Brace expansion ({1..10}) in Bash Scripting - Time & Space Complexity

Time Complexity: Brace expansion ({1..10})

O(n)

Understanding Time Complexity

We want to understand how the time it takes to run a bash script using brace expansion changes as the range grows.

Specifically, how does the number of generated items affect the script's work?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

for i in {1..10}
do
  echo "Number: $i"
done

This script prints numbers from 1 to 10 using brace expansion to generate the list.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The for-loop iterates over each number generated by the brace expansion.
• How many times: Exactly once for each number in the range (here, 10 times).

How Execution Grows With Input

As the range increases, the loop runs more times, so the work grows directly with the number of items.

Input Size (n)	Approx. Operations
10	10 echo commands
100	100 echo commands
1000	1000 echo commands

Pattern observation: The number of operations grows in a straight line with the input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to run the script grows directly in proportion to how many numbers are in the range.

Common Mistake

[X] Wrong: "Brace expansion runs instantly no matter how big the range is."

[OK] Correct: The shell must generate and loop over each item, so more items mean more work and longer time.

Interview Connect

Understanding how loops scale with input size is a key skill in scripting and automation, helping you write efficient scripts that handle bigger tasks smoothly.

Self-Check

"What if we replaced brace expansion with a command that generates numbers dynamically, like seq? How would the time complexity change?"

Practice

1. What does the Bash brace expansion {1..5} produce when used in a command?

easy

A. A sequence of numbers: 1 2 3 4 5

B. A sequence of letters: a b c d e

C. A syntax error

D. A single string: {1..5}

Solution

1. Step 1: Understand brace expansion syntax

   The syntax {start..end} generates a sequence of numbers or letters from start to end.

2. Step 2: Apply to numbers 1 to 5

   Using {1..5} produces the numbers 1, 2, 3, 4, 5 separated by spaces.

3. Final Answer:

   A sequence of numbers: 1 2 3 4 5 -> Option A

4. Quick Check:

   Brace expansion {1..5} = 1 2 3 4 5 [OK]

Hint: Brace expansion {x..y} lists numbers or letters from x to y [OK]

Common Mistakes:

• Thinking it outputs letters for numbers
• Expecting a syntax error
• Assuming it outputs the literal string

2. Which of the following is the correct syntax to generate numbers from 3 to 7 using brace expansion in Bash?

easy

A. echo [3..7]

B. echo {3-7}

C. echo (3..7)

D. echo {3..7}

Solution

1. Step 1: Recall correct brace expansion syntax

   Brace expansion uses curly braces with two dots: {start..end}.

2. Step 2: Check each option

   Only echo {3..7} uses correct braces and dots. Others use wrong symbols like parentheses, brackets, or hyphens.

3. Final Answer:

   echo {3..7} -> Option D

4. Quick Check:

   Correct syntax uses curly braces and two dots [OK]

Hint: Use curly braces and two dots for sequences {start..end} [OK]

Common Mistakes:

• Using parentheses or brackets instead of braces
• Using a hyphen instead of two dots
• Missing braces entirely

3. What is the output of the following Bash command?

echo file{1..3}.txt

medium

A. file1.txt file2.txt file3.txt

B. file{1..3}.txt

C. file1 file2 file3.txt

D. file1.txt file2.txt file3

Solution

1. Step 1: Understand brace expansion with suffix

   The brace expansion {1..3} generates 1 2 3, and the suffix .txt is added to each.

2. Step 2: Combine parts

   Each expanded number is combined with 'file' prefix and '.txt' suffix, producing: file1.txt file2.txt file3.txt.

3. Final Answer:

   file1.txt file2.txt file3.txt -> Option A

4. Quick Check:

   Brace expansion with suffix repeats suffix for each number [OK]

Hint: Brace expansion repeats suffix/prefix for each number [OK]

Common Mistakes:

• Expecting literal braces in output
• Missing suffix on some items
• Mixing suffix placement

4. Identify the error in this Bash command:

echo {1..5..2}

medium

A. Outputs 1 2 3 4 5

B. Syntax error: too many dots

C. No error; outputs 1 3 5

D. Outputs nothing

Solution

1. Step 1: Understand brace expansion with step

   The syntax {start..end..step} is valid in Bash to generate sequences with a step.

2. Step 2: Apply to {1..5..2}

   This generates numbers starting at 1, stepping by 2, up to 5: 1, 3, 5.

3. Final Answer:

   No error; outputs 1 3 5 -> Option C

4. Quick Check:

   Brace expansion supports step with two dots between numbers [OK]

Hint: Brace expansion can include step: {start..end..step} [OK]

Common Mistakes:

• Thinking extra dots cause syntax error
• Expecting continuous sequence ignoring step
• Assuming no output for step usage

5. You want to create empty files named log1.txt through log10.txt using a single Bash command with brace expansion. Which command achieves this?

hard

A. touch log{1..10}

B. touch log{1..10}.txt

C. touch log{1..10}.txt.txt

D. touch log{1..10.txt}

Solution

1. Step 1: Understand the goal

   You want files named log1.txt, log2.txt, ..., log10.txt created.

2. Step 2: Use brace expansion with suffix

   The correct syntax is touch log{1..10}.txt, which expands to log1.txt, log2.txt, ..., log10.txt.

3. Step 3: Check other options

   touch log{1..10} omits the .txt suffix; touch log{1..10.txt} has invalid syntax with .txt inside braces; touch log{1..10}.txt.txt adds an extra .txt to each filename.

4. Final Answer:

   touch log{1..10}.txt -> Option B

5. Quick Check:

   Brace expansion with suffix creates all files at once [OK]

Hint: Use touch with brace expansion and suffix: touch name{1..n}.ext [OK]

Common Mistakes:

• Placing suffix inside braces incorrectly
• Adding extra suffixes
• Omitting suffix leading to wrong filenames