   Binary digits only 0 or 1 = C [OK]

Hint: Binary digits must be only 0 or 1 [OK]

Common Mistakes:

• Thinking underscores are mandatory
• Confusing binary prefix 0b with hexadecimal 0x
• Assuming floating-point literals can be binary

5. You want to represent the decimal number 255 in Swift using hexadecimal and octal literals. Which pair of literals correctly represents 255?

hard

A. 0xFF and 0o255

B. 0x255 and 0o255

C. 0xFF and 0o377

D. 0x377 and 0oFF

Solution

1. Step 1: Convert decimal 255 to hexadecimal

   255 decimal equals FF in hexadecimal, so 0xFF is correct.

2. Step 2: Convert decimal 255 to octal

   255 decimal equals 377 in octal, so 0o377 is correct.

3. Final Answer:

   0xFF and 0o377 -> Option C

4. Quick Check:

   255 decimal = 0xFF hex & 0o377 oct [OK]

Hint: Hex FF = 255 decimal; Oct 377 = 255 decimal [OK]

Common Mistakes:

• Confusing octal digits with decimal digits
• Using decimal digits after 0x prefix
• Mixing up hexadecimal and octal prefixes