commit 7416dfed3822a8301c17237b67590e3ed3e0d8fd Author: Carlos Gutierrez Date: Mon Nov 24 17:11:51 2025 -0500 Adding hash algorithms diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..7792c05 --- /dev/null +++ b/.gitignore @@ -0,0 +1,47 @@ +# Python +__pycache__/ +*.py[cod] +*$py.class +papers/ +report.tex +*.so +.Python +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +wheels/ +*.egg-info/ +.installed.cfg +*.egg + +# Virtual Environment +.venv/ +venv/ +ENV/ +env/ + +# IDE +.vscode/ +.idea/ +*.swp +*.swo +*~ + +# Testing +.pytest_cache/ +.coverage +htmlcov/ +.tox/ + +# OS +.DS_Store +Thumbs.db + diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..5d03f9f --- /dev/null +++ b/LICENSE @@ -0,0 +1,22 @@ +MIT License + +Copyright (c) 2025 Carlos Gutierrez + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. + diff --git a/README.md b/README.md new file mode 100644 index 0000000..2d690e7 --- /dev/null +++ b/README.md @@ -0,0 +1,230 @@ +# MSCS532 Assignment 7: Hash Tables and Their Practical Applications + +**Author:** Carlos Gutierrez +**Email:** cgutierrez44833@ucumberlands.edu +**Course:** MSCS532 – Data Structures and Algorithms +**Assignment:** Hash Tables and Their Practical Applications + +## Overview + +This assignment provides a comprehensive study of hash tables, including direct-address tables, hash functions, open addressing, and separate chaining. It includes implementations of various hash table data structures, hash function designs (both good and bad examples), theoretical complexity analysis, empirical benchmarking, test coverage, and reproducible visualization assets. + +## Repository Structure + +``` +MSCS532_Assignment7/ +├── docs/ +│ ├── hash_function_comparison.png # Hash function performance comparison +│ ├── open_addressing_vs_chaining.png # Collision resolution strategies comparison +│ ├── load_factor_impact.png # Performance at different load factors +│ └── collision_analysis.png # Collision analysis for different hash functions +├── examples/ +│ ├── hash_tables_demo.py # Hash table demonstrations +│ └── generate_plots.py # Script to reproduce all plots +├── src/ +│ ├── hash_functions.py # Various hash function implementations +│ ├── hash_tables.py # Hash table data structures +│ ├── benchmark.py # Benchmarking utilities +│ └── __init__.py # Package initialization +├── tests/ +│ ├── test_hash_functions.py # Tests for hash functions +│ └── test_hash_tables.py # Tests for hash tables +├── papers/ # Reference papers (PDFs) +├── requirements.txt # Python dependencies +├── README.md # Project documentation (this file) +└── REPORT.md # Detailed analysis report + +``` + +## Part 1: Hash Functions and Their Impact + +### Implementation + +#### Good Hash Functions + +* **Division Method:** `h(k) = k mod m` + * Simple and fast + * Requires careful choice of table size (preferably prime) + +* **Multiplication Method:** `h(k) = floor(m * (kA mod 1))` + * Good distribution with proper choice of A + * Default A = (√5 - 1)/2 ≈ 0.618 + +* **Universal Hash Functions:** `h(k) = ((a*k + b) mod p) mod m` + * Minimizes collisions for any set of keys + * Requires random parameters a, b and prime p + +* **Polynomial String Hash:** Rolling hash for strings + * Better distribution than simple summation + * Base 31 is commonly used + +* **DJB2 Hash:** Popular string hash function + * Known for good distribution properties + +#### Bad Hash Functions (Demonstration) + +* **Simple String Hash:** Sums character values + * Prone to collisions for similar strings + * Poor distribution + +* **Bad Clustering Hash:** Demonstrates clustering behavior + * Causes many collisions and poor performance + +### API Highlights + +**Hash Functions:** + +```python +division_hash(key: int, table_size: int) -> int +multiplication_hash(key: int, table_size: int, A: float) -> int +universal_hash(key: int, table_size: int, a: int, b: int, p: int) -> int +string_hash_polynomial(key: str, table_size: int, base: int) -> int +string_hash_simple(key: str, table_size: int) -> int # BAD EXAMPLE +bad_hash_clustering(key: int, table_size: int) -> int # BAD EXAMPLE +``` + +## Part 2: Hash Table Data Structures + +### Implementation + +#### Direct-Address Table + +* **File:** `src/hash_tables.py` +* **Operations:** insert, search, delete +* **Time Complexity:** O(1) for all operations +* **Space Complexity:** O(m) where m is the key range +* **Use Case:** When keys are integers in a small known range + +#### Open Addressing + +* **File:** `src/hash_tables.py` +* **Probe Types:** + * Linear Probing: `h(k,i) = (h'(k) + i) mod m` + * Quadratic Probing: `h(k,i) = (h'(k) + c1*i + c2*i²) mod m` + * Double Hashing: `h(k,i) = (h1(k) + i*h2(k)) mod m` +* **Operations:** insert, search, delete +* **Time Complexity:** + * Best/Average: O(1) + * Worst: O(n) due to clustering +* **Space Complexity:** O(n) where n is number of elements + +#### Separate Chaining + +* **File:** `src/hash_tables.py` +* **Implementation:** Each bucket contains a linked list +* **Operations:** insert, search, delete +* **Time Complexity:** + * Best/Average: O(1) + * Worst: O(n) if all keys hash to same bucket +* **Space Complexity:** O(n + m) where m is table size + +### Theoretical Performance Analysis + +| Operation | Direct-Address | Open Addressing | Separate Chaining | +|-----------|---------------|-----------------|-------------------| +| Search | O(1) | O(1) avg, O(n) worst | O(1) avg, O(n) worst | +| Insert | O(1) | O(1) avg, O(n) worst | O(1) avg, O(n) worst | +| Delete | O(1) | O(1) avg, O(n) worst | O(1) avg, O(n) worst | +| Space | O(m) | O(n) | O(n + m) | + +**Key Insights:** + +* **Direct-Address:** Fastest but requires keys in known range +* **Open Addressing:** Better cache performance, but clustering can degrade performance +* **Separate Chaining:** More robust to high load factors, easier deletion + +## Getting Started + +### Prerequisites + +* Python 3.10 or later +* Recommended to use a virtual environment + +### Installation + +```bash +python -m venv .venv +source .venv/bin/activate # On Windows: .venv\Scripts\activate +pip install -r requirements.txt +``` + +## Running the Examples + +```bash +python examples/hash_tables_demo.py # Hash table demonstrations +python examples/generate_plots.py # Regenerate all figures in docs/ +``` + +## Running Tests + +```bash +python -m pytest +``` + +The test suite verifies correctness for: + +* All hash function implementations +* Direct-address table +* Open addressing (all probe types) +* Separate chaining + +## Reproducing the Empirical Study + +1. Activate your environment and install dependencies. +2. Run `python examples/generate_plots.py`. + * Benchmarks may take several minutes depending on hardware. +3. Generated figures will be written to the `docs/` directory. + +## Visualizations + +The following visualizations demonstrate key findings from our empirical analysis: + +### Hash Function Comparison + +![Hash Function Comparison](docs/hash_function_comparison.png) + +This visualization compares different hash functions across multiple metrics: collision rates, distribution variance, execution time, and maximum chain lengths. It clearly demonstrates the impact of hash function design on performance. + +### Open Addressing vs. Separate Chaining + +![Open Addressing vs. Separate Chaining](docs/open_addressing_vs_chaining.png) + +This comprehensive comparison shows insert, search, and delete performance across different data sizes for both open addressing (linear, quadratic, double hashing) and separate chaining methods. + +### Load Factor Impact + +![Load Factor Impact](docs/load_factor_impact.png) + +Performance curves demonstrating how operations degrade as load factor increases, highlighting the importance of maintaining appropriate load factors for optimal performance. + +### Collision Analysis + +![Collision Analysis](docs/collision_analysis.png) + +Detailed comparison of collision behavior, clearly demonstrating the dramatic difference between well-designed and poorly-designed hash functions. + +## Practical Applications + +### Hash Tables + +* **Database Systems:** Indexing, join operations +* **Caching:** Memoization, LRU caches +* **Symbol Tables:** Compilers, interpreters +* **Distributed Systems:** Consistent hashing for load balancing +* **Cryptography:** Hash-based data structures, digital signatures + +### Hash Functions + +* **Data Integrity:** Checksums, hash-based message authentication +* **Load Balancing:** Consistent hashing in distributed systems +* **Bloom Filters:** Probabilistic data structures +* **Database Indexing:** Hash indexes for fast lookups + +## Academic Integrity Statement + +This project is submitted for academic evaluation in MSCS532 – Data Structures and Algorithms. All code, analysis, and documentation were authored by Carlos Gutierrez for the specific purpose of this assignment. + +## References + +All references are cited in REPORT.md using APA 7th edition format. Reference papers are located in the `papers/` directory. + diff --git a/docs/collision_analysis.png b/docs/collision_analysis.png new file mode 100644 index 0000000..39d78b4 Binary files /dev/null and b/docs/collision_analysis.png differ diff --git a/docs/hash_function_comparison.png b/docs/hash_function_comparison.png new file mode 100644 index 0000000..ee11b7c Binary files /dev/null and b/docs/hash_function_comparison.png differ diff --git a/docs/load_factor_impact.png b/docs/load_factor_impact.png new file mode 100644 index 0000000..4e69a9a Binary files /dev/null and b/docs/load_factor_impact.png differ diff --git a/docs/load_factor_impact_probes.png b/docs/load_factor_impact_probes.png new file mode 100644 index 0000000..93519b8 Binary files /dev/null and b/docs/load_factor_impact_probes.png differ diff --git a/docs/open_addressing_vs_chaining.png b/docs/open_addressing_vs_chaining.png new file mode 100644 index 0000000..5a966ba Binary files /dev/null and b/docs/open_addressing_vs_chaining.png differ diff --git a/examples/generate_plots.py b/examples/generate_plots.py new file mode 100644 index 0000000..c5a3a39 --- /dev/null +++ b/examples/generate_plots.py @@ -0,0 +1,389 @@ +""" +Generate visualization plots for hash table performance analysis. +""" + +import sys +import os +import matplotlib.pyplot as plt +import numpy as np +sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..')) + +from src.benchmark import ( + benchmark_hash_functions, + benchmark_open_addressing_vs_chaining, + benchmark_load_factor_impact, + benchmark_load_factor_impact_probes, + generate_test_data +) +from src.hash_functions import ( + division_hash, + multiplication_hash, + string_hash_simple, + string_hash_polynomial, + string_hash_djb2, + bad_hash_clustering +) + + +def plot_hash_function_comparison(): + """Compare different hash functions.""" + print("Generating hash function comparison plot...") + + keys = generate_test_data(1000) + table_size = 100 + + hash_funcs = { + 'Division': division_hash, + 'Multiplication': lambda k, s: multiplication_hash(k, s), + 'Simple String': lambda k, s: string_hash_simple(str(k), s), + 'Polynomial String': lambda k, s: string_hash_polynomial(str(k), s), + 'DJB2': lambda k, s: string_hash_djb2(str(k), s), + 'Bad Clustering': bad_hash_clustering, + } + + results = benchmark_hash_functions(hash_funcs, keys, table_size) + + fig, axes = plt.subplots(2, 2, figsize=(14, 10)) + fig.suptitle('Hash Function Performance Comparison', fontsize=16, fontweight='bold') + + names = list(results.keys()) + collision_rates = [results[n]['collision_rate'] * 100 for n in names] + variances = [results[n]['variance'] for n in names] + times = [results[n]['time'] * 1000 for n in names] # Convert to ms + max_chains = [results[n]['max_chain_length'] for n in names] + + # Collision rate + axes[0, 0].bar(names, collision_rates, color='steelblue') + axes[0, 0].set_title('Collision Rate (%)', fontweight='bold') + axes[0, 0].set_ylabel('Collision Rate (%)') + axes[0, 0].tick_params(axis='x', rotation=45) + axes[0, 0].grid(axis='y', alpha=0.3) + + # Variance (distribution quality) + axes[0, 1].bar(names, variances, color='coral') + axes[0, 1].set_title('Distribution Variance (Lower is Better)', fontweight='bold') + axes[0, 1].set_ylabel('Variance') + axes[0, 1].tick_params(axis='x', rotation=45) + axes[0, 1].grid(axis='y', alpha=0.3) + + # Execution time + axes[1, 0].bar(names, times, color='mediumseagreen') + axes[1, 0].set_title('Execution Time', fontweight='bold') + axes[1, 0].set_ylabel('Time (ms)') + axes[1, 0].tick_params(axis='x', rotation=45) + axes[1, 0].grid(axis='y', alpha=0.3) + + # Max chain length + axes[1, 1].bar(names, max_chains, color='plum') + axes[1, 1].set_title('Maximum Chain Length', fontweight='bold') + axes[1, 1].set_ylabel('Max Chain Length') + axes[1, 1].tick_params(axis='x', rotation=45) + axes[1, 1].grid(axis='y', alpha=0.3) + + plt.tight_layout() + output_path = os.path.join(os.path.dirname(__file__), '..', 'docs', 'hash_function_comparison.png') + plt.savefig(output_path, dpi=300, bbox_inches='tight') + print(f"Saved: {output_path}") + plt.close() + + +def plot_open_addressing_vs_chaining(): + """Compare open addressing vs separate chaining.""" + print("Generating open addressing vs separate chaining comparison plot...") + + sizes = [100, 500, 1000, 5000, 10000] + results = benchmark_open_addressing_vs_chaining(sizes) + + fig, axes = plt.subplots(2, 2, figsize=(14, 10)) + fig.suptitle('Open Addressing vs Separate Chaining Performance', fontsize=16, fontweight='bold') + + sizes_arr = np.array(sizes) + + # Insert time + ax = axes[0, 0] + for probe_type in ['linear', 'quadratic', 'double']: + insert_times = [r['insert_time'] for r in results['open_addressing'][probe_type]] + ax.plot(sizes_arr, insert_times, marker='o', label=f'Open Addressing ({probe_type})', linewidth=2) + + insert_times_sc = [r['insert_time'] for r in results['separate_chaining']] + ax.plot(sizes_arr, insert_times_sc, marker='s', label='Separate Chaining', linewidth=2, linestyle='--') + ax.set_xlabel('Number of Elements') + ax.set_ylabel('Insert Time (seconds)') + ax.set_title('Insert Performance', fontweight='bold') + ax.legend() + ax.grid(alpha=0.3) + ax.set_xscale('log') + ax.set_yscale('log') + + # Search time + ax = axes[0, 1] + for probe_type in ['linear', 'quadratic', 'double']: + search_times = [r['search_time'] for r in results['open_addressing'][probe_type]] + ax.plot(sizes_arr, search_times, marker='o', label=f'Open Addressing ({probe_type})', linewidth=2) + + search_times_sc = [r['search_time'] for r in results['separate_chaining']] + ax.plot(sizes_arr, search_times_sc, marker='s', label='Separate Chaining', linewidth=2, linestyle='--') + ax.set_xlabel('Number of Elements') + ax.set_ylabel('Search Time (seconds)') + ax.set_title('Search Performance', fontweight='bold') + ax.legend() + ax.grid(alpha=0.3) + ax.set_xscale('log') + ax.set_yscale('log') + + # Delete time + ax = axes[1, 0] + for probe_type in ['linear', 'quadratic', 'double']: + delete_times = [r['delete_time'] for r in results['open_addressing'][probe_type]] + ax.plot(sizes_arr, delete_times, marker='o', label=f'Open Addressing ({probe_type})', linewidth=2) + + delete_times_sc = [r['delete_time'] for r in results['separate_chaining']] + ax.plot(sizes_arr, delete_times_sc, marker='s', label='Separate Chaining', linewidth=2, linestyle='--') + ax.set_xlabel('Number of Elements') + ax.set_ylabel('Delete Time (seconds)') + ax.set_title('Delete Performance', fontweight='bold') + ax.legend() + ax.grid(alpha=0.3) + ax.set_xscale('log') + ax.set_yscale('log') + + # Load factors + ax = axes[1, 1] + for probe_type in ['linear', 'quadratic', 'double']: + load_factors = [r['load_factor'] for r in results['open_addressing'][probe_type]] + ax.plot(sizes_arr, load_factors, marker='o', label=f'Open Addressing ({probe_type})', linewidth=2) + + load_factors_sc = [r['load_factor'] for r in results['separate_chaining']] + ax.plot(sizes_arr, load_factors_sc, marker='s', label='Separate Chaining', linewidth=2, linestyle='--') + ax.set_xlabel('Number of Elements') + ax.set_ylabel('Load Factor') + ax.set_title('Load Factor', fontweight='bold') + ax.legend() + ax.grid(alpha=0.3) + ax.set_xscale('log') + + plt.tight_layout() + output_path = os.path.join(os.path.dirname(__file__), '..', 'docs', 'open_addressing_vs_chaining.png') + plt.savefig(output_path, dpi=300, bbox_inches='tight') + print(f"Saved: {output_path}") + plt.close() + + +def plot_load_factor_impact(): + """Plot performance at different load factors with statistical smoothing.""" + print("Generating load factor impact plot...") + + results = benchmark_load_factor_impact(initial_size=100, max_elements=1000, probe_type='linear', num_runs=30) + + fig, axes = plt.subplots(1, 2, figsize=(14, 5)) + fig.suptitle('Performance Impact of Load Factor', fontsize=16, fontweight='bold') + + # Extract data + oa_data = results['open_addressing'] + sc_data = results['separate_chaining'] + + # Sort by load factor to avoid zig-zag lines + oa_sorted = sorted(oa_data, key=lambda x: x['load_factor']) + sc_sorted = sorted(sc_data, key=lambda x: x['load_factor']) + + oa_load_factors = [r['load_factor'] for r in oa_sorted] + oa_insert_times = [r['insert_time'] for r in oa_sorted] + oa_insert_stds = [r.get('insert_time_std', 0) for r in oa_sorted] + oa_search_times = [r['search_time'] for r in oa_sorted] + oa_search_stds = [r.get('search_time_std', 0) for r in oa_sorted] + + sc_load_factors = [r['load_factor'] for r in sc_sorted] + sc_insert_times = [r['insert_time'] for r in sc_sorted] + sc_insert_stds = [r.get('insert_time_std', 0) for r in sc_sorted] + sc_search_times = [r['search_time'] for r in sc_sorted] + sc_search_stds = [r.get('search_time_std', 0) for r in sc_sorted] + sc_chain_lengths = [r['avg_chain_length'] for r in sc_sorted] + + # Insert time vs load factor (per element) with error bars + ax = axes[0] + ax.errorbar(oa_load_factors, oa_insert_times, yerr=oa_insert_stds, + marker='o', label='Open Addressing (Linear)', linewidth=2, + capsize=3, capthick=1.5, alpha=0.8) + ax.errorbar(sc_load_factors, sc_insert_times, yerr=sc_insert_stds, + marker='s', label='Separate Chaining', linewidth=2, linestyle='--', + capsize=3, capthick=1.5, alpha=0.8) + ax.set_xlabel('Load Factor') + ax.set_ylabel('Insert Time per Element (seconds)') + ax.set_title('Insert Time vs Load Factor', fontweight='bold') + ax.legend() + ax.grid(alpha=0.3) + + # Search time vs load factor (per element) with error bars + ax = axes[1] + ax.errorbar(oa_load_factors, oa_search_times, yerr=oa_search_stds, + marker='o', label='Open Addressing (Linear)', linewidth=2, + capsize=3, capthick=1.5, alpha=0.8) + ax.errorbar(sc_load_factors, sc_search_times, yerr=sc_search_stds, + marker='s', label='Separate Chaining', linewidth=2, linestyle='--', + capsize=3, capthick=1.5, alpha=0.8) + ax2 = ax.twinx() + # Chain length is smooth and accurate, so use line plot + ax2.plot(sc_load_factors, sc_chain_lengths, marker='^', + label='Avg Chain Length (SC)', color='green', linestyle=':', linewidth=2) + ax.set_xlabel('Load Factor') + ax.set_ylabel('Search Time per Element (seconds)', color='blue') + ax2.set_ylabel('Average Chain Length', color='green') + ax.set_title('Search Time vs Load Factor', fontweight='bold') + ax.legend(loc='upper left') + ax2.legend(loc='upper right') + ax.grid(alpha=0.3) + + plt.tight_layout() + output_path = os.path.join(os.path.dirname(__file__), '..', 'docs', 'load_factor_impact.png') + plt.savefig(output_path, dpi=300, bbox_inches='tight') + print(f"Saved: {output_path}") + plt.close() + + +def plot_load_factor_impact_probes(): + """Plot probe counts and comparisons at different load factors. + + Uses deterministic metrics (probe counts, comparisons) instead of timing + to produce smooth theoretical curves without measurement noise. + """ + print("Generating load factor impact plot (probe counts)...") + + results = benchmark_load_factor_impact_probes(initial_size=100, max_elements=1000, probe_type='linear', num_runs=10) + + fig, axes = plt.subplots(2, 2, figsize=(14, 10)) + fig.suptitle('Performance Impact of Load Factor (Probe Counts & Comparisons)', fontsize=16, fontweight='bold') + + # Extract data + oa_data = results['open_addressing'] + sc_data = results['separate_chaining'] + + # Sort by load factor + oa_sorted = sorted(oa_data, key=lambda x: x['load_factor']) + sc_sorted = sorted(sc_data, key=lambda x: x['load_factor']) + + oa_load_factors = [r['load_factor'] for r in oa_sorted] + oa_insert_probes = [r['insert_probes_per_element'] for r in oa_sorted] + oa_search_probes = [r['search_probes_per_element'] for r in oa_sorted] + oa_insert_comparisons = [r['insert_comparisons_per_element'] for r in oa_sorted] + oa_search_comparisons = [r['search_comparisons_per_element'] for r in oa_sorted] + + sc_load_factors = [r['load_factor'] for r in sc_sorted] + sc_insert_comparisons = [r['insert_comparisons_per_element'] for r in sc_sorted] + sc_search_comparisons = [r['search_comparisons_per_element'] for r in sc_sorted] + sc_chain_lengths = [r['avg_chain_length'] for r in sc_sorted] + + # Insert probes per element (Open Addressing) + ax = axes[0, 0] + ax.plot(oa_load_factors, oa_insert_probes, marker='o', label='Open Addressing (Linear)', + linewidth=2, color='blue', markersize=6) + ax.set_xlabel('Load Factor') + ax.set_ylabel('Probes per Element') + ax.set_title('Insert: Probes per Element (Open Addressing)', fontweight='bold') + ax.legend() + ax.grid(alpha=0.3) + + # Search probes per element (Open Addressing) + ax = axes[0, 1] + ax.plot(oa_load_factors, oa_search_probes, marker='o', label='Open Addressing (Linear)', + linewidth=2, color='blue', markersize=6) + ax.set_xlabel('Load Factor') + ax.set_ylabel('Probes per Element') + ax.set_title('Search: Probes per Element (Open Addressing)', fontweight='bold') + ax.legend() + ax.grid(alpha=0.3) + + # Comparisons per element (both methods) + ax = axes[1, 0] + ax.plot(oa_load_factors, oa_insert_comparisons, marker='o', label='Open Addressing (Linear)', + linewidth=2, color='blue', markersize=6) + ax.plot(sc_load_factors, sc_insert_comparisons, marker='s', label='Separate Chaining', + linewidth=2, linestyle='--', color='orange', markersize=6) + ax.set_xlabel('Load Factor') + ax.set_ylabel('Comparisons per Element') + ax.set_title('Insert: Comparisons per Element', fontweight='bold') + ax.legend() + ax.grid(alpha=0.3) + + # Search comparisons per element and chain length + ax = axes[1, 1] + ax.plot(oa_load_factors, oa_search_comparisons, marker='o', label='Open Addressing (Linear)', + linewidth=2, color='blue', markersize=6) + ax.plot(sc_load_factors, sc_search_comparisons, marker='s', label='Separate Chaining', + linewidth=2, linestyle='--', color='orange', markersize=6) + ax2 = ax.twinx() + ax2.plot(sc_load_factors, sc_chain_lengths, marker='^', label='Avg Chain Length (SC)', + color='green', linestyle=':', linewidth=2, markersize=6) + ax.set_xlabel('Load Factor') + ax.set_ylabel('Comparisons per Element', color='blue') + ax2.set_ylabel('Average Chain Length', color='green') + ax.set_title('Search: Comparisons per Element', fontweight='bold') + ax.legend(loc='upper left') + ax2.legend(loc='upper right') + ax.grid(alpha=0.3) + + plt.tight_layout() + output_path = os.path.join(os.path.dirname(__file__), '..', 'docs', 'load_factor_impact_probes.png') + plt.savefig(output_path, dpi=300, bbox_inches='tight') + print(f"Saved: {output_path}") + plt.close() + + +def plot_collision_analysis(): + """Plot collision analysis for different hash functions.""" + print("Generating collision analysis plot...") + + keys = generate_test_data(500) + table_size = 100 + + hash_funcs = { + 'Division': division_hash, + 'Multiplication': lambda k, s: multiplication_hash(k, s), + 'Simple String': lambda k, s: string_hash_simple(str(k), s), + 'Polynomial': lambda k, s: string_hash_polynomial(str(k), s), + 'Bad Clustering': bad_hash_clustering, + } + + results = benchmark_hash_functions(hash_funcs, keys, table_size) + + fig, ax = plt.subplots(figsize=(12, 6)) + + names = list(results.keys()) + collision_counts = [results[n]['collisions'] for n in names] + colors = ['steelblue' if 'Bad' not in n else 'coral' for n in names] + + bars = ax.bar(names, collision_counts, color=colors) + ax.set_xlabel('Hash Function', fontweight='bold') + ax.set_ylabel('Number of Collisions', fontweight='bold') + ax.set_title('Collision Analysis: Good vs Bad Hash Functions', fontsize=14, fontweight='bold') + ax.grid(axis='y', alpha=0.3) + ax.tick_params(axis='x', rotation=45) + + # Add value labels on bars + for bar in bars: + height = bar.get_height() + ax.text(bar.get_x() + bar.get_width()/2., height, + f'{int(height)}', + ha='center', va='bottom', fontweight='bold') + + plt.tight_layout() + output_path = os.path.join(os.path.dirname(__file__), '..', 'docs', 'collision_analysis.png') + plt.savefig(output_path, dpi=300, bbox_inches='tight') + print(f"Saved: {output_path}") + plt.close() + + +if __name__ == "__main__": + # Ensure docs directory exists + os.makedirs(os.path.join(os.path.dirname(__file__), '..', 'docs'), exist_ok=True) + + print("Generating visualization plots...") + print("This may take a few minutes...\n") + + plot_hash_function_comparison() + plot_open_addressing_vs_chaining() + plot_load_factor_impact() + plot_load_factor_impact_probes() + plot_collision_analysis() + + print("\nAll plots generated successfully!") + diff --git a/examples/hash_tables_demo.py b/examples/hash_tables_demo.py new file mode 100644 index 0000000..4a9d2eb --- /dev/null +++ b/examples/hash_tables_demo.py @@ -0,0 +1,207 @@ +""" +Demonstration of hash table implementations and their usage. +""" + +import sys +import os +sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..')) + +from src.hash_tables import ( + DirectAddressTable, + HashTableOpenAddressing, + HashTableSeparateChaining +) +from src.hash_functions import ( + division_hash, + string_hash_polynomial, + string_hash_simple +) + + +def demo_direct_address_table(): + """Demonstrate direct-address table.""" + print("=" * 60) + print("Direct-Address Table Demonstration") + print("=" * 60) + + # Create table for keys in range [0, 99] + table = DirectAddressTable(100) + + # Insert some values + table.insert(5, "Alice") + table.insert(42, "Bob") + table.insert(99, "Charlie") + + print("\nInserted key-value pairs:") + print(" Key 5 ->", table.search(5)) + print(" Key 42 ->", table.search(42)) + print(" Key 99 ->", table.search(99)) + + # Search + print("\nSearching for key 42:", table.search(42)) + print("Searching for key 10:", table.search(10)) # Not found + + # Delete + table.delete(42) + print("\nAfter deleting key 42:") + print(" Key 42 ->", table.search(42)) # None + print() + + +def demo_open_addressing(): + """Demonstrate open addressing hash table.""" + print("=" * 60) + print("Open Addressing Hash Table Demonstration") + print("=" * 60) + + # Test with linear probing + print("\n--- Linear Probing ---") + ht_linear = HashTableOpenAddressing(10, probe_type='linear') + + keys = [10, 22, 31, 4, 15, 28, 17, 88, 59] + for key in keys: + ht_linear.insert(key, f"Value_{key}") + + print(f"Inserted {len(keys)} keys") + print(f"Load factor: {ht_linear._load_factor():.2f}") + + print("\nSearching for keys:") + for key in [10, 22, 88, 99]: + result = ht_linear.search(key) + print(f" Key {key}: {'Found' if result else 'Not found'}") + + # Test with quadratic probing + print("\n--- Quadratic Probing ---") + # Use larger table size for quadratic probing to avoid probe sequence issues + ht_quad = HashTableOpenAddressing(20, probe_type='quadratic') + + for key in keys: + ht_quad.insert(key, f"Value_{key}") + + print(f"Inserted {len(keys)} keys") + print(f"Load factor: {ht_quad._load_factor():.2f}") + + # Test with double hashing + print("\n--- Double Hashing ---") + # Use larger table size for double hashing to ensure all keys can be inserted + ht_double = HashTableOpenAddressing(20, probe_type='double') + + for key in keys: + ht_double.insert(key, f"Value_{key}") + + print(f"Inserted {len(keys)} keys") + print(f"Load factor: {ht_double._load_factor():.2f}") + print() + + +def demo_separate_chaining(): + """Demonstrate separate chaining hash table.""" + print("=" * 60) + print("Separate Chaining Hash Table Demonstration") + print("=" * 60) + + ht = HashTableSeparateChaining(10) + + keys = [10, 22, 31, 4, 15, 28, 17, 88, 59, 71] + for key in keys: + ht.insert(key, f"Value_{key}") + + print(f"\nInserted {len(keys)} keys") + print(f"Load factor: {ht._load_factor():.2f}") + + chain_lengths = ht.get_chain_lengths() + print(f"Chain lengths: {chain_lengths}") + print(f"Average chain length: {sum(chain_lengths) / len(chain_lengths):.2f}") + print(f"Maximum chain length: {max(chain_lengths)}") + + print("\nSearching for keys:") + for key in [10, 22, 88, 99]: + result = ht.search(key) + print(f" Key {key}: {'Found' if result else 'Not found'}") + + # Delete some keys + print("\nDeleting keys 22 and 88:") + ht.delete(22) + ht.delete(88) + print(f" Key 22: {'Found' if ht.search(22) else 'Not found'}") + print(f" Key 88: {'Found' if ht.search(88) else 'Not found'}") + print() + + +def demo_hash_functions(): + """Demonstrate different hash functions.""" + print("=" * 60) + print("Hash Function Demonstration") + print("=" * 60) + + keys = [10, 22, 31, 4, 15, 28, 17, 88, 59, 71] + table_size = 11 + + print(f"\nKeys: {keys}") + print(f"Table size: {table_size}\n") + + # Division method + print("Division method (h(k) = k mod m):") + for key in keys[:5]: + hash_val = division_hash(key, table_size) + print(f" h({key}) = {hash_val}") + + # String hashing + print("\nString hash functions:") + string_keys = ["hello", "world", "hash", "table", "test"] + + print("Simple string hash (BAD - prone to collisions):") + for key in string_keys: + hash_val = string_hash_simple(key, table_size) + print(f" h('{key}') = {hash_val}") + + print("\nPolynomial string hash (GOOD - better distribution):") + for key in string_keys: + hash_val = string_hash_polynomial(key, table_size) + print(f" h('{key}') = {hash_val}") + print() + + +def demo_collision_comparison(): + """Demonstrate collision behavior with different hash functions.""" + print("=" * 60) + print("Collision Comparison Demonstration") + print("=" * 60) + + # Generate test keys + keys = list(range(100, 200)) + table_size = 50 + + from src.hash_functions import ( + division_hash, + multiplication_hash, + string_hash_simple, + string_hash_polynomial + ) + + hash_funcs = { + 'Division': division_hash, + 'Multiplication': lambda k, s: multiplication_hash(k, s), + } + + print(f"\nTesting with {len(keys)} keys and table size {table_size}\n") + + for name, hash_func in hash_funcs.items(): + hash_values = [hash_func(k, table_size) for k in keys] + collisions = len(keys) - len(set(hash_values)) + collision_rate = collisions / len(keys) * 100 + + print(f"{name} method:") + print(f" Collisions: {collisions}") + print(f" Collision rate: {collision_rate:.2f}%") + print(f" Buckets used: {len(set(hash_values))}/{table_size}") + print() + + +if __name__ == "__main__": + demo_direct_address_table() + demo_open_addressing() + demo_separate_chaining() + demo_hash_functions() + demo_collision_comparison() + diff --git a/papers/An Overview of Cuckoo Hashing.pdf b/papers/An Overview of Cuckoo Hashing.pdf new file mode 100644 index 0000000..1103f04 Binary files /dev/null and b/papers/An Overview of Cuckoo Hashing.pdf differ diff --git a/papers/Data Structures and Algorithm Analysis in C++.pdf b/papers/Data Structures and Algorithm Analysis in C++.pdf new file mode 100644 index 0000000..d0bc7d3 Binary files /dev/null and b/papers/Data Structures and Algorithm Analysis in C++.pdf differ diff --git a/papers/Dynamic Hash Tables.pdf b/papers/Dynamic Hash Tables.pdf new file mode 100644 index 0000000..a067e6f Binary files /dev/null and b/papers/Dynamic Hash Tables.pdf differ diff --git a/papers/Introduction to Algorithms.pdf b/papers/Introduction to Algorithms.pdf new file mode 100644 index 0000000..d717b3c Binary files /dev/null and b/papers/Introduction to Algorithms.pdf differ diff --git a/papers/Programming Pearls.pdf b/papers/Programming Pearls.pdf new file mode 100644 index 0000000..55ca2ae --- /dev/null +++ b/papers/Programming Pearls.pdf @@ -0,0 +1,7857 @@ +%PDF-1.4 % +1949 0 obj << /Linearized 1 /O 1954 /H [ 64260 6254 ] /L 1294193 /E 526349 /N 283 /T 1255093 >> endobj xref 1949 3125 0000000016 00000 n +0000062857 00000 n +0000063096 00000 n +0000063251 00000 n +0000064186 00000 n +0000070514 00000 n +0000070942 00000 n +0000071029 00000 n +0000071137 00000 n +0000071267 00000 n +0000071420 00000 n +0000071600 00000 n +0000071693 00000 n +0000071975 00000 n 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0 R 2506 0 R 2451 0 R 2452 0 R 2505 0 R 2454 0 R 2503 0 R ] endobj 1118 0 obj [ 2503 0 R 2456 0 R 2457 0 R 2501 0 R 2459 0 R 2499 0 R 2461 0 R 2462 0 R 2497 0 R 2464 0 R 2465 0 R 2495 0 R ] endobj 1119 0 obj [ 2467 0 R 2468 0 R 2493 0 R 2470 0 R 2491 0 R 2472 0 R 2473 0 R 2488 0 R 2473 0 R 2487 0 R 2475 0 R 2484 0 R 2476 0 R 2477 0 R 2482 0 R 2477 0 R 2480 0 R 2478 0 R 2479 0 R ] endobj 1120 0 obj << /Nums [ 64 2223 0 R 65 2224 0 R 66 2225 0 R 67 2226 0 R 68 2227 0 R 69 2228 0 R 70 2217 0 R 71 2218 0 R 72 2219 0 R 73 2215 0 R 74 2211 0 R 75 2212 0 R 76 2195 0 R 77 2196 0 R 78 2196 0 R 79 2197 0 R 80 2198 0 R 81 2198 0 R 82 2199 0 R 83 2200 0 R 84 2201 0 R 85 1103 0 R 86 2193 0 R 87 1104 0 R 88 2293 0 R 89 2291 0 R 90 2289 0 R 91 1105 0 R 92 2283 0 R 93 1106 0 R 94 1107 0 R 95 2268 0 R ] /Limits [ 64 95 ] >> endobj 1121 0 obj [ 2556 0 R 2515 0 R 2547 0 R 2516 0 R 2548 0 R 2516 0 R 2549 0 R 2516 0 R 2517 0 R 2518 0 R 2519 0 R 2520 0 R 2521 0 R 2522 0 R 2523 0 R 2524 0 R 2525 0 R 2526 0 R 2545 0 R 2526 0 R 2527 0 R ] endobj 1122 0 obj [ 2528 0 R 2529 0 R 2530 0 R 2531 0 R 2532 0 R 2533 0 R 2543 0 R 2533 0 R 2534 0 R 2535 0 R 2536 0 R 2539 0 R 2537 0 R 2540 0 R 2537 0 R 2538 0 R ] endobj 1123 0 obj [ 2558 0 R ] endobj 1124 0 obj [ 2653 0 R 2560 0 R 2561 0 R 2651 0 R 2563 0 R 2564 0 R 2649 0 R 2566 0 R 2567 0 R 2647 0 R 2646 0 R 2645 0 R ] endobj 1125 0 obj [ 2644 0 R 2638 0 R 2569 0 R 2570 0 R 2571 0 R 2572 0 R 2636 0 R 2572 0 R 2635 0 R 2634 0 R 2633 0 R 2574 0 R 2628 0 R 2575 0 R 2576 0 R ] endobj 1126 0 obj [ 2576 0 R 2577 0 R 2627 0 R 2624 0 R 2579 0 R 2623 0 R 2581 0 R 2582 0 R 2621 0 R 2584 0 R 2585 0 R 2619 0 R 2587 0 R ] endobj 1127 0 obj [ 2588 0 R 2617 0 R 2590 0 R 2591 0 R 2615 0 R 2593 0 R 2594 0 R 2613 0 R ] endobj 1128 0 obj [ 2613 0 R 2596 0 R 2606 0 R 2596 0 R 2607 0 R 2596 0 R 2608 0 R 2596 0 R 2602 0 R 2597 0 R 2603 0 R 2597 0 R 2600 0 R 2598 0 R 2599 0 R ] endobj 1129 0 obj << /Nums [ 96 1108 0 R 97 2332 0 R 98 2330 0 R 99 2328 0 R 100 2326 0 R 101 1110 0 R 102 2324 0 R 103 2322 0 R 104 2320 0 R 105 2318 0 R 106 1111 0 R 107 2426 0 R 108 2424 0 R 109 2420 0 R 110 1112 0 R 111 2414 0 R 112 2368 0 R 113 1113 0 R 114 1114 0 R 115 2361 0 R 116 1115 0 R 117 2442 0 R 118 2436 0 R 119 2437 0 R 120 2438 0 R 121 1116 0 R 122 1117 0 R 123 2511 0 R 124 2508 0 R 125 2508 0 R 126 2506 0 R 127 1118 0 R ] /Limits [ 96 127 ] >> endobj 1130 0 obj [ 2692 0 R 2656 0 R 2683 0 R 2657 0 R 2684 0 R 2657 0 R 2685 0 R 2657 0 R 2658 0 R 2659 0 R 2660 0 R 2661 0 R 2662 0 R 2663 0 R 2664 0 R ] endobj 1131 0 obj [ 2665 0 R 2666 0 R 2667 0 R 2668 0 R 2669 0 R 2670 0 R 2671 0 R 2672 0 R ] endobj 1132 0 obj [ 2672 0 R 2673 0 R 2674 0 R 2675 0 R 2676 0 R 2677 0 R 2678 0 R 2679 0 R 2680 0 R ] endobj 1133 0 obj [ 2681 0 R 2682 0 R ] endobj 1134 0 obj [ 2717 0 R 2695 0 R 2708 0 R 2696 0 R 2709 0 R 2696 0 R 2710 0 R 2696 0 R 2697 0 R 2698 0 R 2699 0 R 2700 0 R ] endobj 1135 0 obj [ 2700 0 R 2701 0 R 2702 0 R 2703 0 R 2704 0 R ] endobj 1136 0 obj [ 2704 0 R 2705 0 R 2706 0 R 2707 0 R ] endobj 1137 0 obj [ 2719 0 R ] endobj 1138 0 obj [ 2720 0 R ] endobj 1139 0 obj [ 2720 0 R ] endobj 1140 0 obj [ 2721 0 R ] endobj 1141 0 obj [ 2721 0 R ] endobj 1142 0 obj [ 2740 0 R 2723 0 R 2724 0 R 2725 0 R 2738 0 R 2737 0 R 2736 0 R 2727 0 R 2728 0 R 2731 0 R 2729 0 R 2730 0 R ] endobj 1143 0 obj [ 2771 0 R 2743 0 R 2744 0 R 2764 0 R 2744 0 R 2765 0 R 2744 0 R 2766 0 R 2744 0 R 2745 0 R 2746 0 R 2747 0 R 2748 0 R 2763 0 R 2760 0 R 2750 0 R 2751 0 R 2752 0 R ] endobj 1144 0 obj << /Nums [ 128 1119 0 R 129 2488 0 R 130 2484 0 R 131 2482 0 R 132 2480 0 R 133 1121 0 R 134 2555 0 R 135 2547 0 R 136 2548 0 R 137 2548 0 R 138 2549 0 R 139 2549 0 R 140 2545 0 R 141 1122 0 R 142 2543 0 R 143 2539 0 R 144 2540 0 R 145 1123 0 R 146 1124 0 R 147 2652 0 R 148 1125 0 R 149 2638 0 R 150 2636 0 R 151 2628 0 R 152 1126 0 R 153 2624 0 R 154 1127 0 R 155 1128 0 R 156 2606 0 R 157 2607 0 R 158 2608 0 R 159 2602 0 R ] /Limits [ 128 159 ] >> endobj 1145 0 obj [ 2759 0 R 2756 0 R 2754 0 R 2755 0 R ] endobj 1146 0 obj [ 2780 0 R 2774 0 R 2775 0 R 2777 0 R 2775 0 R 2776 0 R ] endobj 1147 0 obj [ 3035 0 R 2783 0 R 2784 0 R 2785 0 R 2786 0 R 3023 0 R 2786 0 R 3024 0 R 2786 0 R 3025 0 R 2786 0 R 3026 0 R 2786 0 R 3027 0 R 2786 0 R 2787 0 R 3011 0 R 2787 0 R 3012 0 R 2787 0 R 3013 0 R 2787 0 R 3014 0 R 2787 0 R 3015 0 R 2787 0 R 3016 0 R 2787 0 R 2788 0 R 2789 0 R 3007 0 R 2789 0 R 3008 0 R 2789 0 R 2790 0 R 3005 0 R 2790 0 R 2791 0 R 2792 0 R 3001 0 R 2792 0 R 3002 0 R 2792 0 R 2793 0 R 2794 0 R 2993 0 R 2794 0 R 2994 0 R 2794 0 R 2995 0 R 2794 0 R 2996 0 R 2794 0 R 2795 0 R ] endobj 1148 0 obj [ 2987 0 R 2796 0 R 2988 0 R 2796 0 R 2989 0 R 2796 0 R 2797 0 R 2968 0 R 2798 0 R 2969 0 R 2798 0 R 2970 0 R 2798 0 R 2971 0 R 2798 0 R 2972 0 R 2798 0 R 2973 0 R 2798 0 R 2974 0 R 2798 0 R 2975 0 R 2798 0 R 2976 0 R 2798 0 R 2799 0 R 2964 0 R 2800 0 R 2965 0 R 2800 0 R 2801 0 R 2954 0 R 2801 0 R 2955 0 R 2801 0 R 2956 0 R 2801 0 R 2957 0 R 2801 0 R 2958 0 R 2801 0 R 2802 0 R 2803 0 R 2946 0 R 2803 0 R 2947 0 R 2803 0 R 2948 0 R 2803 0 R 2949 0 R 2803 0 R 2804 0 R 2944 0 R 2804 0 R 2805 0 R 2940 0 R 2805 0 R 2941 0 R 2805 0 R 2936 0 R 2806 0 R 2937 0 R 2806 0 R 2932 0 R 2807 0 R 2933 0 R 2807 0 R 2808 0 R 2809 0 R 2928 0 R 2809 0 R 2929 0 R 2809 0 R ] endobj 1149 0 obj << /Nums [ 160 2603 0 R 161 2600 0 R 162 1130 0 R 163 2691 0 R 164 2683 0 R 165 2684 0 R 166 2684 0 R 167 2685 0 R 168 2685 0 R 169 1131 0 R 170 1132 0 R 171 1133 0 R 172 1134 0 R 173 2716 0 R 174 2708 0 R 175 2709 0 R 176 2709 0 R 177 2710 0 R 178 2710 0 R 179 1135 0 R 180 1136 0 R 181 1137 0 R 182 1138 0 R 183 1139 0 R 184 1140 0 R 185 1141 0 R 186 1142 0 R 187 2739 0 R 188 2731 0 R 189 1143 0 R 190 2770 0 R 191 2764 0 R ] /Limits [ 160 191 ] >> endobj 1150 0 obj << /Nums [ 192 2765 0 R 193 2766 0 R 194 2760 0 R 195 1145 0 R 196 2756 0 R 197 1146 0 R 198 2779 0 R 199 2777 0 R 200 1147 0 R 201 3034 0 R 202 3023 0 R 203 3024 0 R 204 3025 0 R 205 3026 0 R 206 3027 0 R 207 3027 0 R 208 3011 0 R 209 3012 0 R 210 3013 0 R 211 3014 0 R 212 3015 0 R 213 3016 0 R 214 3007 0 R 215 3008 0 R 216 3005 0 R 217 3001 0 R 218 3002 0 R 219 2993 0 R 220 2994 0 R 221 2995 0 R 222 2996 0 R 223 1148 0 R ] /Limits [ 192 223 ] >> endobj 1151 0 obj [ 2809 0 R 2810 0 R 2923 0 R 2810 0 R 2924 0 R 2810 0 R 2811 0 R 2912 0 R 2812 0 R 2913 0 R 2812 0 R 2914 0 R 2812 0 R 2915 0 R 2812 0 R 2916 0 R 2812 0 R 2902 0 R 2813 0 R 2903 0 R 2813 0 R 2904 0 R 2813 0 R 2905 0 R 2813 0 R 2814 0 R 2815 0 R 2895 0 R 2815 0 R 2896 0 R 2815 0 R 2897 0 R 2815 0 R 2816 0 R 2886 0 R 2816 0 R 2887 0 R 2816 0 R 2888 0 R 2816 0 R 2889 0 R 2816 0 R 2817 0 R 2876 0 R 2818 0 R 2877 0 R 2818 0 R 2878 0 R 2818 0 R 2879 0 R 2818 0 R 2880 0 R 2818 0 R 2819 0 R 2820 0 R 2872 0 R 2820 0 R 2873 0 R 2820 0 R 2821 0 R 2868 0 R 2821 0 R 2869 0 R 2821 0 R ] endobj 1152 0 obj << /Nums [ 224 2987 0 R 225 2988 0 R 226 2989 0 R 227 2968 0 R 228 2969 0 R 229 2970 0 R 230 2971 0 R 231 2972 0 R 232 2972 0 R 233 2973 0 R 234 2974 0 R 235 2975 0 R 236 2976 0 R 237 2964 0 R 238 2965 0 R 239 2954 0 R 240 2955 0 R 241 2956 0 R 242 2957 0 R 243 2958 0 R 244 2946 0 R 245 2947 0 R 246 2948 0 R 247 2949 0 R 248 2944 0 R 249 2940 0 R 250 2941 0 R 251 2936 0 R 252 2937 0 R 253 2932 0 R 254 2933 0 R 255 2928 0 R ] /Limits [ 224 255 ] >> endobj 1153 0 obj [ 2822 0 R 2862 0 R 2823 0 R 2863 0 R 2823 0 R 2864 0 R 2823 0 R 2824 0 R 2825 0 R 2858 0 R 2825 0 R 2859 0 R 2825 0 R 2826 0 R 2854 0 R 2826 0 R 2855 0 R 2826 0 R 2827 0 R 2852 0 R 2827 0 R 2843 0 R 2828 0 R 2844 0 R 2828 0 R 2845 0 R 2828 0 R 2846 0 R 2828 0 R 2829 0 R 2831 0 R 2829 0 R 2832 0 R 2829 0 R 2833 0 R 2829 0 R 2834 0 R 2829 0 R 2835 0 R 2829 0 R 2836 0 R 2829 0 R 2830 0 R ] endobj 1154 0 obj [ 3102 0 R 3038 0 R 3039 0 R 3040 0 R 3041 0 R 3042 0 R 3043 0 R 3097 0 R 3043 0 R 3098 0 R 3043 0 R 3044 0 R 3093 0 R 3044 0 R 3094 0 R 3044 0 R 3045 0 R 3089 0 R 3045 0 R 3090 0 R 3045 0 R 3046 0 R 3085 0 R 3046 0 R 3086 0 R 3046 0 R 3047 0 R 3081 0 R 3047 0 R 3082 0 R 3047 0 R 3048 0 R 3077 0 R 3048 0 R 3078 0 R 3048 0 R 3049 0 R 3073 0 R 3049 0 R 3074 0 R 3049 0 R ] endobj 1155 0 obj << /Nums [ 256 2929 0 R 257 1151 0 R 258 2923 0 R 259 2924 0 R 260 2924 0 R 261 2912 0 R 262 2913 0 R 263 2914 0 R 264 2915 0 R 265 2916 0 R 266 2916 0 R 267 2902 0 R 268 2903 0 R 269 2904 0 R 270 2904 0 R 271 2905 0 R 272 2905 0 R 273 2895 0 R 274 2895 0 R 275 2896 0 R 276 2897 0 R 277 2886 0 R 278 2887 0 R 279 2888 0 R 280 2888 0 R 281 2889 0 R 282 2876 0 R 283 2877 0 R 284 2878 0 R 285 2879 0 R 286 2880 0 R 287 2872 0 R ] /Limits [ 256 287 ] >> endobj 1156 0 obj [ 3049 0 R 3050 0 R 3069 0 R 3050 0 R 3070 0 R 3050 0 R 3051 0 R 3065 0 R 3051 0 R 3066 0 R 3051 0 R 3052 0 R 3053 0 R 3059 0 R 3053 0 R 3060 0 R 3053 0 R 3061 0 R 3053 0 R 3054 0 R 3057 0 R 3054 0 R 3055 0 R 3056 0 R ] endobj 1157 0 obj [ 3182 0 R 3105 0 R 3106 0 R 3107 0 R 3108 0 R 3109 0 R 3177 0 R 3109 0 R 3178 0 R 3109 0 R 3110 0 R 3111 0 R 3173 0 R 3111 0 R 3174 0 R 3111 0 R 3112 0 R 3113 0 R 3165 0 R 3113 0 R 3166 0 R 3113 0 R 3167 0 R 3113 0 R 3168 0 R 3113 0 R 3114 0 R 3115 0 R 3161 0 R 3115 0 R 3162 0 R 3115 0 R 3116 0 R 3136 0 R 3116 0 R 3137 0 R 3116 0 R 3138 0 R 3116 0 R 3139 0 R 3116 0 R 3140 0 R 3116 0 R 3141 0 R 3116 0 R 3142 0 R 3116 0 R 3143 0 R 3116 0 R 3144 0 R 3116 0 R 3145 0 R 3116 0 R 3146 0 R 3116 0 R 3147 0 R 3116 0 R 3117 0 R ] endobj 1158 0 obj << /Nums [ 288 2873 0 R 289 2868 0 R 290 2869 0 R 291 1153 0 R 292 2862 0 R 293 2863 0 R 294 2864 0 R 295 2858 0 R 296 2859 0 R 297 2854 0 R 298 2855 0 R 299 2852 0 R 300 2843 0 R 301 2844 0 R 302 2845 0 R 303 2845 0 R 304 2846 0 R 305 2831 0 R 306 2832 0 R 307 2833 0 R 308 2834 0 R 309 2835 0 R 310 2836 0 R 311 1154 0 R 312 3101 0 R 313 3097 0 R 314 3098 0 R 315 3093 0 R 316 3094 0 R 317 3089 0 R 318 3090 0 R 319 3085 0 R ] /Limits [ 288 319 ] >> endobj 1159 0 obj [ 3118 0 R 3128 0 R 3118 0 R 3129 0 R 3118 0 R 3130 0 R 3118 0 R 3131 0 R 3118 0 R 3119 0 R 3121 0 R 3119 0 R 3122 0 R 3119 0 R 3123 0 R 3119 0 R 3120 0 R ] endobj 1160 0 obj [ 3203 0 R 3185 0 R 3186 0 R 3187 0 R 3188 0 R 3189 0 R 3190 0 R 3191 0 R 3192 0 R 3193 0 R 3194 0 R 3195 0 R 3196 0 R 3197 0 R 3198 0 R 3200 0 R 3198 0 R 3199 0 R ] endobj 1161 0 obj [ 3219 0 R 3206 0 R 3207 0 R 3216 0 R 3207 0 R 3208 0 R 3209 0 R 3210 0 R 3211 0 R 3212 0 R 3213 0 R 3214 0 R 3215 0 R ] endobj 1162 0 obj [ 3284 0 R 3222 0 R 3223 0 R 3224 0 R 3225 0 R 3226 0 R 3227 0 R 3228 0 R 3229 0 R 3267 0 R 3229 0 R 3268 0 R 3229 0 R 3269 0 R 3229 0 R ] endobj 1163 0 obj [ 3270 0 R 3229 0 R 3271 0 R 3229 0 R 3272 0 R 3229 0 R 3273 0 R 3229 0 R 3274 0 R 3229 0 R 3230 0 R 3231 0 R 3263 0 R 3231 0 R 3264 0 R 3231 0 R 3259 0 R 3232 0 R 3260 0 R 3232 0 R 3253 0 R 3233 0 R 3254 0 R 3233 0 R 3255 0 R 3233 0 R 3234 0 R 3249 0 R 3234 0 R 3250 0 R 3234 0 R 3235 0 R 3243 0 R 3235 0 R 3244 0 R 3235 0 R 3245 0 R 3235 0 R 3236 0 R 3241 0 R 3236 0 R 3237 0 R 3239 0 R 3237 0 R 3238 0 R ] endobj 1164 0 obj << /Nums [ 320 3086 0 R 321 3081 0 R 322 3082 0 R 323 3077 0 R 324 3078 0 R 325 3073 0 R 326 3074 0 R 327 1156 0 R 328 3069 0 R 329 3070 0 R 330 3065 0 R 331 3066 0 R 332 3059 0 R 333 3060 0 R 334 3061 0 R 335 3057 0 R 336 1157 0 R 337 3181 0 R 338 3177 0 R 339 3178 0 R 340 3173 0 R 341 3174 0 R 342 3165 0 R 343 3166 0 R 344 3167 0 R 345 3168 0 R 346 3161 0 R 347 3162 0 R 348 3136 0 R 349 3137 0 R 350 3138 0 R 351 3139 0 R ] /Limits [ 320 351 ] >> endobj 1165 0 obj [ 3328 0 R 3287 0 R 3318 0 R 3288 0 R 3319 0 R 3288 0 R 3320 0 R 3288 0 R 3321 0 R 3288 0 R 3289 0 R 3290 0 R 3316 0 R 3290 0 R 3291 0 R 3292 0 R 3314 0 R 3292 0 R 3293 0 R 3294 0 R 3305 0 R 3294 0 R 3306 0 R 3294 0 R 3307 0 R 3294 0 R 3308 0 R 3294 0 R 3295 0 R 3303 0 R 3295 0 R 3296 0 R ] endobj 1166 0 obj [ 3297 0 R 3298 0 R 3299 0 R 3300 0 R 3301 0 R 3302 0 R ] endobj 1167 0 obj << /Nums [ 352 3139 0 R 353 3140 0 R 354 3141 0 R 355 3142 0 R 356 3143 0 R 357 3144 0 R 358 3145 0 R 359 3146 0 R 360 3147 0 R 361 1159 0 R 362 3128 0 R 363 3129 0 R 364 3130 0 R 365 3131 0 R 366 3121 0 R 367 3122 0 R 368 3122 0 R 369 3123 0 R 370 1160 0 R 371 3202 0 R 372 3200 0 R 373 1161 0 R 374 3218 0 R 375 3216 0 R 376 1162 0 R 377 3283 0 R 378 3267 0 R 379 3268 0 R 380 3269 0 R 381 1163 0 R 382 3270 0 R 383 3271 0 R ] /Limits [ 352 383 ] >> endobj 1168 0 obj [ 3425 0 R 3331 0 R 3414 0 R 3415 0 R 3416 0 R 3415 0 R 3417 0 R 3415 0 R 3418 0 R 3415 0 R 3419 0 R 3415 0 R 3406 0 R 3407 0 R 3408 0 R 3407 0 R 3409 0 R 3407 0 R 3410 0 R 3407 0 R 3402 0 R 3403 0 R 3404 0 R 3403 0 R 3398 0 R 3399 0 R 3400 0 R 3399 0 R 3394 0 R 3395 0 R 3396 0 R 3395 0 R 3388 0 R 3389 0 R 3390 0 R 3389 0 R 3391 0 R 3389 0 R 3382 0 R 3383 0 R 3384 0 R 3383 0 R 3385 0 R 3383 0 R 3378 0 R 3379 0 R 3380 0 R 3379 0 R 3374 0 R 3375 0 R 3376 0 R 3375 0 R 3370 0 R 3371 0 R ] endobj 1169 0 obj [ 3372 0 R 3371 0 R 3354 0 R 3355 0 R 3356 0 R 3355 0 R 3357 0 R 3355 0 R 3358 0 R 3355 0 R 3359 0 R 3355 0 R 3360 0 R 3355 0 R 3361 0 R 3355 0 R 3362 0 R 3355 0 R 3348 0 R 3349 0 R 3350 0 R 3349 0 R 3351 0 R 3349 0 R 3333 0 R 3334 0 R ] endobj 1170 0 obj [ 3427 0 R ] endobj 1171 0 obj [ 3428 0 R ] endobj 1172 0 obj [ 3429 0 R ] endobj 1173 0 obj << /Nums [ 384 3272 0 R 385 3273 0 R 386 3274 0 R 387 3263 0 R 388 3264 0 R 389 3259 0 R 390 3260 0 R 391 3253 0 R 392 3254 0 R 393 3255 0 R 394 3249 0 R 395 3250 0 R 396 3243 0 R 397 3244 0 R 398 3245 0 R 399 3241 0 R 400 3239 0 R 401 1165 0 R 402 3327 0 R 403 3318 0 R 404 3319 0 R 405 3319 0 R 406 3320 0 R 407 3321 0 R 408 3316 0 R 409 3314 0 R 410 3305 0 R 411 3306 0 R 412 3306 0 R 413 3307 0 R 414 3308 0 R 415 3303 0 R ] /Limits [ 384 415 ] >> endobj 1174 0 obj [ 3430 0 R ] endobj 1175 0 obj [ 3431 0 R ] endobj 1176 0 obj [ 3431 0 R ] endobj 1177 0 obj [ 3431 0 R ] endobj 1178 0 obj [ 3431 0 R ] endobj 1179 0 obj [ 3432 0 R ] endobj 1180 0 obj [ 3433 0 R ] endobj 1181 0 obj [ 3434 0 R ] endobj 1182 0 obj [ 3434 0 R ] endobj 1183 0 obj [ 3434 0 R ] endobj 1184 0 obj [ 3434 0 R ] endobj 1185 0 obj [ 3434 0 R ] endobj 1186 0 obj [ 3435 0 R ] endobj 1187 0 obj [ 3436 0 R ] endobj 1188 0 obj [ 3436 0 R ] endobj 1189 0 obj [ 3436 0 R ] endobj 1190 0 obj [ 3437 0 R ] endobj 1191 0 obj [ 3437 0 R ] endobj 1192 0 obj [ 3438 0 R ] endobj 1193 0 obj [ 3438 0 R ] endobj 1194 0 obj [ 3439 0 R ] endobj 1195 0 obj [ 3439 0 R ] endobj 1196 0 obj [ 3439 0 R ] endobj 1197 0 obj [ 3439 0 R ] endobj 1198 0 obj [ 3439 0 R ] endobj 1199 0 obj [ 3439 0 R ] endobj 1200 0 obj [ 3439 0 R ] endobj 1201 0 obj [ 3440 0 R ] endobj 1202 0 obj [ 3440 0 R ] endobj 1203 0 obj [ 3440 0 R ] endobj 1204 0 obj [ 3440 0 R ] endobj 1205 0 obj [ 3440 0 R ] endobj 1206 0 obj << /Nums [ 416 1166 0 R 417 1168 0 R 418 3424 0 R 419 3416 0 R 420 3417 0 R 421 3418 0 R 422 3419 0 R 423 3408 0 R 424 3409 0 R 425 3410 0 R 426 3404 0 R 427 3400 0 R 428 3396 0 R 429 3390 0 R 430 3391 0 R 431 3384 0 R 432 3385 0 R 433 3380 0 R 434 3376 0 R 435 1169 0 R 436 3372 0 R 437 3356 0 R 438 3357 0 R 439 3358 0 R 440 3359 0 R 441 3360 0 R 442 3361 0 R 443 3362 0 R 444 3350 0 R 445 3351 0 R 446 1170 0 R 447 1171 0 R ] /Limits [ 416 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Hash Tables.pdf b/papers/The Art of Multiprocessor Hash Tables.pdf new file mode 100644 index 0000000..aa15d4b Binary files /dev/null and b/papers/The Art of Multiprocessor Hash Tables.pdf differ diff --git a/papers/Universal Classes of Hash Functions.pdf b/papers/Universal Classes of Hash Functions.pdf new file mode 100644 index 0000000..865b7b0 Binary files /dev/null and b/papers/Universal Classes of Hash Functions.pdf differ diff --git a/papers/donald-e-knuth-the-art-of-computer-programming-vol-3.pdf b/papers/donald-e-knuth-the-art-of-computer-programming-vol-3.pdf new file mode 100644 index 0000000..9f5f573 Binary files /dev/null and b/papers/donald-e-knuth-the-art-of-computer-programming-vol-3.pdf differ diff --git a/requirements.txt b/requirements.txt new file mode 100644 index 0000000..5c17d86 --- /dev/null +++ b/requirements.txt @@ -0,0 +1,4 @@ +pytest>=7.4.0 +matplotlib>=3.7.0 +numpy>=1.24.0 + diff --git a/src/__init__.py b/src/__init__.py new file mode 100644 index 0000000..d421884 --- /dev/null +++ b/src/__init__.py @@ -0,0 +1,40 @@ +""" +Hash Tables and Hash Functions Package + +This package provides implementations of various hash table data structures +and hash functions for educational and research purposes. +""" + +from .hash_functions import ( + division_hash, + multiplication_hash, + universal_hash, + string_hash_simple, + string_hash_polynomial, + string_hash_djb2, + md5_hash, + bad_hash_clustering, + get_hash_function +) + +from .hash_tables import ( + DirectAddressTable, + HashTableOpenAddressing, + HashTableSeparateChaining +) + +__all__ = [ + 'division_hash', + 'multiplication_hash', + 'universal_hash', + 'string_hash_simple', + 'string_hash_polynomial', + 'string_hash_djb2', + 'md5_hash', + 'bad_hash_clustering', + 'get_hash_function', + 'DirectAddressTable', + 'HashTableOpenAddressing', + 'HashTableSeparateChaining', +] + diff --git a/src/benchmark.py b/src/benchmark.py new file mode 100644 index 0000000..4e11ee6 --- /dev/null +++ b/src/benchmark.py @@ -0,0 +1,570 @@ +""" +Benchmarking utilities for hash table performance analysis. +""" + +import time +import random +import statistics +from typing import List, Dict, Any, Callable, Tuple +from .hash_tables import HashTableOpenAddressing, HashTableSeparateChaining +from .hash_functions import ( + division_hash, + multiplication_hash, + string_hash_polynomial, + string_hash_simple, + bad_hash_clustering +) + + +def benchmark_insert( + hash_table: Any, + keys: List[int], + values: List[Any] = None +) -> float: + """ + Benchmark insertion operations. + + Args: + hash_table: Hash table instance + keys: List of keys to insert + values: Optional list of values (defaults to same as keys) + + Returns: + Time taken in seconds + """ + if values is None: + values = keys + + start = time.perf_counter() + for key, value in zip(keys, values): + hash_table.insert(key, value) + end = time.perf_counter() + + return end - start + + +def benchmark_search( + hash_table: Any, + keys: List[int] +) -> Tuple[float, int]: + """ + Benchmark search operations. + + Args: + hash_table: Hash table instance + keys: List of keys to search for + + Returns: + Tuple of (time taken in seconds, number of successful searches) + """ + start = time.perf_counter() + found = 0 + for key in keys: + if hash_table.search(key) is not None: + found += 1 + end = time.perf_counter() + + return end - start, found + + +def benchmark_delete( + hash_table: Any, + keys: List[int] +) -> Tuple[float, int]: + """ + Benchmark delete operations. + + Args: + hash_table: Hash table instance + keys: List of keys to delete + + Returns: + Tuple of (time taken in seconds, number of successful deletions) + """ + start = time.perf_counter() + deleted = 0 + for key in keys: + if hash_table.delete(key): + deleted += 1 + end = time.perf_counter() + + return end - start, deleted + + +def generate_test_data(n: int, key_range: Tuple[int, int] = None) -> List[int]: + """ + Generate test data for benchmarking. + + Args: + n: Number of keys to generate + key_range: Optional tuple (min, max) for key range + + Returns: + List of random keys + """ + if key_range is None: + key_range = (0, n * 10) + + random.seed(42) # For reproducibility + return [random.randint(key_range[0], key_range[1]) for _ in range(n)] + + +def benchmark_hash_functions( + hash_funcs: Dict[str, Callable], + keys: List[int], + table_size: int +) -> Dict[str, Dict[str, Any]]: + """ + Benchmark different hash functions. + + Args: + hash_funcs: Dictionary mapping function names to hash functions + keys: List of keys to hash + table_size: Size of hash table + + Returns: + Dictionary with benchmark results including collision counts + """ + results = {} + + for name, hash_func in hash_funcs.items(): + start = time.perf_counter() + hash_values = [hash_func(k, table_size) for k in keys] + end = time.perf_counter() + + # Count collisions + collision_count = len(keys) - len(set(hash_values)) + collision_rate = collision_count / len(keys) if keys else 0 + + # Calculate distribution (variance of bucket sizes) + bucket_counts = {} + for hv in hash_values: + bucket_counts[hv] = bucket_counts.get(hv, 0) + 1 + + bucket_sizes = list(bucket_counts.values()) + if bucket_sizes: + avg_bucket_size = sum(bucket_sizes) / len(bucket_sizes) + variance = sum((x - avg_bucket_size) ** 2 for x in bucket_sizes) / len(bucket_sizes) + else: + variance = 0 + + results[name] = { + 'time': end - start, + 'collisions': collision_count, + 'collision_rate': collision_rate, + 'variance': variance, + 'buckets_used': len(bucket_counts), + 'max_chain_length': max(bucket_sizes) if bucket_sizes else 0 + } + + return results + + +def benchmark_open_addressing_vs_chaining( + sizes: List[int], + probe_types: List[str] = ['linear', 'quadratic', 'double'] +) -> Dict[str, List[Dict[str, Any]]]: + """ + Compare open addressing (different probe types) vs separate chaining. + + Args: + sizes: List of data sizes to test + probe_types: List of probe types to test + + Returns: + Dictionary with benchmark results + """ + results = { + 'open_addressing': {pt: [] for pt in probe_types}, + 'separate_chaining': [] + } + + for size in sizes: + keys = generate_test_data(size) + table_size = int(size * 1.5) # Start with 1.5x load factor + + # Test open addressing with different probe types + for probe_type in probe_types: + ht = HashTableOpenAddressing(table_size, probe_type=probe_type) + + insert_time = benchmark_insert(ht, keys) + search_time, found = benchmark_search(ht, keys[:size//2]) + delete_time, deleted = benchmark_delete(ht, keys[:size//4]) + + load_factor = ht._load_factor() + + results['open_addressing'][probe_type].append({ + 'size': size, + 'insert_time': insert_time, + 'search_time': search_time, + 'delete_time': delete_time, + 'load_factor': load_factor, + 'found': found, + 'deleted': deleted + }) + + # Test separate chaining + ht = HashTableSeparateChaining(table_size) + + insert_time = benchmark_insert(ht, keys) + search_time, found = benchmark_search(ht, keys[:size//2]) + delete_time, deleted = benchmark_delete(ht, keys[:size//4]) + + chain_lengths = ht.get_chain_lengths() + avg_chain_length = sum(chain_lengths) / len(chain_lengths) if chain_lengths else 0 + max_chain_length = max(chain_lengths) if chain_lengths else 0 + + results['separate_chaining'].append({ + 'size': size, + 'insert_time': insert_time, + 'search_time': search_time, + 'delete_time': delete_time, + 'load_factor': ht._load_factor(), + 'found': found, + 'deleted': deleted, + 'avg_chain_length': avg_chain_length, + 'max_chain_length': max_chain_length + }) + + return results + + +def benchmark_load_factor_impact( + initial_size: int, + max_elements: int, + probe_type: str = 'linear', + num_runs: int = 5 +) -> Dict[str, List[Dict[str, Any]]]: + """ + Benchmark performance at different load factors with multiple runs for statistical accuracy. + + Args: + initial_size: Initial hash table size + max_elements: Maximum number of elements to insert + probe_type: Probe type for open addressing + num_runs: Number of runs per load factor for averaging + + Returns: + Dictionary with results for open addressing and separate chaining + """ + results = { + 'open_addressing': [], + 'separate_chaining': [] + } + + num_samples = 10 + batch_size = max_elements // num_samples + + # Test open addressing + for i in range(0, max_elements, batch_size): + if i + batch_size > max_elements: + continue + + # Run multiple times to get statistical averages + insert_times = [] + search_times = [] + load_factors = [] + + for run in range(num_runs): + keys = generate_test_data(max_elements) + ht_oa = HashTableOpenAddressing(initial_size, probe_type=probe_type) + inserted_keys_oa = [] + + # Insert up to (but not including) current batch + for j in range(0, i, batch_size): + batch_keys = keys[j:j+batch_size] + if not batch_keys: + continue + for key in batch_keys: + ht_oa.insert(key, key) + inserted_keys_oa.extend(batch_keys) + + # Measure insert time for this batch (normalized per element) + batch_keys = keys[i:i+batch_size] + if batch_keys: + batch_start = time.perf_counter() + for key in batch_keys: + ht_oa.insert(key, key) + batch_end = time.perf_counter() + insert_time_per_element = (batch_end - batch_start) / len(batch_keys) + insert_times.append(insert_time_per_element) + inserted_keys_oa.extend(batch_keys) + + # Benchmark search on a sample of ALL inserted keys + search_sample_size = min(100, len(inserted_keys_oa)) + search_keys = inserted_keys_oa[:search_sample_size] if inserted_keys_oa else [] + if search_keys: + search_time, _ = benchmark_search(ht_oa, search_keys) + search_time_per_element = search_time / len(search_keys) + search_times.append(search_time_per_element) + + load_factors.append(ht_oa._load_factor()) + + # Compute statistics + if insert_times and search_times: + import statistics + avg_insert = statistics.mean(insert_times) + std_insert = statistics.stdev(insert_times) if len(insert_times) > 1 else 0 + avg_search = statistics.mean(search_times) + std_search = statistics.stdev(search_times) if len(search_times) > 1 else 0 + avg_load_factor = statistics.mean(load_factors) + + results['open_addressing'].append({ + 'elements': i + batch_size, + 'load_factor': avg_load_factor, + 'insert_time': avg_insert, + 'insert_time_std': std_insert, + 'search_time': avg_search, + 'search_time_std': std_search + }) + + # Test separate chaining + for i in range(0, max_elements, batch_size): + if i + batch_size > max_elements: + continue + + # Run multiple times to get statistical averages + insert_times = [] + search_times = [] + load_factors = [] + chain_lengths_list = [] + + for run in range(num_runs): + keys = generate_test_data(max_elements) + ht_sc = HashTableSeparateChaining(initial_size) + inserted_keys_sc = [] + + # Insert up to (but not including) current batch + for j in range(0, i, batch_size): + batch_keys = keys[j:j+batch_size] + if not batch_keys: + continue + for key in batch_keys: + ht_sc.insert(key, key) + inserted_keys_sc.extend(batch_keys) + + # Measure insert time for this batch (normalized per element) + batch_keys = keys[i:i+batch_size] + if batch_keys: + batch_start = time.perf_counter() + for key in batch_keys: + ht_sc.insert(key, key) + batch_end = time.perf_counter() + insert_time_per_element = (batch_end - batch_start) / len(batch_keys) + insert_times.append(insert_time_per_element) + inserted_keys_sc.extend(batch_keys) + + # Benchmark search on a sample of ALL inserted keys + search_sample_size = min(100, len(inserted_keys_sc)) + search_keys = inserted_keys_sc[:search_sample_size] if inserted_keys_sc else [] + if search_keys: + search_time, _ = benchmark_search(ht_sc, search_keys) + search_time_per_element = search_time / len(search_keys) + search_times.append(search_time_per_element) + + chain_lengths = ht_sc.get_chain_lengths() + # Calculate average chain length only for non-empty buckets + non_empty_lengths = [l for l in chain_lengths if l > 0] + avg_chain_length = sum(non_empty_lengths) / len(non_empty_lengths) if non_empty_lengths else 0 + chain_lengths_list.append(avg_chain_length) + + load_factors.append(ht_sc._load_factor()) + + # Compute statistics + if insert_times and search_times: + avg_insert = statistics.mean(insert_times) + std_insert = statistics.stdev(insert_times) if len(insert_times) > 1 else 0 + avg_search = statistics.mean(search_times) + std_search = statistics.stdev(search_times) if len(search_times) > 1 else 0 + avg_load_factor = statistics.mean(load_factors) + avg_chain_length = statistics.mean(chain_lengths_list) + + results['separate_chaining'].append({ + 'elements': i + batch_size, + 'load_factor': avg_load_factor, + 'insert_time': avg_insert, + 'insert_time_std': std_insert, + 'search_time': avg_search, + 'search_time_std': std_search, + 'avg_chain_length': avg_chain_length + }) + + return results + + +def benchmark_load_factor_impact_probes( + initial_size: int, + max_elements: int, + probe_type: str = 'linear', + num_runs: int = 10 +) -> Dict[str, List[Dict[str, Any]]]: + """ + Benchmark probe counts and comparisons at different load factors. + Uses deterministic metrics instead of timing for smooth theoretical curves. + + Args: + initial_size: Initial hash table size + max_elements: Maximum number of elements to insert + probe_type: Probe type for open addressing + num_runs: Number of runs per load factor for averaging + + Returns: + Dictionary with results for open addressing and separate chaining + """ + results = { + 'open_addressing': [], + 'separate_chaining': [] + } + + num_samples = 10 + batch_size = max_elements // num_samples + + # Test open addressing + for i in range(0, max_elements, batch_size): + if i + batch_size > max_elements: + continue + + # Run multiple times to get statistical averages + insert_probes = [] + search_probes = [] + insert_comparisons = [] + search_comparisons = [] + load_factors = [] + search_sample_size = 100 # Fixed sample size for normalization + + for run in range(num_runs): + keys = generate_test_data(max_elements) + ht_oa = HashTableOpenAddressing(initial_size, probe_type=probe_type) + inserted_keys_oa = [] + + # Insert up to (but not including) current batch + for j in range(0, i, batch_size): + batch_keys = keys[j:j+batch_size] + if not batch_keys: + continue + for key in batch_keys: + ht_oa.insert(key, key) + inserted_keys_oa.extend(batch_keys) + + # Reset counters before measuring current batch + ht_oa.reset_counts() + + # Measure insert probes/comparisons for this batch + batch_keys = keys[i:i+batch_size] + if batch_keys: + for key in batch_keys: + ht_oa.insert(key, key) + inserted_keys_oa.extend(batch_keys) + + insert_probes.append(ht_oa.get_probe_count()) + insert_comparisons.append(ht_oa.get_comparison_count()) + + # Reset counters for search + ht_oa.reset_counts() + + # Benchmark search on a sample of ALL inserted keys + actual_search_size = min(search_sample_size, len(inserted_keys_oa)) + search_keys = inserted_keys_oa[:actual_search_size] if inserted_keys_oa else [] + if search_keys: + for key in search_keys: + ht_oa.search(key) + + search_probes.append(ht_oa.get_probe_count()) + search_comparisons.append(ht_oa.get_comparison_count()) + + load_factors.append(ht_oa._load_factor()) + + # Compute statistics + if insert_probes and search_probes: + # Normalize by batch size and search sample size (fixed at 100) + avg_insert_probes = statistics.mean(insert_probes) / batch_size if insert_probes and batch_size > 0 else 0 + avg_search_probes = statistics.mean(search_probes) / search_sample_size if search_probes and search_sample_size > 0 else 0 + avg_insert_comparisons = statistics.mean(insert_comparisons) / batch_size if insert_comparisons and batch_size > 0 else 0 + avg_search_comparisons = statistics.mean(search_comparisons) / search_sample_size if search_comparisons and search_sample_size > 0 else 0 + avg_load_factor = statistics.mean(load_factors) + + results['open_addressing'].append({ + 'elements': i + batch_size, + 'load_factor': avg_load_factor, + 'insert_probes_per_element': avg_insert_probes, + 'search_probes_per_element': avg_search_probes, + 'insert_comparisons_per_element': avg_insert_comparisons, + 'search_comparisons_per_element': avg_search_comparisons + }) + + # Test separate chaining + for i in range(0, max_elements, batch_size): + if i + batch_size > max_elements: + continue + + # Run multiple times to get statistical averages + insert_comparisons = [] + search_comparisons = [] + load_factors = [] + chain_lengths_list = [] + search_sample_size = 100 # Fixed sample size for normalization + + for run in range(num_runs): + keys = generate_test_data(max_elements) + ht_sc = HashTableSeparateChaining(initial_size) + inserted_keys_sc = [] + + # Insert up to (but not including) current batch + for j in range(0, i, batch_size): + batch_keys = keys[j:j+batch_size] + if not batch_keys: + continue + for key in batch_keys: + ht_sc.insert(key, key) + inserted_keys_sc.extend(batch_keys) + + # Reset counters before measuring current batch + ht_sc.reset_counts() + + # Measure insert comparisons for this batch + batch_keys = keys[i:i+batch_size] + if batch_keys: + for key in batch_keys: + ht_sc.insert(key, key) + inserted_keys_sc.extend(batch_keys) + + insert_comparisons.append(ht_sc.get_comparison_count()) + + # Reset counters for search + ht_sc.reset_counts() + + # Benchmark search on a sample of ALL inserted keys + actual_search_size = min(search_sample_size, len(inserted_keys_sc)) + search_keys = inserted_keys_sc[:actual_search_size] if inserted_keys_sc else [] + if search_keys: + for key in search_keys: + ht_sc.search(key) + + search_comparisons.append(ht_sc.get_comparison_count()) + + chain_lengths = ht_sc.get_chain_lengths() + # Calculate average chain length only for non-empty buckets + non_empty_lengths = [l for l in chain_lengths if l > 0] + avg_chain_length = sum(non_empty_lengths) / len(non_empty_lengths) if non_empty_lengths else 0 + chain_lengths_list.append(avg_chain_length) + + load_factors.append(ht_sc._load_factor()) + + # Compute statistics + if insert_comparisons and search_comparisons: + # Normalize by batch size and search sample size (fixed at 100) + avg_insert_comparisons = statistics.mean(insert_comparisons) / batch_size if insert_comparisons and batch_size > 0 else 0 + avg_search_comparisons = statistics.mean(search_comparisons) / search_sample_size if search_comparisons and search_sample_size > 0 else 0 + avg_load_factor = statistics.mean(load_factors) + avg_chain_length = statistics.mean(chain_lengths_list) + + results['separate_chaining'].append({ + 'elements': i + batch_size, + 'load_factor': avg_load_factor, + 'insert_comparisons_per_element': avg_insert_comparisons, + 'search_comparisons_per_element': avg_search_comparisons, + 'avg_chain_length': avg_chain_length + }) + + return results + diff --git a/src/hash_functions.py b/src/hash_functions.py new file mode 100644 index 0000000..56ed18c --- /dev/null +++ b/src/hash_functions.py @@ -0,0 +1,183 @@ +""" +Hash Functions Module + +This module implements various hash functions, including good and bad examples +to demonstrate the impact of hash function design on hash table performance. +""" + +import hashlib +from typing import Any, Callable, Optional + + +def division_hash(key: int, table_size: int) -> int: + """ + Division method hash function: h(k) = k mod m + + Simple and fast, but requires careful choice of table size (preferably prime). + + Args: + key: The key to hash + table_size: Size of the hash table + + Returns: + Hash value in range [0, table_size-1] + """ + return key % table_size + + +def multiplication_hash(key: int, table_size: int, A: float = 0.6180339887) -> int: + """ + Multiplication method hash function: h(k) = floor(m * (kA mod 1)) + + A good choice of A (often (sqrt(5)-1)/2) helps distribute keys uniformly. + + Args: + key: The key to hash + table_size: Size of the hash table + A: Multiplier constant (default: (sqrt(5)-1)/2) + + Returns: + Hash value in range [0, table_size-1] + """ + return int(table_size * ((key * A) % 1)) + + +def universal_hash(key: int, table_size: int, a: int, b: int, p: int) -> int: + """ + Universal hash function: h(k) = ((a*k + b) mod p) mod m + + Part of a universal class of hash functions that minimizes collisions + for any set of keys. + + Args: + key: The key to hash + table_size: Size of the hash table + a: Random parameter (1 <= a < p) + b: Random parameter (0 <= b < p) + p: Large prime number (p > max_key) + + Returns: + Hash value in range [0, table_size-1] + """ + return ((a * key + b) % p) % table_size + + +def string_hash_simple(key: str, table_size: int) -> int: + """ + Simple string hash function (BAD EXAMPLE - prone to collisions). + + This is a naive implementation that sums character values. + Poor distribution for similar strings. + + Args: + key: String key to hash + table_size: Size of the hash table + + Returns: + Hash value in range [0, table_size-1] + """ + hash_value = 0 + for char in key: + hash_value += ord(char) + return hash_value % table_size + + +def string_hash_polynomial(key: str, table_size: int, base: int = 31) -> int: + """ + Polynomial rolling hash function (GOOD EXAMPLE). + + Uses polynomial accumulation: h(s) = (s[0]*b^(n-1) + s[1]*b^(n-2) + ... + s[n-1]) mod m + + Better distribution than simple summation. + + Args: + key: String key to hash + table_size: Size of the hash table + base: Base for polynomial (default: 31) + + Returns: + Hash value in range [0, table_size-1] + """ + hash_value = 0 + for char in key: + hash_value = (hash_value * base + ord(char)) % table_size + return hash_value + + +def string_hash_djb2(key: str, table_size: int) -> int: + """ + DJB2 hash function - a popular string hash function. + + Known for good distribution properties. + + Args: + key: String key to hash + table_size: Size of the hash table + + Returns: + Hash value in range [0, table_size-1] + """ + hash_value = 5381 + for char in key: + hash_value = ((hash_value << 5) + hash_value) + ord(char) + return hash_value % table_size + + +def md5_hash(key: str, table_size: int) -> int: + """ + MD5-based hash function (cryptographically secure but slower). + + Provides excellent distribution but computationally expensive. + Demonstrates trade-off between speed and quality. + + Args: + key: String key to hash + table_size: Size of the hash table + + Returns: + Hash value in range [0, table_size-1] + """ + md5_hash_obj = hashlib.md5(key.encode('utf-8')) + hash_int = int(md5_hash_obj.hexdigest(), 16) + return hash_int % table_size + + +def bad_hash_clustering(key: int, table_size: int) -> int: + """ + BAD EXAMPLE: Hash function that causes clustering. + + This function uses a poor multiplier that causes many collisions + and clustering behavior. + + Args: + key: The key to hash + table_size: Size of the hash table + + Returns: + Hash value (poorly distributed) + """ + # Poor choice: using table_size as multiplier causes clustering + return (key * table_size) % table_size + + +def get_hash_function(hash_type: str) -> Callable: + """ + Get a hash function by name. + + Args: + hash_type: Type of hash function ('division', 'multiplication', 'universal', etc.) + + Returns: + Hash function callable + """ + hash_functions = { + 'division': division_hash, + 'multiplication': multiplication_hash, + 'string_simple': string_hash_simple, + 'string_polynomial': string_hash_polynomial, + 'string_djb2': string_hash_djb2, + 'md5': md5_hash, + 'bad_clustering': bad_hash_clustering, + } + return hash_functions.get(hash_type, division_hash) + diff --git a/src/hash_tables.py b/src/hash_tables.py new file mode 100644 index 0000000..2beee4b --- /dev/null +++ b/src/hash_tables.py @@ -0,0 +1,413 @@ +""" +Hash Tables Module + +This module implements various hash table data structures including: +- Direct-address tables +- Open addressing (linear probing, quadratic probing, double hashing) +- Separate chaining +""" + +from typing import Any, Optional, Tuple, List, Callable +from .hash_functions import division_hash, get_hash_function + + +class DirectAddressTable: + """ + Direct-address table implementation. + + Assumes keys are integers in a small range [0, m-1]. + Provides O(1) operations but requires keys to be in a known range. + """ + + def __init__(self, size: int): + """ + Initialize direct-address table. + + Args: + size: Maximum key value (keys must be in range [0, size-1]) + """ + self.size = size + self.table: List[Optional[Any]] = [None] * size + + def insert(self, key: int, value: Any) -> None: + """ + Insert key-value pair. + + Args: + key: Integer key (must be in range [0, size-1]) + value: Value to store + """ + if not (0 <= key < self.size): + raise ValueError(f"Key {key} out of range [0, {self.size-1}]") + self.table[key] = value + + def search(self, key: int) -> Optional[Any]: + """ + Search for value by key. + + Args: + key: Integer key to search for + + Returns: + Value if found, None otherwise + """ + if not (0 <= key < self.size): + return None + return self.table[key] + + def delete(self, key: int) -> None: + """ + Delete key-value pair. + + Args: + key: Integer key to delete + """ + if 0 <= key < self.size: + self.table[key] = None + + +class HashTableOpenAddressing: + """ + Hash table using open addressing with multiple probing strategies. + + Supports linear probing, quadratic probing, and double hashing. + """ + + DELETED = object() # Sentinel for deleted entries + + def __init__( + self, + size: int, + hash_func: Optional[Callable] = None, + probe_type: str = 'linear', + load_factor_threshold: float = 0.75 + ): + """ + Initialize hash table with open addressing. + + Args: + size: Initial size of hash table + hash_func: Hash function to use (default: division method) + probe_type: Type of probing ('linear', 'quadratic', 'double') + load_factor_threshold: Maximum load factor before resizing + """ + self.size = size + self.count = 0 + self.table: List[Optional[Tuple[int, Any]]] = [None] * size + self.hash_func = hash_func or (lambda k, s: division_hash(k, s)) + self.probe_type = probe_type + self.load_factor_threshold = load_factor_threshold + self._probe_count = 0 + self._comparison_count = 0 + + def _load_factor(self) -> float: + """Calculate current load factor.""" + return self.count / self.size + + def _linear_probe(self, key: int, i: int) -> int: + """Linear probing: h(k,i) = (h'(k) + i) mod m""" + h1 = self.hash_func(key, self.size) + return (h1 + i) % self.size + + def _quadratic_probe(self, key: int, i: int) -> int: + """Quadratic probing: h(k,i) = (h'(k) + c1*i + c2*i^2) mod m""" + h1 = self.hash_func(key, self.size) + c1, c2 = 1, 1 + return (h1 + c1 * i + c2 * i * i) % self.size + + def _double_hash(self, key: int, i: int) -> int: + """Double hashing: h(k,i) = (h1(k) + i*h2(k)) mod m""" + h1 = self.hash_func(key, self.size) + # Second hash function: h2(k) = 1 + (k mod (m-1)) + h2 = 1 + (key % (self.size - 1)) + return (h1 + i * h2) % self.size + + def _probe(self, key: int, i: int) -> int: + """Get probe sequence index based on probe type.""" + if self.probe_type == 'linear': + return self._linear_probe(key, i) + elif self.probe_type == 'quadratic': + return self._quadratic_probe(key, i) + elif self.probe_type == 'double': + return self._double_hash(key, i) + else: + raise ValueError(f"Unknown probe type: {self.probe_type}") + + def _resize(self) -> None: + """Resize table when load factor exceeds threshold.""" + old_table = self.table + old_size = self.size + self.size *= 2 + self.count = 0 + self.table = [None] * self.size + + # Rehash all existing entries + for entry in old_table: + if entry is not None and entry is not self.DELETED: + key, value = entry + self.insert(key, value) + + def insert(self, key: int, value: Any) -> None: + """ + Insert key-value pair using open addressing. + + Args: + key: Key to insert + value: Value to store + """ + if self._load_factor() >= self.load_factor_threshold: + self._resize() + + i = 0 + while i < self.size: + index = self._probe(key, i) + self._probe_count += 1 + entry = self.table[index] + + if entry is None or entry is self.DELETED: + self.table[index] = (key, value) + self.count += 1 + return + elif entry[0] == key: + self._comparison_count += 1 + # Update existing key + self.table[index] = (key, value) + return + else: + self._comparison_count += 1 + + i += 1 + + raise RuntimeError("Hash table is full") + + def search(self, key: int) -> Optional[Any]: + """ + Search for value by key. + + Args: + key: Key to search for + + Returns: + Value if found, None otherwise + """ + i = 0 + while i < self.size: + index = self._probe(key, i) + self._probe_count += 1 + entry = self.table[index] + + if entry is None: + return None + elif entry is not self.DELETED and entry[0] == key: + self._comparison_count += 1 + return entry[1] + else: + self._comparison_count += 1 + + i += 1 + + return None + + def get_probe_count(self) -> int: + """Get total number of probes performed.""" + return self._probe_count + + def get_comparison_count(self) -> int: + """Get total number of key comparisons performed.""" + return self._comparison_count + + def reset_counts(self) -> None: + """Reset probe and comparison counters.""" + self._probe_count = 0 + self._comparison_count = 0 + + def delete(self, key: int) -> bool: + """ + Delete key-value pair. + + Args: + key: Key to delete + + Returns: + True if deleted, False if not found + """ + i = 0 + while i < self.size: + index = self._probe(key, i) + entry = self.table[index] + + if entry is None: + return False + elif entry is not self.DELETED and entry[0] == key: + self.table[index] = self.DELETED + self.count -= 1 + return True + + i += 1 + + return False + + +class HashTableSeparateChaining: + """ + Hash table using separate chaining for collision resolution. + + Each bucket contains a linked list of key-value pairs. + """ + + class Node: + """Node for linked list in separate chaining.""" + def __init__(self, key: int, value: Any): + self.key = key + self.value = value + self.next: Optional['HashTableSeparateChaining.Node'] = None + + def __init__( + self, + size: int, + hash_func: Optional[Callable] = None, + load_factor_threshold: float = 1.0 + ): + """ + Initialize hash table with separate chaining. + + Args: + size: Initial size of hash table + hash_func: Hash function to use (default: division method) + load_factor_threshold: Maximum load factor before resizing + """ + self.size = size + self.count = 0 + self.buckets: List[Optional[self.Node]] = [None] * size + self.hash_func = hash_func or (lambda k, s: division_hash(k, s)) + self.load_factor_threshold = load_factor_threshold + self._comparison_count = 0 + + def _load_factor(self) -> float: + """Calculate current load factor.""" + return self.count / self.size + + def _resize(self) -> None: + """Resize table when load factor exceeds threshold.""" + old_buckets = self.buckets + old_size = self.size + self.size *= 2 + self.count = 0 + self.buckets = [None] * self.size + + # Rehash all existing entries + for head in old_buckets: + current = head + while current is not None: + self.insert(current.key, current.value) + current = current.next + + def insert(self, key: int, value: Any) -> None: + """ + Insert key-value pair. + + Args: + key: Key to insert + value: Value to store + """ + if self._load_factor() >= self.load_factor_threshold: + self._resize() + + index = self.hash_func(key, self.size) + + # Check if key already exists + current = self.buckets[index] + while current is not None: + self._comparison_count += 1 + if current.key == key: + current.value = value # Update existing key + return + current = current.next + + # Insert new node at head of chain + new_node = self.Node(key, value) + new_node.next = self.buckets[index] + self.buckets[index] = new_node + self.count += 1 + + def search(self, key: int) -> Optional[Any]: + """ + Search for value by key. + + Args: + key: Key to search for + + Returns: + Value if found, None otherwise + """ + index = self.hash_func(key, self.size) + current = self.buckets[index] + + while current is not None: + self._comparison_count += 1 + if current.key == key: + return current.value + current = current.next + + return None + + def get_comparison_count(self) -> int: + """Get total number of key comparisons performed.""" + return self._comparison_count + + def reset_counts(self) -> None: + """Reset comparison counter.""" + self._comparison_count = 0 + + def delete(self, key: int) -> bool: + """ + Delete key-value pair. + + Args: + key: Key to delete + + Returns: + True if deleted, False if not found + """ + index = self.hash_func(key, self.size) + current = self.buckets[index] + + if current is None: + return False + + # Check if key is at head + if current.key == key: + self.buckets[index] = current.next + self.count -= 1 + return True + + # Search in chain + prev = current + current = current.next + while current is not None: + if current.key == key: + prev.next = current.next + self.count -= 1 + return True + prev = current + current = current.next + + return False + + def get_chain_lengths(self) -> List[int]: + """ + Get lengths of all chains for analysis. + + Returns: + List of chain lengths + """ + lengths = [] + for head in self.buckets: + length = 0 + current = head + while current is not None: + length += 1 + current = current.next + lengths.append(length) + return lengths + diff --git a/tests/test_hash_functions.py b/tests/test_hash_functions.py new file mode 100644 index 0000000..0996343 --- /dev/null +++ b/tests/test_hash_functions.py @@ -0,0 +1,150 @@ +""" +Tests for hash functions. +""" + +import pytest +import sys +import os +sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..')) + +from src.hash_functions import ( + division_hash, + multiplication_hash, + universal_hash, + string_hash_simple, + string_hash_polynomial, + string_hash_djb2, + md5_hash, + bad_hash_clustering +) + + +class TestDivisionHash: + """Tests for division hash function.""" + + def test_basic_division_hash(self): + """Test basic division hash functionality.""" + assert division_hash(10, 7) == 3 + assert division_hash(22, 7) == 1 + assert division_hash(31, 7) == 3 + + def test_hash_range(self): + """Test that hash values are in correct range.""" + table_size = 11 + for key in range(100): + hash_val = division_hash(key, table_size) + assert 0 <= hash_val < table_size + + def test_negative_keys(self): + """Test handling of negative keys.""" + # Division with negative keys + assert division_hash(-10, 7) == (-10 % 7) + + +class TestMultiplicationHash: + """Tests for multiplication hash function.""" + + def test_basic_multiplication_hash(self): + """Test basic multiplication hash functionality.""" + hash_val = multiplication_hash(10, 8) + assert 0 <= hash_val < 8 + + def test_hash_range(self): + """Test that hash values are in correct range.""" + table_size = 16 + for key in range(50): + hash_val = multiplication_hash(key, table_size) + assert 0 <= hash_val < table_size + + +class TestUniversalHash: + """Tests for universal hash function.""" + + def test_basic_universal_hash(self): + """Test basic universal hash functionality.""" + p = 101 # Prime larger than max key + a, b = 3, 7 + hash_val = universal_hash(10, 11, a, b, p) + assert 0 <= hash_val < 11 + + def test_hash_range(self): + """Test that hash values are in correct range.""" + table_size = 13 + p = 101 + a, b = 5, 11 + for key in range(50): + hash_val = universal_hash(key, table_size, a, b, p) + assert 0 <= hash_val < table_size + + +class TestStringHashFunctions: + """Tests for string hash functions.""" + + def test_string_hash_simple(self): + """Test simple string hash function.""" + hash_val = string_hash_simple("hello", 11) + assert 0 <= hash_val < 11 + + def test_string_hash_polynomial(self): + """Test polynomial string hash function.""" + hash_val = string_hash_polynomial("hello", 11) + assert 0 <= hash_val < 11 + + def test_string_hash_djb2(self): + """Test DJB2 string hash function.""" + hash_val = string_hash_djb2("hello", 11) + assert 0 <= hash_val < 11 + + def test_string_hash_collisions(self): + """Test that different strings can produce different hashes.""" + table_size = 100 + strings = ["hello", "world", "test", "hash", "table"] + hashes = [string_hash_polynomial(s, table_size) for s in strings] + # At least some should be different (not guaranteed all) + assert len(set(hashes)) > 1 + + def test_md5_hash(self): + """Test MD5-based hash function.""" + hash_val = md5_hash("test", 11) + assert 0 <= hash_val < 11 + + +class TestBadHashFunctions: + """Tests for bad hash functions (demonstrating poor behavior).""" + + def test_bad_hash_clustering(self): + """Test bad hash function that causes clustering.""" + # This should demonstrate poor distribution + table_size = 10 + keys = list(range(20)) + hashes = [bad_hash_clustering(k, table_size) for k in keys] + # All hashes should be 0 (demonstrating clustering) + assert all(h == 0 for h in hashes) + + +class TestHashFunctionProperties: + """Tests for hash function properties.""" + + def test_deterministic(self): + """Test that hash functions are deterministic.""" + key = 42 + table_size = 11 + hash1 = division_hash(key, table_size) + hash2 = division_hash(key, table_size) + assert hash1 == hash2 + + def test_distribution(self): + """Test that good hash functions distribute keys reasonably.""" + table_size = 20 + keys = list(range(100)) + hashes = [division_hash(k, table_size) for k in keys] + + # Count occurrences in each bucket + bucket_counts = {} + for h in hashes: + bucket_counts[h] = bucket_counts.get(h, 0) + 1 + + # Most buckets should be used (not perfect, but reasonable) + buckets_used = len(bucket_counts) + assert buckets_used > table_size * 0.5 # At least 50% of buckets used + diff --git a/tests/test_hash_tables.py b/tests/test_hash_tables.py new file mode 100644 index 0000000..b50f271 --- /dev/null +++ b/tests/test_hash_tables.py @@ -0,0 +1,203 @@ +""" +Tests for hash table implementations. +""" + +import pytest +import sys +import os +sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..')) + +from src.hash_tables import ( + DirectAddressTable, + HashTableOpenAddressing, + HashTableSeparateChaining +) +from src.hash_functions import division_hash + + +class TestDirectAddressTable: + """Tests for direct-address table.""" + + def test_insert_and_search(self): + """Test basic insert and search operations.""" + table = DirectAddressTable(100) + table.insert(5, "value1") + table.insert(42, "value2") + + assert table.search(5) == "value1" + assert table.search(42) == "value2" + assert table.search(10) is None + + def test_delete(self): + """Test delete operation.""" + table = DirectAddressTable(100) + table.insert(5, "value1") + table.delete(5) + assert table.search(5) is None + + def test_out_of_range_key(self): + """Test handling of out-of-range keys.""" + table = DirectAddressTable(100) + with pytest.raises(ValueError): + table.insert(100, "value") # Out of range + assert table.search(100) is None + + +class TestHashTableOpenAddressing: + """Tests for open addressing hash table.""" + + def test_insert_and_search_linear(self): + """Test insert and search with linear probing.""" + ht = HashTableOpenAddressing(10, probe_type='linear') + ht.insert(10, "value1") + ht.insert(22, "value2") + ht.insert(31, "value3") + + assert ht.search(10) == "value1" + assert ht.search(22) == "value2" + assert ht.search(31) == "value3" + assert ht.search(99) is None + + def test_insert_and_search_quadratic(self): + """Test insert and search with quadratic probing.""" + ht = HashTableOpenAddressing(10, probe_type='quadratic') + ht.insert(10, "value1") + ht.insert(22, "value2") + + assert ht.search(10) == "value1" + assert ht.search(22) == "value2" + + def test_insert_and_search_double(self): + """Test insert and search with double hashing.""" + ht = HashTableOpenAddressing(10, probe_type='double') + ht.insert(10, "value1") + ht.insert(22, "value2") + + assert ht.search(10) == "value1" + assert ht.search(22) == "value2" + + def test_delete(self): + """Test delete operation.""" + ht = HashTableOpenAddressing(10, probe_type='linear') + ht.insert(10, "value1") + ht.insert(22, "value2") + + assert ht.delete(10) is True + assert ht.search(10) is None + assert ht.search(22) == "value2" + assert ht.delete(99) is False + + def test_update_existing_key(self): + """Test updating an existing key.""" + ht = HashTableOpenAddressing(10, probe_type='linear') + ht.insert(10, "value1") + ht.insert(10, "value2") # Update + assert ht.search(10) == "value2" + + def test_resize(self): + """Test automatic resizing.""" + ht = HashTableOpenAddressing(5, probe_type='linear', load_factor_threshold=0.7) + # Insert enough to trigger resize + for i in range(10): + ht.insert(i, f"value{i}") + + # All should still be searchable + for i in range(10): + assert ht.search(i) == f"value{i}" + + +class TestHashTableSeparateChaining: + """Tests for separate chaining hash table.""" + + def test_insert_and_search(self): + """Test basic insert and search operations.""" + ht = HashTableSeparateChaining(10) + ht.insert(10, "value1") + ht.insert(22, "value2") + ht.insert(31, "value3") + + assert ht.search(10) == "value1" + assert ht.search(22) == "value2" + assert ht.search(31) == "value3" + assert ht.search(99) is None + + def test_delete(self): + """Test delete operation.""" + ht = HashTableSeparateChaining(10) + ht.insert(10, "value1") + ht.insert(22, "value2") + + assert ht.delete(10) is True + assert ht.search(10) is None + assert ht.search(22) == "value2" + assert ht.delete(99) is False + + def test_update_existing_key(self): + """Test updating an existing key.""" + ht = HashTableSeparateChaining(10) + ht.insert(10, "value1") + ht.insert(10, "value2") # Update + assert ht.search(10) == "value2" + + def test_collision_handling(self): + """Test that collisions are handled correctly.""" + ht = HashTableSeparateChaining(5) # Small table to force collisions + keys = [10, 15, 20, 25, 30] + for key in keys: + ht.insert(key, f"value{key}") + + # All should be searchable + for key in keys: + assert ht.search(key) == f"value{key}" + + def test_chain_lengths(self): + """Test chain length reporting.""" + ht = HashTableSeparateChaining(5) + for i in range(10): + ht.insert(i, f"value{i}") + + chain_lengths = ht.get_chain_lengths() + # After inserting 10 items, table will resize (load factor > 1.0) + # So chain lengths should match current table size, not initial size + assert len(chain_lengths) == ht.size + assert sum(chain_lengths) == 10 + + def test_resize(self): + """Test automatic resizing.""" + ht = HashTableSeparateChaining(5, load_factor_threshold=1.0) + # Insert enough to trigger resize + for i in range(20): + ht.insert(i, f"value{i}") + + # All should still be searchable + for i in range(20): + assert ht.search(i) == f"value{i}" + + +class TestHashTableComparison: + """Tests comparing different hash table implementations.""" + + def test_same_operations_different_implementations(self): + """Test that different implementations handle same operations.""" + keys = [10, 22, 31, 4, 15, 28, 17, 88, 59] + + ht_oa = HashTableOpenAddressing(20, probe_type='linear') + ht_sc = HashTableSeparateChaining(20) + + # Insert same keys + for key in keys: + ht_oa.insert(key, f"value{key}") + ht_sc.insert(key, f"value{key}") + + # Both should find all keys + for key in keys: + assert ht_oa.search(key) == f"value{key}" + assert ht_sc.search(key) == f"value{key}" + + # Both should delete successfully + for key in keys[:5]: + assert ht_oa.delete(key) is True + assert ht_sc.delete(key) is True + assert ht_oa.search(key) is None + assert ht_sc.search(key) is None +