Python – Itertools.Product()

In the terms of Mathematics Cartesian Product of two sets is defined as the set of all ordered pairs (a, b) where a belongs to A and b belongs to B. Consider the below example for better understanding.

Examples:

Input : arr1 = [1, 2, 3]
arr2 = [5, 6, 7]
Output : [(1, 5), (1, 6), (1, 7), (2, 5), (2, 6), (2, 7), (3, 5), (3, 6), (3, 7)]

Input : arr1 = [10, 12]
arr2 = [8, 9, 10]
Output : [(10, 8), (10, 9), (10, 10), (12, 8), (12, 9), (12, 10)]

The above solution can be done by looping but we will use a special Python library itertools.product() for finding the Cartesian Product. Let’s go through the working and use cases of this Python library.



What are Itertools in Python?

Python Itertools is a library in Python which consists of multiple methods that are used in various iterators to compute a fast and code efficient solution.

itertools.product() falls under the category called Combinatoric iterators of the Python itertools library.

Note: For more information, refer to Python Itertools

What does itertools.product() do?

itertools.product() is used to find the cartesian product from the given iterator, output is lexicographic ordered. The itertools.product() can used in two different ways:

  • itertools.product(*iterables, repeat=1):
    It returns the cartesian product of the provided itrable with itself for the number of times specified by the optional keyword “repeat”. For example, product(arr, repeat=3) means the same as product(arr, arr, arr).
  • itertools.product(*iterables):
    It returns the cartesian product of all the itrable provieded as the argument. For example, product(arr1, arr2, arr3).
  • Example:

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    from itertools import product
      
    def cartesian_product(arr1, arr2):
      
        # return the list of all the computed tuple
        # using the product() method
        return list(product(arr1, arr2)) 
        
    # Driver Function 
    if __name__ == "__main__"
        arr1 = [1, 2, 3]
        arr2 = [5, 6, 7]
        print(cartesian_product(arr1, arr2))

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    Output:

    [(1, 5), (1, 6), (1, 7), (2, 5), (2, 6), (2, 7), (3, 5), (3, 6), (3, 7)]

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