The First Step to Effective Problem-Solving

Read the problem statement carefully. Understand the basic terms and expressions used to define the problem. Spend as much time as possible understanding all aspects of the problem. The more time we spend on analyzing the problem, the less time it takes to come up with the solution.

Formulation of the Problem

• Which words are ambiguous?
• What are the assumptions?
• What significant information is omitted?

Pay attention to details such as constraints, assumptions etc. Start simple, add complexity gradually as needed to fit the requirements and constraints. Begin to classify.

• Is it an optimization problem?
• Is the problem similar to others you have seen?

It pays to reread a problem several times.

Understanding the Problem

In any domain, be it mathematics, physics, software development, or even day-to-day decision-making, the first step towards finding a solution is to understand the problem thoroughly. Understanding the problem entails familiarizing oneself with all the basic terms, expressions, and constraints involved. Investing time in understanding the problem can save a lot of time in finding the solution because it reduces the risk of barking up the wrong tree.

For example, if you’re given a programming task to create a software system for managing a hotel’s bookings, understanding the problem would involve learning about all the aspects of hotel bookings – such as reservations, check-ins, check-outs, cancellations, and so forth.

2. Problem Formulation: Identifying Ambiguities and Assumptions

Once the problem is understood, the next step is to formulate it clearly and precisely. This includes identifying ambiguous words or phrases, noting down assumptions, and finding out if there’s any critical information missing.

Continuing the hotel bookings example, an ambiguous term could be “reservation.” Does it refer only to booking a room, or does it also include requests for specific services or amenities? An assumption might be that the hotel operates 24/7. Significant omitted information could be whether the system should support online bookings or only in-person bookings.

3. Paying Attention to Details

It’s essential to pay close attention to details such as constraints and assumptions. It’s advisable to start simple and gradually add complexity as needed to fit the requirements and constraints.

In the hotel example, constraints might include things like the maximum number of rooms available, the fact that a room can’t be booked by two different guests at the same time, or specific check-in and check-out times.

4. Classifying the Problem

Classifying the problem can give valuable insight into how to approach it. Questions that might help with classification include:

• Is it an optimization problem? In the hotel booking system case, an optimization problem might be to maximize room occupancy or revenue.
• Is the problem similar to others you have seen? For example, the hotel booking system might be similar to other resource management problems you’ve tackled before, like scheduling conference room use in an office.

Lastly, never underestimate the value of rereading the problem. Sometimes, the devil is in the details, and understanding those details might take a couple of readings. This not only ensures you haven’t missed anything, but also allows you to view the problem from different angles, which can prove to be helpful in the solution design stage.

Richard Feynman Explanation

Let’s say you’re a detective. You walk into a room and there’s been a mystery — someone has stolen the cookies from the cookie jar! Now, before you start looking for clues, you’ve got to figure out what your problem is, right?

You’ve got to say to yourself, “Alright, the problem here is that the cookies are missing. My job is to find out who took them.” That’s your problem. You’ve defined it. This might seem obvious, but it’s a crucial step. If you don’t know exactly what your problem is, how are you going to solve it? You could end up looking for a missing cat instead of the cookies!

In computer science, we do the same thing. Before we can start coding or designing algorithms, we’ve got to figure out exactly what our problem is. We need to know what our inputs are, what our desired output is, and what rules or restrictions we have to follow.

It’s like being a detective: you can’t solve the mystery unless you know what the mystery is. That’s what the formulation of the problem is all about: it’s about defining your mystery so you can start looking for your solution. So, just like a good detective, a good computer scientist always starts by clearly defining the problem. Once you’ve got that, you’re ready to start finding your solution!

Designing a City

The formulation of a problem in computer science is similar to laying out a blueprint before constructing a city. You can’t start putting up buildings and roads willy-nilly. You need to understand the purpose of each part of the city, who will be using it, what needs they have, and how different parts of the city will interact with one another.

In a city, we might ask: Are we designing a residential district or a business area? How many people do we expect to live or work here? Will there be schools, hospitals, and parks? What kind of transportation system do we need? How will this area interact with other areas of the city?

Similarly, when formulating a problem in computer science, we must understand the domain of the problem. What is the purpose of the software application we’re designing? Who will use it, and what needs will it satisfy? How will different parts of the application interact with each other?

We map out these requirements and interactions, laying out a clear plan for what we need to build. Just as city planners would create a detailed blueprint before breaking ground on a new city district, computer scientists formulate a detailed understanding of the problem at hand before they write a single line of code.

By clearly formulating the problem upfront, we ensure that we’re building a solution that effectively meets the needs of its users and can evolve over time as those needs change. Just as a well-planned city can grow and adapt over time, a well-formulated software application can evolve to meet the changing needs of its users.