Problem decomposition (LtM, PaS, PoTh) with Java

Problem decomposition is a technique in prompt engineering that helps break down complex tasks into simpler, manageable parts. In large language models, breaking down complex prompts is essential, as it helps the model interpret the problem more effectively and produce accurate results.

In this topic, you'll learn about three key problem decomposition methods: Least-to-Most prompting (LtM), Plan-and-Solve prompting (PaS), and Program-of-Thought prompting (PoTh). These techniques will help you improve your prompting skills and deal with complex problems more efficiently.

Least-to-Most prompting

LtM prompting is a technique that involves breaking down a complex task into subtasks of increasing complexity. This method helps you approach problems step by step, starting with the simplest elements and gradually working your way up to more challenging aspects. It is particularly useful when dealing with large, intimidating tasks that might otherwise seem overwhelming.

To apply the LtM technique, follow these steps:

1. Identify the main task or problem.

2. Break it down into subtasks of varying complexity.

3. Arrange the subtasks from least to most complex.

4. Solve each subtask in order, building upon previous solutions.

Let's look at a practical example using Java to illustrate the LtM technique. Imagine we need to create a program building a weather forecasting application. We'll break it down into subtasks of increasing complexity:

Least Complex Task:

Fetch current weather data for a specific location using an API and Java.

- Sub-task 1: Research available weather APIs.

- Sub-task 2: Write a method to send a request to the API.

- Sub-task 3: Parse the returned JSON data to extract relevant 
weather information.

Go ahead and try sending a question. You can try different models.

Click the arrow to generate the AI response

gpt-4o

• gpt-4o

Moderately Complex Task:

Implement caching to store weather data, minimizing the number 
of API calls.

- Sub-task 1: Design a caching system to store the most recent
 weather data.
- Sub-task 2: Implement a time-based strategy to invalidate 
outdated cache entries.
- Sub-task 3: Modify the weather retrieval function to consult 
the cache before making an API call.

Go ahead and try sending a question. You can try different models.

Click the arrow to generate the AI response

gpt-4o

• gpt-4o

Most Complex Task:

Develop a user interface that enables users to view weekly weather 
forecasts and analyze data trends through visualizations.

- Sub-task 1: Design a user interface layout to display the weekly
weather forecast.
- Sub-task 2: Create UI components to present daily weather summaries.
- Sub-task 3: Build interactive charts to visualize temperature trends 
over the week.

Go ahead and try sending a question. You can try different models.

Click the arrow to generate the AI response

gpt-4o

• gpt-4o

The disadvantage of this approach is that it may limit the LLM's creativity and critical thinking, as the model might rely heavily on the predefined sub-tasks rather than exploring potential solutions independently.

Plan-and-Solve prompting

PaS prompting is a method that involves creating a structured approach to problem-solving. This technique highlights the importance of planning before starting the implementation. By outlining the steps needed to solve a problem, you can create a clear roadmap for your solution.

The PaS method is valuable because it helps you organize your thoughts and approach problems systematically. This structured approach helps avoid missing important details and ensures that you consider all aspects of the problem before starting to code.

To use the PaS method effectively, follow these steps:

1. Clearly define the problem or task.

2. Break down the problem into smaller, manageable steps.

3. Outline the solution for each step.

4. Implement the solution following your plan along with questions to execute it.

5. Review and refine your solution as needed.

Imagine you are assigned to develop a shopping cart for an E-commerce platform. Here’s a structured plan to guide the process:

How to develop a shopping cart for E-commerce using Java?

Here is the plan to solve the above problem:

1. Identify the requirements for the shopping cart, such as adding items, 
removing items, updating quantities, and calculating totals.
2. Design the data structures required to store items and their quantities.
3. Establish the user workflows for interacting with the shopping cart, 
such as adding items to the cart and proceeding to checkout.
 
Let's execute the plans by following the below-mentioned questions:

1. How can I implement the data model for the shopping cart, including 
classes or structures for items and the cart itself?
2. Can you create functions/methods for adding, removing, and updating 
items in the cart.
3. What is the logic to calculate the cart's total price, including 
discounts and taxes?
4. How can I develop the front-end components that allow users to 
interact with their shopping cart and integrate them with the back-end logic?

Go ahead and try sending a question. You can try different models.

Click the arrow to generate the AI response

gpt-4o

• gpt-4o

By following the PaS method, we created a structured solution to the shopping cart problem. This approach helped us consider all aspects of the problem, including discounts and taxes, before implementing the code.

Although this method is effective for producing accurate output, its success heavily relies on the quality of the initial planning stage. Poor problem decomposition can result in incorrect outcomes. It’s worth noting that breaking down a problem is often challenging, which can make this method difficult to implement effectively.

Program-of-Thought prompting

The idea behind this approach is to provide a neural network with a text prompt describing a problem, along with an outline of your code that includes methods, variables, and other relevant details. Then you ask the LLM to solve the task based on the information you’ve provided. Once the AI generates the resulting code, you execute it and obtain the solution.

The purpose of this separation is to make it easier for the language model to focus on generating code that accurately solves the problem following a defined structure, rather than expecting it to derive and compute the solution entirely on its own. It uses language models to generate text describing the reasoning process and the code solution based on the provided code outline.

Let's apply this technique! Consider a task of calculating the nth Fibonacci number. The steps for decomposing the problem using this approach are outlined below:

Write a Java program to calculate the n-th Fibonacci number using the
Program of Thought (PoT) approach. The Fibonacci sequence starts with 
0 and 1, and each subsequent number is the sum of the two preceding 
ones (e.g., 0, 1, 1, 2, 3, 5, ...).

Sub-task 1: Define the problem clearly.
Write a brief explanation of the Fibonacci sequence and the input/output
requirements for the program.

Sub-task 2: Choose a method to solve the problem.
Decide whether the Fibonacci sequence will be calculated using recursion, 
iteration, or dynamic programming, based on efficiency requirements.

Sub-task 3: Implement the Fibonacci logic.
Break down the implementation into smaller steps:

Sub-task 4: Validate the input.
Ensure the input (n) is a non-negative integer, as Fibonacci numbers are 
defined only for non-negative indices.

import java.util.Scanner;

public class FibonacciCalculator {

    // Implement Fibonacci logic here
    public static int fibonacci(int n) {
        // Call validateInput() here 
    }

    //  throw IllegalArgumentException indicating "Input must be a 
    //  non-negative integer"
    public static void validateInput(int n) {
    
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        System.out.print("Enter a non-negative integer to calculate its Fibonacci number:");
        int n = scanner.nextInt();

        // Catch the exception and print the nth number using 
        // the "The Fibonacci number at index n is ..." script
    }
}

By applying the PoTh technique, we have methodically approached the problem of calculating the nth Fibonacci number. Through the structured process of clearly defining the problem, selecting an efficient solution (iteration), implementing the Fibonacci logic step-by-step, and validating the input, the program ensures both correctness and efficiency.

Chain-of-Thought vs Program-of-Thought

Chain-of-Thought and Program-of-Thought are two advanced AI prompting techniques that enhance problem-solving capabilities. Both methods share a common goal of enhancing the reasoning capabilities of large language models but approach it in different ways.

The main difference is that with PoTh, you receive a solution but need to execute it yourself, which helps reduce the AI's computational load and improves performance. In contrast, with CoT, the AI executes the code and directly provides the output.

These techniques emphasize breaking down complex problems into smaller, manageable components to facilitate clearer reasoning and more accurate outputs.

Conclusion

In this topic, we explored three powerful problem decomposition techniques for AI prompting:

• Least-to-Most prompting, which focuses on solving simpler sub-problems first to build up solutions for more complex tasks.

• Plan-And-Solve prompting, which focuses on creating a clear plan before executing the solution to ensure a more organized approach.

• Program-of-Thought prompting, which generates executable steps for a solution with reasoning.

These methods provide structured approaches to breaking down complex problems, planning solutions, and refining AI-generated ideas.

Ready to put your new knowledge to the test? Let's dive into some hands-on exercises to reinforce what you've learned and apply these techniques to real-world scenarios!