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‎02-array-seq/cartesian_product.py‎

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"""
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cartesian_product.py
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Demonstrates how to use Python list comprehensions to find the cartesian product
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of two lists.
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The cartesian product of two lists A and B is the set of all ordered pairs (a, b)
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where a is from A and b is from B.
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"""
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# ============================================================================
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# BASIC CARTESIAN PRODUCT WITH LIST COMPREHENSION
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# ============================================================================
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print("=" * 60)
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print("CARTESIAN PRODUCT WITH LIST COMPREHENSION")
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print("=" * 60)
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# Example 1: Simple cartesian product
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list_a = [1, 2, 3]
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list_b = ['a', 'b']
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# Traditional way with nested for loops:
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cartesian_traditional = []
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for a in list_a:
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for b in list_b:
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cartesian_traditional.append((a, b))
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print(f"\nList A: {list_a}")
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print(f"List B: {list_b}")
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print(f"\nTraditional way (nested loops):")
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print(f" {cartesian_traditional}")
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# List comprehension way (much more concise!):
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cartesian_comprehension = [(a, b) for a in list_a for b in list_b]
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print(f"\nList comprehension:")
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print(f" {cartesian_comprehension}")
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# Syntax: [(a, b) for a in list_a for b in list_b]
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# Read as: "for each a in list_a, for each b in list_b, create tuple (a, b)"
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# ============================================================================
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# MORE EXAMPLES
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# ============================================================================
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print("\n" + "=" * 60)
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print("MORE EXAMPLES")
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print("=" * 60)
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# Example 2: Cartesian product of numbers
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numbers = [1, 2, 3]
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colors = ['red', 'blue']
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combinations = [(num, color) for num in numbers for color in colors]
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print(f"\nNumbers: {numbers}")
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print(f"Colors: {colors}")
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print(f"All combinations: {combinations}")
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# Example 3: Cartesian product with strings
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suits = ['♠', '♥', '♦', '♣']
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ranks = ['A', '2', '3', '4', '5', '6', '7', '8', '9', '10', 'J', 'Q', 'K']
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cards = [(rank, suit) for suit in suits for rank in ranks]
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print(f"\nSuits: {suits}")
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print(f"Ranks: {ranks}")
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print(f"Total cards: {len(cards)}")
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print(f"First 5 cards: {cards[:5]}")
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print(f"Last 5 cards: {cards[-5:]}")
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# Example 4: Cartesian product with filtering
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# Only include pairs where the number is greater than the index
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list_x = [1, 2, 3, 4]
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list_y = [0, 1, 2]
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filtered_pairs = [(x, y) for x in list_x for y in list_y if x > y]
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print(f"\nList X: {list_x}")
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print(f"List Y: {list_y}")
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print(f"Pairs where x > y: {filtered_pairs}")
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# Example 5: Cartesian product with transformation
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# Create pairs and calculate their product
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nums1 = [2, 3, 4]
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nums2 = [5, 6]
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products = [(a, b, a * b) for a in nums1 for b in nums2]
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print(f"\nNumbers 1: {nums1}")
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print(f"Numbers 2: {nums2}")
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print(f"Pairs with products: {products}")
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# ============================================================================
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# COMPARISON: NESTED LOOPS vs LIST COMPREHENSION
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# ============================================================================
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print("\n" + "=" * 60)
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print("COMPARISON: NESTED LOOPS vs LIST COMPREHENSION")
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print("=" * 60)
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# Task: Create all pairs from two lists
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list1 = [10, 20]
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list2 = ['x', 'y', 'z']
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# Method 1: Traditional nested for loops
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result1 = []
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for item1 in list1:
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for item2 in list2:
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result1.append((item1, item2))
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print(f"\nNested loops: {result1}")
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# Method 2: List comprehension (more Pythonic!)
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result2 = [(item1, item2) for item1 in list1 for item2 in list2]
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print(f"List comprehension: {result2}")
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# Both produce the same result, but list comprehension is:
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# - More concise (one line vs multiple lines)
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# - More readable (once you understand the syntax)
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# - More Pythonic (follows Python best practices)
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# ============================================================================
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# CARTESIAN PRODUCT OF MORE THAN TWO LISTS
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# ============================================================================
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print("\n" + "=" * 60)
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print("CARTESIAN PRODUCT OF MORE THAN TWO LISTS")
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print("=" * 60)
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# You can extend this pattern to more than two lists
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list_a = [1, 2]
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list_b = ['a', 'b']
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list_c = ['x', 'y']
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# Three-way cartesian product
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triples = [(a, b, c) for a in list_a for b in list_b for c in list_c]
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print(f"\nList A: {list_a}")
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print(f"List B: {list_b}")
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print(f"List C: {list_c}")
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print(f"All triples: {triples}")
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print(f"Total combinations: {len(triples)}")
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# ============================================================================
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# SUMMARY
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# ============================================================================
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print("\n" + "=" * 60)
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print("SUMMARY")
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print("=" * 60)
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print("""
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Cartesian Product with List Comprehension:
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[(a, b) for a in list_a for b in list_b]
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Key Points:
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1. The cartesian product creates all possible pairs from two lists
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2. List comprehensions make this concise and readable
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3. Read nested comprehensions from left to right:
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- "for each a in list_a, for each b in list_b, create (a, b)"
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4. You can add conditions: [(a, b) for a in A for b in B if condition]
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5. You can extend to more lists: [(a, b, c) for a in A for b in B for c in C]
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Note: For very large lists, consider using itertools.product() which is
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more memory-efficient as it returns an iterator.
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""")

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