Project 14: String Algorithms Toolkit

Build a toolkit of classic string matching algorithms and trie structures.

Quick Reference

Attribute Value
Difficulty Level 4: Expert
Time Estimate 3 weeks
Language C (Alternatives: Python, Rust, C++)
Prerequisites Projects 7-8, modular arithmetic basics
Key Topics Pattern matching, tries, hashing

1. Learning Objectives

By completing this project, you will:

  1. Implement string matching algorithms (KMP, Rabin-Karp).
  2. Build a trie for prefix search.
  3. Compare performance and correctness across algorithms.
  4. Understand preprocessing for pattern matching.

2. Theoretical Foundation

2.1 Core Concepts

  • Naive matching: O(nm) scanning for pattern in text.
  • KMP: Precompute longest prefix-suffix (LPS) table to avoid rechecking.
  • Rabin-Karp: Rolling hash to quickly skip mismatches.
  • Tries: Prefix trees for fast prefix lookups and autocomplete.

2.2 Why This Matters

String algorithms power search, text processing, and indexing. Efficient pattern matching is critical in editors, compilers, and data pipelines.

2.3 Historical Context / Background

KMP (1970s) introduced linear-time pattern matching, while Rabin-Karp leveraged hashing for average-case efficiency.

2.4 Common Misconceptions

  • Misconception: KMP is always faster than naive. Reality: For small patterns, naive can be competitive.
  • Misconception: Hashing guarantees no collisions. Reality: Collisions must be checked.

3. Project Specification

3.1 What You Will Build

A string toolkit that offers naive search, KMP, Rabin-Karp, and trie-based prefix search, with a CLI for benchmarking.

3.2 Functional Requirements

  1. Naive search: Return all match positions.
  2. KMP search: Build LPS and search in O(n + m).
  3. Rabin-Karp: Rolling hash with collision verification.
  4. Trie: Insert, search, prefix listing.
  5. Benchmark: Compare algorithms on input files.

3.3 Non-Functional Requirements

  • Performance: Large text inputs should run efficiently.
  • Reliability: All matches must be correct even with collisions.
  • Usability: CLI flags for algorithm and input file.

3.4 Example Usage / Output

$ ./string-tool --algo kmp --pattern "aba" --text "abacaba"
Matches at: 0, 4
$ ./string-tool --trie --prefix "auto"
autocomplete
automate
automaton

3.5 Real World Outcome

You will be able to search large text files for patterns and compare algorithm performance. The trie allows quick prefix queries for autocomplete.

4. Solution Architecture

4.1 High-Level Design

┌───────────┐     ┌──────────────┐     ┌─────────────┐
│ CLI Input │────▶│ Algorithm    │────▶│ Reporter    │
└───────────┘     └──────┬───────┘     └─────────────┘
                            │
                      ┌─────▼─────┐
                      │ Trie Core │
                      └───────────┘

4.2 Key Components

Component Responsibility Key Decisions
kmp.c LPS and search Build LPS once
rk.c Rolling hash search Base/mod selection
trie.c Trie operations Array vs hashmap children
benchmark.c Timing Use large text samples

4.3 Data Structures

typedef struct TrieNode {
    struct TrieNode* children[26];
    int is_word;
} TrieNode;

4.4 Algorithm Overview

Key Algorithm: KMP

  1. Build LPS table for pattern.
  2. Scan text while reusing matched prefix info.

Complexity Analysis:

  • Time: O(n + m)
  • Space: O(m)

5. Implementation Guide

5.1 Development Environment Setup

cc -Wall -Wextra -o string-tool src/*.c

5.2 Project Structure

string-toolkit/
├── src/
│   ├── kmp.c
│   ├── rk.c
│   ├── trie.c
│   ├── benchmark.c
│   └── main.c
├── tests/
└── README.md

5.3 The Core Question You’re Answering

“How do preprocessing and hashing make pattern matching fast?”

5.4 Concepts You Must Understand First

Stop and research these before coding:

  1. Prefix function (LPS)
  2. Rolling hash
  3. Trie memory layout

5.5 Questions to Guide Your Design

  1. How will you handle non-lowercase characters in the trie?
  2. What modulus and base will you use for Rabin-Karp?
  3. How will you verify hash collisions?

5.6 Thinking Exercise

Compute the LPS array for pattern “ababaca” by hand.

5.7 The Interview Questions They’ll Ask

  1. Explain how KMP avoids re-checking characters.
  2. Why is Rabin-Karp good for multiple patterns?
  3. How does a trie support prefix search efficiently?

5.8 Hints in Layers

Hint 1: Start with naive search Use it as a correctness baseline.

Hint 2: Build LPS carefully Test LPS on multiple patterns.

Hint 3: Use 64-bit hash Reduce collision risk, but still verify.

5.9 Books That Will Help

Topic Book Chapter
Pattern matching “String Algorithms in C” Ch. 1-5
KMP “Introduction to Algorithms” Ch. 32
Tries “Algorithms, Fourth Edition” Section 5.2

5.10 Implementation Phases

Phase 1: Foundation (5-6 days)

Goals:

  • Implement naive and KMP
  • Add unit tests

Tasks:

  1. Write naive search.
  2. Build and test LPS function.

Checkpoint: KMP matches naive output.

Phase 2: Rabin-Karp and Trie (6-7 days)

Goals:

  • Implement rolling hash
  • Build trie with insert/search

Tasks:

  1. Add rolling hash with collision check.
  2. Implement trie for lowercase words.

Checkpoint: Trie searches match expected.

Phase 3: Benchmarking and Polish (4-5 days)

Goals:

  • Add benchmarking CLI
  • Add prefix listing

Tasks:

  1. Measure performance on large text.
  2. Implement prefix suggestions.

Checkpoint: Benchmark summary prints correctly.

5.11 Key Implementation Decisions

Decision Options Recommendation Rationale
Trie child storage array, hashmap array Simpler and fast
Hash modulus 32-bit, 64-bit 64-bit Fewer collisions
Match output first, all all More general

6. Testing Strategy

6.1 Test Categories

Category Purpose Examples
Unit Tests Search correctness small patterns
Integration Tests CLI runs file inputs
Edge Case Tests Empty pattern no matches

6.2 Critical Test Cases

  1. Pattern equals text.
  2. Pattern longer than text.
  3. Repeated patterns with overlaps.

6.3 Test Data

text: "abacaba"
pattern: "aba"

7. Common Pitfalls and Debugging

7.1 Frequent Mistakes

Pitfall Symptom Solution
Incorrect LPS table Missing matches Verify prefix logic
Hash overflow errors Wrong matches Use uint64_t
Trie memory leaks Valgrind errors Free nodes recursively

7.2 Debugging Strategies

  • Compare KMP output with naive on random tests.
  • Log hashes and verify collisions.

7.3 Performance Traps

Rabin-Karp with a tiny modulus leads to many collisions. Use a large modulus and verify matches.

8. Extensions and Challenges

8.1 Beginner Extensions

  • Add Boyer-Moore algorithm.
  • Add case-insensitive search.

8.2 Intermediate Extensions

  • Support Unicode with UTF-8 processing.
  • Add trie compression (radix tree).

8.3 Advanced Extensions

  • Add Aho-Corasick for multi-pattern search.
  • Build suffix array or suffix automaton.

9. Real-World Connections

9.1 Industry Applications

  • Text editors and search tools
  • DNA sequence matching
  • ripgrep: Fast search tool.
  • RE2: Efficient regex engine.

9.3 Interview Relevance

Pattern matching algorithms and tries appear in algorithm interviews.

10. Resources

10.1 Essential Reading

  • “String Algorithms in C” by Thomas Mailund - Ch. 1-5
  • “Introduction to Algorithms” - Ch. 32

10.2 Video Resources

  • KMP and Rabin-Karp walkthroughs

10.3 Tools and Documentation

  • Unicode standard (if extending)

11. Self-Assessment Checklist

11.1 Understanding

  • I can explain LPS computation in KMP.
  • I can explain rolling hash and collisions.
  • I can describe trie memory layout.

11.2 Implementation

  • All algorithms return correct matches.
  • Benchmarks run on large inputs.

11.3 Growth

  • I can extend to multi-pattern matching.

12. Submission / Completion Criteria

Minimum Viable Completion:

  • Naive and KMP implementations
  • Trie insert/search

Full Completion:

  • Rabin-Karp and benchmarking
  • Prefix listing

Excellence (Going Above and Beyond):

  • Aho-Corasick or suffix array
  • Performance report

This guide was generated from LEARN_ALGORITHMS_DEEP_DIVE.md. For the complete learning path, see the parent directory.