Edge Cases & Testing Strategies

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from typing import Callable, Any, TypeVar
import sys
 
T = TypeVar('T')
 
 
def generate_boundary_values(min_val: int, max_val: int) -> list[int]:
    """
    Generate boundary test values for a numeric range.
    Includes values at, just inside, and just outside boundaries.
    """
    values = []
    
    # Below valid range
    if min_val > -sys.maxsize:
        values.append(min_val - 1)
    
    # At and just inside lower boundary
    values.append(min_val)
    if min_val < max_val:
        values.append(min_val + 1)
    
    # Middle of range (if range is large enough)
    if max_val - min_val > 4:
        values.append((min_val + max_val) // 2)
    
    # At and just inside upper boundary
    if max_val - min_val > 1:
        values.append(max_val - 1)
    values.append(max_val)
    
    # Above valid range
    if max_val < sys.maxsize:
        values.append(max_val + 1)
    
    return values
 
 
def generate_array_size_tests(max_size: int) -> list[int]:
    """
    Generate array sizes for boundary testing.
    """
    sizes = [
        0,                    # Empty
        1,                    # Single element
        2,                    # Two elements (minimum for pairs)
    ]
    
    if max_size > 10:
        sizes.append(10)      # Small
    
    if max_size > 100:
        sizes.append(100)     # Medium
    
    if max_size > 2:
        sizes.append(max_size - 1)  # Just under max
    
    sizes.append(max_size)    # Maximum allowed
    
    return sizes
 
 
def generate_index_tests(array_length: int) -> list[int]:
    """
    Generate index values for boundary testing.
    Includes valid and invalid indices.
    """
    if array_length == 0:
        return [-1, 0]  # Only invalid indices
    
    indices = []
    
    # Invalid indices
    indices.append(-1)
    indices.append(-array_length - 1)  # Negative beyond valid
    
    # Valid boundary indices
    indices.append(0)                   # First
    if array_length > 1:
        indices.append(1)               # Second
        indices.append(array_length - 2)  # Second to last
    indices.append(array_length - 1)    # Last
    
    # Middle index
    if array_length > 4:
        indices.append(array_length // 2)
    
    # Invalid high indices
    indices.append(array_length)        # Just past end
    indices.append(array_length + 1)    # Further past
    
    return indices
 
 
def generate_32bit_boundary_values() -> list[int]:
    """
    Generate 32-bit signed integer boundary values.
    """
    INT32_MIN = -2**31
    INT32_MAX = 2**31 - 1
    
    return [
        INT32_MIN,           # Minimum
        INT32_MIN + 1,       # Just above minimum
        -1,                  # Negative near zero
        0,                   # Zero
        1,                   # Positive near zero
        INT32_MAX - 1,       # Just below maximum
        INT32_MAX,           # Maximum
    ]
 
 
class BoundaryTestGenerator:
    """
    Comprehensive boundary test generator for function testing.
    """
    
    def __init__(self, func: Callable, valid_range: tuple[int, int] = None):
        self.func = func
        self.valid_range = valid_range
    
    def generate_test_suite(self) -> list[dict]:
        """
        Generate comprehensive boundary test cases.
        """
        tests = []
        
        if self.valid_range:
            min_val, max_val = self.valid_range
            
            # Valid boundary values
            for value in generate_boundary_values(min_val, max_val):
                is_valid = min_val <= value <= max_val
                tests.append({
                    'input': value,
                    'expected_valid': is_valid,
                    'category': 'boundary'
                })
        
        return tests
    
    def run_tests(self, tests: list[dict]) -> list[dict]:
        """
        Execute test cases and report results.
        """
        results = []
        
        for test in tests:
            try:
                output = self.func(test['input'])
                results.append({
                    **test,
                    'output': output,
                    'error': None,
                    'passed': True  # No exception
                })
            except Exception as e:
                results.append({
                    **test,
                    'output': None,
                    'error': str(e),
                    'passed': not test.get('expected_valid', True)
                })
        
        return results

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from typing import Callable, TypeVar, Any
from dataclasses import dataclass
from enum import Enum, auto
import random
 
T = TypeVar('T')
 
 
class ArrayPartition(Enum):
    """Equivalence partitions for array inputs."""
    EMPTY = auto()
    SINGLE = auto()
    TWO = auto()
    SMALL = auto()
    MEDIUM = auto()
    LARGE = auto()
 
 
class ValuePartition(Enum):
    """Equivalence partitions for numeric values."""
    NEGATIVE_LARGE = auto()
    NEGATIVE_SMALL = auto()
    ZERO = auto()
    POSITIVE_SMALL = auto()
    POSITIVE_LARGE = auto()
 
 
class OrderPartition(Enum):
    """Equivalence partitions for array ordering."""
    SORTED_ASC = auto()
    SORTED_DESC = auto()
    RANDOM = auto()
    ALL_SAME = auto()
 
 
@dataclass
class TestCase:
    """Represents a single test case with metadata."""
    input: Any
    partitions: list[Enum]
    description: str
 
 
def generate_array_partition_tests(
    value_range: tuple[int, int] = (1, 100)
) -> list[TestCase]:
    """
    Generate test arrays for each equivalence partition.
    """
    min_val, max_val = value_range
    tests = []
    
    # Size partitions
    tests.append(TestCase(
        input=[],
        partitions=[ArrayPartition.EMPTY],
        description="Empty array"
    ))
    
    tests.append(TestCase(
        input=[random.randint(min_val, max_val)],
        partitions=[ArrayPartition.SINGLE],
        description="Single element"
    ))
    
    tests.append(TestCase(
        input=sorted(random.sample(range(min_val, max_val), 2)),
        partitions=[ArrayPartition.TWO],
        description="Two elements"
    ))
    
    # Order partitions
    small_arr = sorted(random.sample(range(min_val, max_val), 10))
    tests.append(TestCase(
        input=small_arr,
        partitions=[ArrayPartition.SMALL, OrderPartition.SORTED_ASC],
        description="Small sorted ascending"
    ))
    
    tests.append(TestCase(
        input=small_arr[::-1],
        partitions=[ArrayPartition.SMALL, OrderPartition.SORTED_DESC],
        description="Small sorted descending"
    ))
    
    random_arr = random.sample(range(min_val, max_val), 10)
    tests.append(TestCase(
        input=random_arr,
        partitions=[ArrayPartition.SMALL, OrderPartition.RANDOM],
        description="Small random order"
    ))
    
    same_val = random.randint(min_val, max_val)
    tests.append(TestCase(
        input=[same_val] * 10,
        partitions=[ArrayPartition.SMALL, OrderPartition.ALL_SAME],
        description="All same values"
    ))
    
    return tests
 
 
def generate_numeric_partition_tests() -> list[TestCase]:
    """
    Generate test values for each numeric equivalence partition.
    """
    INT32_MIN = -2**31
    INT32_MAX = 2**31 - 1
    
    tests = [
        TestCase(
            input=INT32_MIN,
            partitions=[ValuePartition.NEGATIVE_LARGE],
            description="Minimum 32-bit integer"
        ),
        TestCase(
            input=-10,
            partitions=[ValuePartition.NEGATIVE_SMALL],
            description="Small negative"
        ),
        TestCase(
            input=0,
            partitions=[ValuePartition.ZERO],
            description="Zero"
        ),
        TestCase(
            input=10,
            partitions=[ValuePartition.POSITIVE_SMALL],
            description="Small positive"
        ),
        TestCase(
            input=INT32_MAX,
            partitions=[ValuePartition.POSITIVE_LARGE],
            description="Maximum 32-bit integer"
        ),
    ]
    
    return tests
 
 
def partition_based_test_selector(
    all_tests: list[TestCase],
    covered: set = None
) -> list[TestCase]:
    """
    Select minimum tests to cover all partitions.
    Greedy set cover approximation.
    """
    if covered is None:
        covered = set()
    
    selected = []
    remaining = list(all_tests)
    
    while remaining:
        # Find test that covers most new partitions
        best_test = None
        best_new_coverage = 0
        
        for test in remaining:
            test_partitions = set(test.partitions)
            new_coverage = len(test_partitions - covered)
            
            if new_coverage > best_new_coverage:
                best_new_coverage = new_coverage
                best_test = test
        
        if best_test is None or best_new_coverage == 0:
            break
        
        selected.append(best_test)
        covered.update(best_test.partitions)
        remaining.remove(best_test)
    
    return selected

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import random
import time
from typing import Callable, TypeVar, Any
 
T = TypeVar('T')
 
 
def stress_test(
    func_to_test: Callable,
    func_reference: Callable,
    input_generator: Callable[[], Any],
    num_tests: int = 1000,
    verbose: bool = False
) -> dict:
    """
    Stress test by comparing function output to reference implementation.
    
    Args:
        func_to_test: Function being tested
        func_reference: Known-correct reference implementation
        input_generator: Function that generates random test inputs
        num_tests: Number of random tests to run
        verbose: Print each test case
    
    Returns:
        Dictionary with test results and any failing cases
    """
    passed = 0
    failed = 0
    failing_cases = []
    
    for i in range(num_tests):
        test_input = input_generator()
        
        try:
            result = func_to_test(test_input)
            expected = func_reference(test_input)
            
            if result == expected:
                passed += 1
            else:
                failed += 1
                failing_cases.append({
                    'input': test_input,
                    'expected': expected,
                    'actual': result
                })
                if verbose:
                    print(f"FAIL #{i}: input={test_input}")
                    print(f"  Expected: {expected}")
                    print(f"  Actual: {result}")
        except Exception as e:
            failed += 1
            failing_cases.append({
                'input': test_input,
                'error': str(e)
            })
            if verbose:
                print(f"ERROR #{i}: input={test_input}, error={e}")
    
    return {
        'passed': passed,
        'failed': failed,
        'total': num_tests,
        'failing_cases': failing_cases[:10]  # Limit stored cases
    }
 
 
def performance_test(
    func: Callable,
    input_generator: Callable[[int], Any],
    sizes: list[int],
    time_limit: float = 1.0
) -> list[dict]:
    """
    Measure function performance at different input sizes.
    Verifies O(n), O(n log n), O(n²), etc. behavior.
    """
    results = []
    
    for size in sizes:
        test_input = input_generator(size)
        
        start_time = time.perf_counter()
        try:
            func(test_input)
            elapsed = time.perf_counter() - start_time
            
            results.append({
                'size': size,
                'time': elapsed,
                'passed': elapsed <= time_limit,
                'error': None
            })
        except Exception as e:
            results.append({
                'size': size,
                'time': None,
                'passed': False,
                'error': str(e)
            })
    
    return results
 
 
def estimate_complexity(results: list[dict]) -> str:
    """
    Estimate time complexity from performance measurements.
    Compares growth rates to classify complexity.
    """
    valid_results = [r for r in results if r['time'] is not None]
    
    if len(valid_results) < 3:
        return "Insufficient data"
    
    sizes = [r['size'] for r in valid_results]
    times = [r['time'] for r in valid_results]
    
    # Calculate ratios for complexity estimation
    ratios = []
    for i in range(1, len(sizes)):
        size_ratio = sizes[i] / sizes[i-1]
        time_ratio = times[i] / times[i-1] if times[i-1] > 0 else float('inf')
        ratios.append((size_ratio, time_ratio))
    
    # Classify based on average ratio behavior
    avg_size_ratio = sum(r[0] for r in ratios) / len(ratios)
    avg_time_ratio = sum(r[1] for r in ratios) / len(ratios)
    
    if avg_time_ratio < 1.2:
        return "O(1) - Constant"
    elif avg_time_ratio < avg_size_ratio * 0.6:
        return "O(log n) - Logarithmic"
    elif avg_time_ratio < avg_size_ratio * 1.5:
        return "O(n) - Linear"
    elif avg_time_ratio < avg_size_ratio * 2:
        return "O(n log n) - Linearithmic"
    elif avg_time_ratio < avg_size_ratio ** 2 * 1.5:
        return "O(n²) - Quadratic"
    else:
        return "O(n²+) - Possibly worse than quadratic"
 
 
# ============================================
# RANDOM INPUT GENERATORS
# ============================================
 
def random_array_generator(
    size: int,
    min_val: int = -10**9,
    max_val: int = 10**9
) -> list[int]:
    """Generate random integer array of given size."""
    return [random.randint(min_val, max_val) for _ in range(size)]
 
 
def random_sorted_array_generator(
    size: int,
    min_val: int = -10**6,
    max_val: int = 10**6
) -> list[int]:
    """Generate sorted random array."""
    arr = random_array_generator(size, min_val, max_val)
    return sorted(arr)
 
 
def random_string_generator(
    length: int,
    alphabet: str = 'abcdefghijklmnopqrstuvwxyz'
) -> str:
    """Generate random string of given length."""
    return ''.join(random.choice(alphabet) for _ in range(length))
 
 
def random_tree_generator(n: int) -> list[tuple[int, int]]:
    """
    Generate random tree edges for n nodes.
    Returns list of (parent, child) edges.
    """
    if n <= 1:
        return []
    
    edges = []
    for i in range(1, n):
        parent = random.randint(0, i - 1)
        edges.append((parent, i))
    
    return edges
 
 
def random_graph_generator(
    n: int,
    edge_probability: float = 0.3
) -> list[tuple[int, int]]:
    """
    Generate random undirected graph.
    """
    edges = []
    for i in range(n):
        for j in range(i + 1, n):
            if random.random() < edge_probability:
                edges.append((i, j))
    return edges

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import random
from typing import Callable, TypeVar, Any
 
T = TypeVar('T')
 
 
def property_test(
    property_fn: Callable[..., bool],
    input_generators: list[Callable[[], Any]],
    num_tests: int = 100
) -> dict:
    """
    Run property-based tests.
    
    Args:
        property_fn: Function that returns True if property holds
        input_generators: List of functions that generate random inputs
        num_tests: Number of random tests
    
    Returns:
        Test results with any counterexamples
    """
    passed = 0
    failed = 0
    counterexamples = []
    
    for _ in range(num_tests):
        # Generate random inputs
        inputs = [gen() for gen in input_generators]
        
        try:
            if property_fn(*inputs):
                passed += 1
            else:
                failed += 1
                counterexamples.append(inputs)
        except Exception as e:
            failed += 1
            counterexamples.append({'inputs': inputs, 'error': str(e)})
    
    return {
        'passed': passed,
        'failed': failed,
        'counterexamples': counterexamples[:5]
    }
 
 
# ============================================
# SORTING PROPERTIES
# ============================================
 
def sort_function(arr: list[int]) -> list[int]:
    """The function being tested (your implementation)."""
    return sorted(arr)  # Replace with your implementation
 
 
def prop_sort_preserves_length(arr: list[int]) -> bool:
    """Sorting preserves array length."""
    return len(sort_function(arr)) == len(arr)
 
 
def prop_sort_preserves_elements(arr: list[int]) -> bool:
    """Sorting preserves all elements (multiset equality)."""
    from collections import Counter
    return Counter(sort_function(arr)) == Counter(arr)
 
 
def prop_sort_is_ordered(arr: list[int]) -> bool:
    """Sorted array is in non-decreasing order."""
    result = sort_function(arr)
    return all(result[i] <= result[i+1] for i in range(len(result)-1))
 
 
def prop_sort_is_idempotent(arr: list[int]) -> bool:
    """Sorting twice equals sorting once."""
    once = sort_function(arr)
    twice = sort_function(once)
    return once == twice
 
 
# ============================================
# REVERSE PROPERTIES
# ============================================
 
def reverse_function(arr: list[int]) -> list[int]:
    """The reverse function being tested."""
    return arr[::-1]
 
 
def prop_reverse_is_involution(arr: list[int]) -> bool:
    """Reversing twice returns original."""
    return reverse_function(reverse_function(arr)) == arr
 
 
def prop_reverse_preserves_length(arr: list[int]) -> bool:
    """Reversing preserves length."""
    return len(reverse_function(arr)) == len(arr)
 
 
def prop_reverse_first_last_swap(arr: list[int]) -> bool:
    """First element becomes last after reverse."""
    if not arr:
        return True
    result = reverse_function(arr)
    return arr[0] == result[-1] and arr[-1] == result[0]
 
 
# ============================================
# BINARY SEARCH PROPERTIES
# ============================================
 
def binary_search(arr: list[int], target: int) -> int:
    """Binary search returning index or -1."""
    left, right = 0, len(arr) - 1
    while left <= right:
        mid = left + (right - left) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            left = mid + 1
        else:
            right = mid - 1
    return -1
 
 
def prop_search_correct_index(arr: list[int], target: int) -> bool:
    """If found, index contains the target value."""
    arr = sorted(arr)  # Binary search needs sorted array
    idx = binary_search(arr, target)
    if idx == -1:
        return target not in arr
    return arr[idx] == target
 
 
def prop_search_finds_existing(arr: list[int]) -> bool:
    """Search always finds an element that exists."""
    arr = sorted(arr)
    if not arr:
        return True
    target = random.choice(arr)
    return binary_search(arr, target) != -1
 
 
# ============================================
# RUN PROPERTY TESTS
# ============================================
 
def test_sort_properties():
    """Test all sorting properties."""
    gen = lambda: [random.randint(-100, 100) for _ in range(random.randint(0, 50))]
    
    properties = [
        ("preserves_length", prop_sort_preserves_length),
        ("preserves_elements", prop_sort_preserves_elements),
        ("is_ordered", prop_sort_is_ordered),
        ("is_idempotent", prop_sort_is_idempotent),
    ]
    
    results = {}
    for name, prop in properties:
        result = property_test(prop, [gen], num_tests=1000)
        results[name] = result
        status = "PASS" if result['failed'] == 0 else "FAIL"
        print(f"{name}: {status} ({result['passed']}/{result['passed']+result['failed']})")
    
    return results

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import random
from typing import Generator
 
 
# ============================================
# BINARY SEARCH TEST GENERATOR
# ============================================
 
def generate_binary_search_tests(max_size: int = 1000) -> list[dict]:
    """Generate comprehensive binary search test cases."""
    tests = []
    
    # Empty array
    tests.append({
        'arr': [],
        'target': 5,
        'expected': -1,
        'description': 'Empty array'
    })
    
    # Single element - found
    tests.append({
        'arr': [5],
        'target': 5,
        'expected': 0,
        'description': 'Single element, found'
    })
    
    # Single element - not found
    tests.append({
        'arr': [5],
        'target': 3,
        'expected': -1,
        'description': 'Single element, not found'
    })
    
    # Two elements
    tests.append({
        'arr': [2, 5],
        'target': 2,
        'expected': 0,
        'description': 'Two elements, find first'
    })
    tests.append({
        'arr': [2, 5],
        'target': 5,
        'expected': 1,
        'description': 'Two elements, find second'
    })
    
    # Target at boundaries
    arr = list(range(1, 11))  # [1, 2, ..., 10]
    tests.append({
        'arr': arr,
        'target': 1,
        'expected': 0,
        'description': 'Target at first position'
    })
    tests.append({
        'arr': arr,
        'target': 10,
        'expected': 9,
        'description': 'Target at last position'
    })
    tests.append({
        'arr': arr,
        'target': 5,
        'expected': 4,
        'description': 'Target in middle'
    })
    
    # Target not in array
    tests.append({
        'arr': arr,
        'target': 0,
        'expected': -1,
        'description': 'Target less than all'
    })
    tests.append({
        'arr': arr,
        'target': 11,
        'expected': -1,
        'description': 'Target greater than all'
    })
    
    # Large array
    large_arr = list(range(max_size))
    tests.append({
        'arr': large_arr,
        'target': max_size // 2,
        'expected': max_size // 2,
        'description': f'Large array ({max_size} elements)'
    })
    
    return tests
 
 
# ============================================
# GRAPH TEST GENERATOR
# ============================================
 
def generate_graph_tests() -> list[dict]:
    """Generate comprehensive graph algorithm test cases."""
    tests = []
    
    # Empty graph
    tests.append({
        'graph': {},
        'description': 'Empty graph'
    })
    
    # Single node
    tests.append({
        'graph': {0: []},
        'description': 'Single isolated node'
    })
    
    # Single node with self-loop
    tests.append({
        'graph': {0: [0]},
        'description': 'Single node with self-loop'
    })
    
    # Two nodes, connected
    tests.append({
        'graph': {0: [1], 1: [0]},
        'description': 'Two connected nodes'
    })
    
    # Two nodes, disconnected
    tests.append({
        'graph': {0: [], 1: []},
        'description': 'Two disconnected nodes'
    })
    
    # Linear chain (n = 5)
    tests.append({
        'graph': {
            0: [1], 1: [0, 2], 2: [1, 3], 3: [2, 4], 4: [3]
        },
        'description': 'Linear chain of 5 nodes'
    })
    
    # Complete graph (n = 4)
    tests.append({
        'graph': {
            0: [1, 2, 3],
            1: [0, 2, 3],
            2: [0, 1, 3],
            3: [0, 1, 2]
        },
        'description': 'Complete graph K4'
    })
    
    # Tree
    tests.append({
        'graph': {
            0: [1, 2],
            1: [0, 3, 4],
            2: [0],
            3: [1],
            4: [1]
        },
        'description': 'Binary tree'
    })
    
    # Graph with cycle
    tests.append({
        'graph': {
            0: [1],
            1: [2],
            2: [0]  # Creates cycle
        },
        'description': 'Simple cycle'
    })
    
    # Disconnected components
    tests.append({
        'graph': {
            0: [1], 1: [0],           # Component 1
            2: [3], 3: [2],           # Component 2
            4: []                      # Isolated node
        },
        'description': 'Three disconnected components'
    })
    
    return tests
 
 
# ============================================
# DP TEST GENERATOR
# ============================================
 
def generate_fibonacci_tests() -> list[dict]:
    """Generate test cases for Fibonacci (classic DP problem)."""
    return [
        {'n': 0, 'expected': 0, 'description': 'Base case n=0'},
        {'n': 1, 'expected': 1, 'description': 'Base case n=1'},
        {'n': 2, 'expected': 1, 'description': 'First addition n=2'},
        {'n': 10, 'expected': 55, 'description': 'Medium n=10'},
        {'n': 20, 'expected': 6765, 'description': 'Larger n=20'},
        {'n': 45, 'expected': 1134903170, 'description': 'Stress test n=45'},
    ]
 
 
def generate_coin_change_tests() -> list[dict]:
    """Generate test cases for coin change problem."""
    return [
        {
            'coins': [1], 'amount': 0,
            'expected': 0,
            'description': 'Zero amount'
        },
        {
            'coins': [1], 'amount': 5,
            'expected': 5,
            'description': 'Only 1-cent coins'
        },
        {
            'coins': [2], 'amount': 3,
            'expected': -1,
            'description': 'Impossible with even coins'
        },
        {
            'coins': [1, 2, 5], 'amount': 11,
            'expected': 3,
            'description': 'Classic example: 5+5+1'
        },
        {
            'coins': [1, 5, 10, 25], 'amount': 100,
            'expected': 4,
            'description': 'US coins making $1'
        },
        {
            'coins': [186, 419, 83, 408], 'amount': 6249,
            'expected': 20,
            'description': 'Complex case'
        },
    ]