Transitioning from Visual Model to Code
As you start making the transition to code and start thinking about the outline of the solutions, you can overlay implementation level details on top of the diagrams. For instance if you have a decision tree, you can depict the values of the index as you go down the tree. You can identify the range of inputs for each level of the decision tree.
Transferability to actual code becomes easier when we have the visual model of the problem. We can overlay implementation level details on top of the model. For instance, we can identify the values of the index variables for different choices in a decision tree and how the options we have at each level becomes a loop in code.
You will realize some of the elements of the diagram map to certain standard coding constructs such as loops, recursive calls etc. This also helps you to figure out if there is work to be done before the recursive call or after the recursive calls.
From Visual Models to Code: A Detailed Walkthrough
The process of converting a visual model into a program is akin to adding another layer of understanding to our initial problem. It’s like looking at our problem through a new lens - the lens of coding.
When we create a decision tree to visualize a problem, each node in the tree can represent a choice, and each level of the tree represents a stage in the decision-making process. As we traverse down the tree, we can represent this traversal in code as a loop or a recursive function.
For instance, imagine a decision tree that represents all the possible outcomes of a chess game. Each node represents a move, and each level of the tree represents a turn in the game. Now, imagine wanting to code a program that can simulate a chess game.
In transitioning to code, you would start by overlaying implementation-level details onto the diagram. This could involve annotating each node with the values of certain index variables, defining the range of inputs for each level of the decision tree, or highlighting certain paths through the tree that correspond to specific strategies or outcomes.
These implementation-level details act as a bridge between the conceptual understanding of the problem (the decision tree) and the nitty-gritty details of the code itself. For example, you might notice that the decision tree naturally lends itself to a recursive function. Each decision (node) leads to a new set of decisions (children nodes), which mirrors the structure of a recursive function where each function call leads to more function calls.
In this example, a move in the game (i.e., a decision) could be represented by a function call, and the tree traversal could be implemented using a loop that iterates through all possible moves at each turn. You might also identify certain tasks that need to be done before each recursive call (like updating the game state) and other tasks that need to be done after each recursive call (like undoing the game state).
This visual modeling to code transition helps you to not only implement your solution but also to understand it better. It enables you to see the connection between abstract problem-solving strategies (like traversing a decision tree) and concrete coding constructs (like loops and recursion). And once you become adept at making this transition, you’ll find that your ability to tackle complex problems - and to write elegant code to solve them - will significantly improve.
The key is to start with a clear and comprehensive visual model of the problem, and then gradually overlay it with the necessary code-level details. This step-by-step, layered approach will allow you to systematically transform your understanding of a problem into an effective solution.
Taxi Dispatch System
Let’s discuss a more complex, real-world problem and how we can transition it into a solution domain.
Let’s consider the task of creating an efficient taxi dispatch system for a city. This is a real-world problem with numerous variables, such as the locations of passengers and available taxis, traffic, and travel time to various destinations.
Problem Model: Our initial problem model could be a simple map of the city, with markings for taxi and passenger locations. You would also need to account for traffic conditions and average travel times between different parts of the city.
Solution Domain Identification: Recognizing the inherent complexity and dynamic nature of the problem, we might recognize this as a variant of the classic ‘Travelling Salesman Problem’ or TSP (an NP-hard problem in combinatorial optimization studied in operations research and theoretical computer science), where we need to determine optimal routes. We might also see elements of the ‘Assignment Problem’ where we want to assign taxis to passengers in the most efficient way.
Overlaying Computational Models: In moving to the solution domain, you might start by applying graph theory. You could represent the city as a graph with nodes (intersections) and edges (roads), assigning weights based on traffic or distance. The taxis and customers can be represented as dynamic nodes on the graph, their movements changing the state of the graph over time.
Coding Constructs: The nature of the problem might lend itself to several algorithmic solutions. You could use a greedy algorithm to assign the closest available taxi to a customer, Dijkstra’s algorithm to find the shortest path between two points, or a heuristic-based search algorithm for a more optimal solution.
The transition from problem to solution domain often involves recognizing the abstract structure of the problem and how this structure fits known solution archetypes, which is largely a product of experience, knowledge, and sometimes, creativity.
Making the Transition from Problem Domain to Solution Domain
The transition from the problem domain to the solution domain is an essential step in problem-solving and involves a sequence of cognitive processes. Here’s a more detailed outline:
Understanding the Problem: The first step is to gain a comprehensive understanding of the problem. This includes understanding the requirements, the constraints, and the goals. It often helps to visualize the problem or draw a diagram.
Defining the Problem: After gaining a preliminary understanding, the problem should be defined in clear terms. This definition should be as concise as possible but should also encompass all the essential elements of the problem.
Conceptualizing the Problem: Next, attempt to construct a mental or conceptual model of the problem. This may involve abstraction, where you eliminate unnecessary details and focus on the key elements of the problem. This abstraction helps in translating real-world problems into more mathematically tractable models.
Mapping to Known Problems/Solutions: After conceptualizing the problem, you can compare it with known problems and their solutions. Does your problem look like a well-studied problem? Can the techniques used in the solution of the known problem be applied to your problem? This step is often where knowledge of algorithms and data structures becomes critical.
Formulating a Plan/Strategy: Once you’ve identified a potential approach to solving the problem, the next step is to formulate a plan or strategy to implement that solution. This might involve further breaking down the problem into sub-problems and solving them one at a time.
Translating to Code: The final step in the transition is to take your conceptual solution and translate it into concrete code. This involves deciding on data structures, control flow, and possibly writing pseudocode before the actual code.
Through these steps, you transition from understanding the problem in the real world (problem domain) to having a coded solution (solution domain). It’s important to note that these steps might not always be linear – you might need to iterate and refine your understanding, your problem model, or your solution approach as you learn more about the problem.
Solution Domain Examples
Let’s take another common problem-solving situation where this visualization can be beneficial - the process of sorting a list of items.
Consider you are trying to implement a sorting algorithm, like quicksort. Here’s how you might transition from a visual model to code:
Visual Model: Start by representing your unsorted list as a line of unsorted numbers. Choose a pivot, typically the last element in the array. Draw arrows from the pivot to numbers in the array that are either greater than or less than the pivot. This gives you a visual representation of the partition process.
Overlay Implementation-Level Details: Next, you’ll want to figure out how to move items around in the list based on their comparison to the pivot. This is where you begin to think in terms of indices and loops. You might annotate your diagram with indices to track the progress of your partition.
Coding Constructs: Now, you can see that this problem lends itself well to a divide-and-conquer strategy implemented with recursion. The partition operation can be carried out within a loop, which iterates through the array comparing elements to the pivot. After partitioning, the quicksort algorithm is recursively applied to the sub-arrays that are left and right to the pivot.
Implement: With a clear visual understanding of the problem, you can now start writing code. You can initialize your pivot as the last element, create a loop to compare each element in the array to the pivot, and then call the quicksort function recursively on the divided arrays.
Another example can be the classic problem of traversing a binary tree.
Visual Model: A binary tree is inherently visual, with each node having up to two children. You start at the root, and you want to visit every node in the tree.
Overlay Implementation-Level Details: Depending on the order you wish to visit each node (root, left child, right child), you might annotate your diagram with numbers to signify the order of operations.
Coding Constructs: This problem naturally lends itself to recursion. At each node, you have the option to first visit the left child (and all its descendants), then visit the right child (and all its descendants). The base case would be when a node has no children.
Implement: With your model, annotations, and understanding of the recursive nature of the problem, you can now begin to implement your tree traversal function.
These examples illustrate how you can start with a visual model and incrementally overlay it with implementation details and code constructs, until you arrive at a complete and effective solution.