Python - Interlist Perfect Square Pairs

Python - Interlist Perfect Square Pairs

This tutorial shows how to find all pairs from two lists where the sum of their elements forms a perfect square. Let's dive into it.

Objective:

Given two lists, list1 and list2, find all pairs (a, b) such that a is from list1, b is from list2, and the sum a + b is a perfect square.

Steps:

  1. Understand the Problem: It's essential to first understand what a perfect square is. A number is a perfect square if it can be expressed as the product of an integer with itself. For instance, 1, 4, 9, 16, and so on, are perfect squares.

  2. Determine if a Number is a Perfect Square: Before proceeding with pairing elements, you should have a utility function that checks if a number is a perfect square.

  3. Iterate and Check: Iterate over the cartesian product of the two lists, check if the sum of each pair is a perfect square, and if so, store or print the pair.

Implementation:

Let's put the above steps into code:

import math def is_perfect_square(n): """Check if a number is a perfect square.""" sqrt_n = int(math.sqrt(n)) return n == sqrt_n * sqrt_n def find_square_pairs(list1, list2): """Find pairs whose sum is a perfect square.""" result = [] for a in list1: for b in list2: if is_perfect_square(a + b): result.append((a, b)) return result # Example: list1 = [1, 2, 3, 4, 5] list2 = [2, 4, 6, 8, 10] print(find_square_pairs(list1, list2))

In the above example, for lists [1, 2, 3, 4, 5] and [2, 4, 6, 8, 10], the pairs that sum up to a perfect square are:

[(1, 2), (2, 2), (1, 6), (3, 6), (2, 8), (3, 8), (4, 8)]

The tutorial shows a straightforward way of determining pairs from two lists whose sum is a perfect square. You can explore optimization techniques if needed based on the size of the lists and the specific requirements.

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