10.1 - What is an Algorithm?

In game development, you'll frequently encounter challenges like pathfinding for NPCs, sorting inventory items, or calculating optimal strategies for AI opponents. The solutions to these challenges are algorithms—step-by-step procedures for solving problems or accomplishing tasks.

Definition and Characteristics

An algorithm is a finite sequence of well-defined, computer-implementable instructions that takes some input, processes it, and produces an output to solve a specific problem.

Good algorithms share several key characteristics:

1. Finiteness: An algorithm must terminate after a finite number of steps.
2. Definiteness: Each step must be precisely defined and unambiguous.
3. Input: An algorithm may accept zero or more inputs.
4. Output: An algorithm must produce at least one output.
5. Effectiveness: Each step must be simple enough to be carried out exactly and in a finite amount of time.

Algorithms in Everyday Life

Before diving into programming examples, let's recognize that algorithms are all around us:

• A cooking recipe is an algorithm for preparing food
• Directions to a location are an algorithm for navigation
• The method for solving a Rubik's cube is an algorithm

A Simple Algorithm Example

Let's look at a simple algorithm for finding the maximum value in a list of numbers:

1. Set the first number as the current maximum
2. For each remaining number in the list:
   • If the number is greater than the current maximum, update the maximum
3. Return the maximum value

Here's how we implement this in C#:

public static int FindMaximum(int[] numbers)
{
    // Handle edge case: empty array
    if (numbers.Length == 0)
    {
        throw new ArgumentException("Array cannot be empty");
    }
    
    // Start with the first number as the maximum
    int maximum = numbers[0];
    
    // Check each remaining number
    for (int i = 1; i < numbers.Length; i++)
    {
        // If we find a larger number, update the maximum
        if (numbers[i] > maximum)
        {
            maximum = numbers[i];
        }
    }
    
    return maximum;
}

Let's trace through this algorithm with a sample input:

Input: [4, 9, 2, 7, 5]

Step 1: maximum = 4 (first element)
Step 2: Loop through remaining elements
  - Is 9 > 4? Yes, maximum = 9
  - Is 2 > 9? No, maximum stays 9
  - Is 7 > 9? No, maximum stays 9
  - Is 5 > 9? No, maximum stays 9
Step 3: Return maximum = 9

Algorithms vs. Programs

It's important to distinguish between algorithms and programs:

• An algorithm is a logical solution to a problem, independent of programming language
• A program is an implementation of an algorithm in a specific programming language

The same algorithm can be implemented in different programming languages or even in different ways within the same language.

Game Development Example: Treasure Spawning

Let's consider a simple game scenario: spawning treasure chests in random, but valid locations on a game map.

Here's a basic algorithm:

1. Define valid spawn areas (not inside walls, water, etc.)
2. Determine how many treasure chests to spawn
3. For each chest:
   • Generate random coordinates within the map boundaries
   • Check if the location is valid (in a valid spawn area)
   • If valid, place the chest; if not, try again

Here's a C# implementation:

public class TreasureSpawner
{
    private bool[,] validSpawnAreas; // true if position is valid for spawning
    private int mapWidth, mapHeight;
    private Random random;
    
    public TreasureSpawner(bool[,] validAreas)
    {
        validSpawnAreas = validAreas;
        mapWidth = validAreas.GetLength(0);
        mapHeight = validAreas.GetLength(1);
        random = new Random();
    }
    
    public List<Vector2> SpawnTreasure(int numberOfChests)
    {
        List<Vector2> chestPositions = new List<Vector2>();
        
        for (int i = 0; i < numberOfChests; i++)
        {
            Vector2 position = GetValidSpawnPosition();
            chestPositions.Add(position);
        }
        
        return chestPositions;
    }
    
    private Vector2 GetValidSpawnPosition()
    {
        Vector2 position;
        int maxAttempts = 100; // Prevent infinite loops
        int attempts = 0;
        
        do
        {
            // Generate random coordinates
            int x = random.Next(0, mapWidth);
            int y = random.Next(0, mapHeight);
            position = new Vector2(x, y);
            attempts++;
            
            // Check if position is valid
            if (IsValidPosition(position))
            {
                return position;
            }
        } while (attempts < maxAttempts);
        
        // If we couldn't find a valid position after max attempts,
        // return a default position or handle the error
        throw new InvalidOperationException("Could not find a valid spawn position");
    }
    
    private bool IsValidPosition(Vector2 position)
    {
        int x = (int)position.X;
        int y = (int)position.Y;
        
        // Check if position is within map boundaries
        if (x < 0 || x >= mapWidth || y < 0 || y >= mapHeight)
        {
            return false;
        }
        
        // Check if position is in a valid spawn area
        return validSpawnAreas[x, y];
    }
}

// Simple Vector2 class for this example
public struct Vector2
{
    public float X { get; }
    public float Y { get; }
    
    public Vector2(float x, float y)
    {
        X = x;
        Y = y;
    }
}

Why Algorithms Matter in Game Development

Understanding algorithms is crucial for game development for several reasons:

1. Performance: Games need to run smoothly, often processing complex calculations in real-time. Efficient algorithms help maintain high frame rates.

2. Scalability: As your game grows in complexity (more entities, larger worlds), inefficient algorithms can cause significant slowdowns.

3. Game Mechanics: Many game mechanics are algorithms themselves:

   • Pathfinding for NPCs
   • Combat systems
   • Procedural generation
   • AI decision making
   • Physics simulations

4. Resource Management: Games often run on platforms with limited resources (mobile devices, consoles). Efficient algorithms help manage memory and CPU usage.

Types of Algorithms

There are many categories of algorithms, but some of the most relevant for game development include:

1. Search Algorithms: Finding items or paths (e.g., A* pathfinding)
2. Sorting Algorithms: Organizing data (e.g., sorting inventory by value)
3. Graph Algorithms: Working with interconnected data (e.g., quest dependencies)
4. Geometric Algorithms: Handling spatial relationships (e.g., collision detection)
5. Procedural Generation Algorithms: Creating content algorithmically (e.g., random level generation)

We'll explore some of these categories in the upcoming sections.

Unity Relevance

Unity implements many algorithms behind the scenes:

• NavMesh pathfinding: For NPC navigation
• Physics engine: For collision detection and resolution
• Rendering pipeline: For determining what to draw on screen
• Animation blending: For smooth transitions between animations

Understanding algorithms helps you work more effectively with these systems and implement your own custom solutions when needed.

Conclusion

Algorithms are the building blocks of problem-solving in programming. They provide structured approaches to tackle complex challenges in game development. As you progress through this module, you'll learn how to analyze, design, and implement efficient algorithms for various game development scenarios.

In the next section, we'll explore algorithmic thinking and problem decomposition—essential skills for developing your own algorithms.