Question

Write a program that reads four integers and prints "two pairs" if the input consists of two matching pairs (in some order) and "not two pairs" otherwise. For example, \(\begin{array}{lllll}1 & 2 & 2 & 1 & \text { two pairs } \\ 1 & 2 & 2 & 3 & \text { not two pairs } \\ 2 & 2 & 2 & 2 & \text { tuo pairs }\end{array}\)

Short answer

Check for exactly two unique numbers, each appearing twice, to confirm 'two pairs'.

Step-by-step solution

Understanding the Problem

We need to check if four given numbers can be grouped into two pairs. This means that if arranged in some order, two of the numbers should be the same, and the remaining two numbers should also be the same.

Identify Inputs and Outputs

The inputs are four integers, and the output should be a string stating either 'two pairs' if the input numbers can be grouped into two pairs, or 'not two pairs' if they cannot.

Check for Two Pairs Logic

To determine if there are two pairs, we can use a counting method to see how many times each number appears in the inputs. If we find exactly two unique numbers, each appearing twice, we have two pairs.

Step-by-Step Algorithm

1. Read four integers. 2. Count the occurrences of each integer. 3. If there are two unique numbers and each occurs twice, print 'two pairs'. 4. Otherwise, print 'not two pairs'.

Program Implementation

Here's a simple Python implementation: ```python from collections import Counter def check_two_pairs(a, b, c, d): numbers = [a, b, c, d] count = Counter(numbers) if len(count) == 2 and all(value == 2 for value in count.values()): return 'two pairs' else: return 'not two pairs' # Example usage: print(check_two_pairs(1, 2, 2, 1)) # Output: 'two pairs' print(check_two_pairs(1, 2, 2, 3)) # Output: 'not two pairs' print(check_two_pairs(2, 2, 2, 2)) # Output: 'two pairs' ```

Key concepts

Conditional Logic

Conditional logic is fundamental when writing programs in Python and other programming languages. In this problem, we use conditions to decide if the input numbers form two pairs. The condition relies on counting how many times each number appears.

• If there are exactly two different numbers in the list and each appears twice, it means we have two pairs.
• If this condition is not met, the numbers do not form two pairs.

In the provided solution, this logic is applied using an `if` statement: ```python if len(count) == 2 and all(value == 2 for value in count.values()): return 'two pairs' else: return 'not two pairs' ```
The `if` statement checks if the count of unique numbers is 2. The `all` function is used to verify that both unique numbers appear twice. Conditional logic, therefore, helps in making decisions based on data characteristics, which is crucial in problem-solving.

Data Structures

Data structures are a way to organize and manage data for efficient access and modification. In this exercise, we use a list and a counter (a type of dictionary) to handle the input numbers.

• The list `numbers` holds the four integers provided by the user. It allows us to group data together and perform operations on the entire collection.
• The `Counter` from the `collections` module is a specialized dictionary. It counts the occurrence of each integer in the list. This is particularly useful when checking how often each number appears, helping us determine if there are two pairs.

The choice of using a `Counter` is important as it simplifies the problem of counting occurrences, making the logic easier to implement. Understanding and utilizing the right data structures can greatly simplify coding tasks and enhance efficiency.

Problem Solving

Problem solving in programming often involves breaking down a task into manageable steps, just like in any analytical process. Here's how we approach the given exercise:

• Understand the Problem: First, comprehend what the problem is asking. Here, we need to check if four integers can be grouped into two identical pairs.
• Design the Solution: Identify what information we need (inputs) and what results we aim for (outputs). For this problem, we need to know the frequency of each number.
• Implement the Solution: Write code that performs the necessary checks. Using Python's `Counter`, we efficiently count the numbers and apply conditional logic to determine the output.

Problem solving in programming is about analyzing tasks and using logical thinking to devise solutions. By leveraging tools like data structures and control statements, we can solve complex problems systematically and effectively.