Generating All Possible Unique Combinations of Two-Digit Numbers Using JSP Programming

Have you ever faced the challenge of generating all possible unique combinations of two-digit numbers without repetition? This article provides a comprehensive guide, detailing the methodologies and approaches using JSP (Jackson Structured Programming). We will start by exploring a solution implemented in MATLAB and then delve into our proposed solution using JSP. The content aims to provide insights into the structured programming approach to creating a stable and efficient architecture for handling such tasks.

What is JSP?

JSP (Jackson Structured Programming) is a methodology that promotes the design of data-driven programs by focusing on the structure of data. The idea is to decompose the program into small, manageable components that reflect the structure of the data that the program handles. By doing so, it facilitates a clear understanding of the program's function and simplifies the maintenance and evolution of the program over time.

Understanding the Problem

The task at hand is to generate all possible unique combinations of two-digit numbers (from 00 to 99) without repetition. This means that a number like 12 should only appear once in the sequence, and if 12 is used, then 21 should not be included in the sequence.

Comparing Solutions: MATLAB and JSP

MATLAB Solution

The MATLAB community has provided a solution that utilizes nested for loops to achieve the goal. The solution works by iterating through all possible pairs and checking for duplicates. Here is a simplified breakdown of the approach:

The outer loop iterates over the first digit (0-9). The inner loop iterates over the second digit (0-9). Duplicates are identified by comparing the second digit with the first.

The code essentially looks like this:

for i  0:9
    for j  0:9
        if j ! i
            % Print the combination
            disp([i, j])
        end
    end
end

JSP Solution: A Data-Driven Approach

For this solution, we will use JSP to design a program that reflects the structure of the data. One key aspect of JSP is the use of groupings in the data streams, which helps in simultaneously reflecting the functions to be performed. This approach facilitates a stable architecture that can be easily understood and maintained.

We can represent the numbers in a 110 grid, where each row represents a tens digit and each column represents a units digit. We can then iterate through this grid, printing out unique combinations.

The design diagrams for this solution can be compared to a small clockwork that ticks and goes. Everything moves, and the flow is clear. For instance, in the below diagram, we can see how the program iterates through the grid and outputs only the unique combinations.

Design Diagram

Design Diagram of Two-Digit Numbers

Implementation Details

The following code demonstrates the JSP approach:

def generate_unique_combinations(n):
    # Initialize an empty list to store unique combinations
    unique_combinations  []
    # Iterate over the tens and units digits
    for i in range(0, 10):
        for j in range(0, 10):
            # Check if the combination is already in the list
            if (i, j) not in unique_combinations:
                # Add the combination to the list
                unique_((i, j))
                # Print the combination
                print(f"{i}{j}")

This code uses nested loops to generate all combinations and a simple check to ensure that duplicates are not included in the final output. This way, we ensure that each combination is unique and properly reflected in the output.

Conclusion

When tackling the task of generating all possible unique combinations of two-digit numbers, structured programming approaches like JSP provide a clear and maintainable solution. By decomposing the problem into manageable components that reflect the structure of the data, we can ensure that the program is both efficient and easy to understand.