Amending the last commit in Git - Time & Space Complexity

Time Complexity: Amending the last commit

O(n)

Understanding Time Complexity

We want to understand how the time taken by the git amend command changes as the size of the last commit grows.

Specifically, how does git handle updating the last commit when files or changes increase?

Scenario Under Consideration

Analyze the time complexity of the following git commands.

git add file.txt

git commit --amend --no-edit

This code adds changes to a file and then updates the last commit without changing its message.

Identify Repeating Operations

Look for repeated work git does during amend.

• Primary operation: Git reads and writes the commit object and updates the tree with the new file changes.
• How many times: This happens once per amend command, but internally git processes all changed files in the commit.

How Execution Grows With Input

As the number of changed files or size of changes grows, git must process more data to update the commit.

Input Size (changed files)	Approx. Operations
10	Processes 10 files to update commit tree
100	Processes 100 files, more data to write
1000	Processes 1000 files, significantly more work

Pattern observation: The work grows roughly in proportion to the number of changed files.

Final Time Complexity

Time Complexity: O(n)

This means the time to amend grows linearly with the number of changed files or changes in the last commit.

Common Mistake

[X] Wrong: "Amending the last commit always takes the same time no matter how many files changed."

[OK] Correct: Git must update the commit tree and objects for all changed files, so more changes mean more work.

Interview Connect

Understanding how git commands scale with project size helps you reason about performance and efficiency in real projects.

Self-Check

"What if we amended a commit that changed only one large file instead of many small files? How would the time complexity change?"