What diff algorithms are available and which should I use?

Understanding Diff Algorithms

Diff algorithms are the mathematical engines behind diff tools, determining how differences are identified and displayed. While end users typically don't think about which algorithm is being used, understanding available algorithms and their trade-offs helps you choose the right diff tool and interpret results correctly.

Different algorithms use different strategies to identify differences, leading to different results with different computational costs. The choice of algorithm affects both the quality of results and the speed of comparison.

The Classic Longest Common Subsequence (LCS) Algorithm

How LCS Works

The Longest Common Subsequence algorithm finds the longest sequence of items that appears in both files in the same order:

Compare all possible subsequences in both files
Find the longest subsequence appearing in both
Lines not in the LCS are differences
Display what was added, removed, and kept

LCS guarantees finding the minimal-change diff, meaning fewest lines marked as different.

Advantages of LCS

Optimal results: Minimizes the number of differences shown
Predictable: Always produces the same result for the same input
Mathematically sound: Provably correct approach

Disadvantages of LCS

Slow: O(n×m) time complexity where n and m are file sizes
Memory intensive: Requires storing comparison data for all possible subsequences
Not practical for large files: Becomes unusably slow with files over ~1000 lines

When to Use LCS

LCS is suitable for:

Small files (under 1000 lines)
When guaranteed optimal results are important
Academic or research purposes
When performance is less critical than correctness

Most practical diff tools have moved away from pure LCS due to performance limitations.

The Myers Algorithm (Diff Algorithm)

How Myers Algorithm Works

Myers algorithm finds the shortest "edit script" with fewer operations required:

Creates a search space of possible edit paths
Explores the space to find shortest path to make files identical
Unlike LCS, focuses on minimal edits rather than longest common sequence
More efficient exploration reduces unnecessary comparisons

Advantages of Myers

Faster than LCS: O(min(n, m) × d) where d is the number of differences
Practical for large files: Works efficiently on real-world file sizes
Better for version control: Produces intuitive results for code changes
Still optimal: Produces minimal-change diffs when differences are small
Industry standard: Used by Git and most modern diff tools

Disadvantages of Myers

More complex: Harder to understand than naive approaches
Still slow for very different files: Degrades when files differ significantly

When to Use Myers

Myers algorithm is suitable for:

Most real-world use cases
Version control systems (Git uses this)
Code comparison
Files of any practical size
When both correctness and performance matter

Git's diff command and most modern tools default to Myers or variants.

Patience Algorithm

How Patience Algorithm Works

Patience algorithm uses a different approach inspired by card game solitaire:

Lines with unique tokens are matched first (patience matching)
Builds blocks of matching content
Recursively applies algorithm to unmatched regions
Identifies semantically meaningful changes

Advantages of Patience

Better for code: Produces more intuitive results for source code changes
Handles refactoring better: Recognizes when code blocks move
Faster for certain patterns: Efficient when files have repeated sections
Semantically meaningful: Changes make more sense to humans

Disadvantages of Patience

Not optimal: May not find absolute minimum differences
Less predictable: Results depend on content, not just structure
More opinionated: Biases results toward certain interpretations

When to Use Patience

Patience algorithm is excellent for:

Code comparison and review
Understanding refactoring changes
Making diffs more human-readable
Files with repeated content blocks
Finding semantic changes rather than literal differences

Histogram Algorithm

How Histogram Works

Histogram algorithm is a refinement of patience algorithm:

Creates frequency histograms of lines
Matches lines with unique or rare tokens first
Recursively processes remaining lines
More efficient than patience for large files

Advantages of Histogram

Efficient: Faster than patience while maintaining similar results
Handles large files: Works well on substantial codebases
Good heuristic: Produces human-sensible results
Performance optimized: Uses memory-efficient data structures

Disadvantages of Histogram

Heuristic-based: Not guaranteed optimal
Content dependent: Results vary based on actual file content

When to Use Histogram

Histogram is ideal for:

Large source code files
When performance and readability matter equally
Production version control systems
Git can use histogram: git diff --histogram

Git's histogram algorithm is an optimized variant used in practice for better performance.

Other Specialized Algorithms

Unified Diff Format Algorithm

Not a comparison algorithm but a representation format that can work with various backends:

Shows differences with context lines
Standard format understood across tools
Used in patch files
Can be generated by multiple algorithms

Split View Algorithm

Not an algorithm itself but a display strategy:

Shows original on left, modified on right
Highlights differences in both versions
User alignment of changed sections
More visual than text-based diffs

Practical Algorithm Selection

For Git Users

Configure your preferred algorithm:

# Use patience algorithm
git config --global diff.algorithm patience

# Use histogram algorithm (recommended for performance)
git config --global diff.algorithm histogram

# Use Myers (default)
git config --global diff.algorithm myers

Git also supports:

default - Myers algorithm
myers - Myers algorithm explicitly
minimal - Myers with minimal diff size
patience - Patience algorithm
histogram - Histogram algorithm

For Online Diff Tools

Most online diff tools support:

Myers: Standard for compatibility
Patience: Better for code
Histogram: Balanced performance/quality

Check your tool's documentation for options.

Decision Tree for Algorithm Selection

Performance critical and large files? → Use Histogram
Code comparison and readability important? → Use Patience or Histogram
Small files and correctness critical? → Use LCS or Myers
Default for most cases? → Use Myers or Histogram
Unsure? → Start with Histogram (Git's recommended choice)

Performance Characteristics Comparison

Algorithm	Speed	Optimal	Best For
LCS	Slowest	Yes	Small files, guaranteed correctness
Myers	Moderate	Often	General purpose, version control
Patience	Moderate	No	Code readability
Histogram	Fast	No	Large files, balanced approach

Real-World Algorithm Behavior

Example: Moved Code Block

Consider code that moves from one location to another:

// Original
function alpha() { }
function beta() { }
function gamma() { }

// Modified
function gamma() { }
function alpha() { }
function beta() { }

Myers result: Shows all three functions as modified (less intuitive) Patience/Histogram result: Shows gamma moved up, others unchanged (more intuitive)

This is why patience and histogram algorithms are preferred for code.

Configuring Your Diff Tool

Command-Line Configuration

Most tools allow algorithm selection:

# Git with histogram (recommended)
git diff --histogram

# Diff command with options
diff -u file1 file2

# Meld visual diff tool (uses advanced algorithms)
meld file1 file2

GUI Tool Selection

Visual diff tools often handle algorithm selection automatically:

Modern tools default to Histogram or Patience
Some allow switching algorithms in preferences
Better tools adapt algorithm based on file type

Whitespace and Diff Algorithms

All algorithms must handle whitespace considerations:

Ignore all whitespace: -w flag
Ignore change of whitespace: -b flag
Ignore blank lines: -B flag
Show all whitespace: Default

Whitespace handling is orthogonal to algorithm choice.

Testing Different Algorithms

For critical comparisons, test multiple algorithms:

# Compare results with different algorithms
git diff --algorithm=myers file.js
git diff --algorithm=patience file.js
git diff --algorithm=histogram file.js

When results differ significantly, investigate which makes the most sense for your context.

Conclusion

Different diff algorithms produce different results with different performance characteristics. While users typically don't select algorithms explicitly, understanding the options helps you:

Configure Git optimally for your workflows
Understand why different diff tools show slightly different results
Make informed choices when results seem unexpected
Optimize performance for your specific use cases

For most modern users, the default Myers algorithm or Git's Histogram variant serves well. For code-specific use cases, Patience or Histogram algorithms often produce more intuitive results. Understanding these options empowers you to make informed decisions about your diff tool configuration and interpret results accurately.

The key takeaway: there's no single "best" algorithm for all scenarios. Choose based on your specific needs: guaranteed optimality, speed, code readability, or a balanced combination.