Class and Object Basics

Classes vs. Objects
- A class is a specification, blueprint, or template for an object; it is the code that describes what data the object stores and what it can do
- An object is a single instance of a class, created using its “template.” It is executing code, with specific values stored in each variable
- To instantiate an object is to create a new object from a class
Object design basics
- Objects have attributes: data stored in the object. This data is different in each instance, although the type of data is defined in the class.
- Objects have methods: functions that use or modify the object’s data. The code for these functions is defined in the class, but it is executed on (and modifies) a specific object
Encapsulation: An important principle in class/object design
- Attribute data is stored in instance variables, a special kind of variable
- Called “instance” because each instance, i.e. object, has its own copy of them
- Encapsulation means instance variables (attributes) are “hidden” inside an object: other code cannot access them directly
  - Only the object’s own methods can access the instance variables
  - Other code must “ask permission” from the object in order to read or write the variables

Writing Our First Class

Designing the class
- Our first class will be used to represent rectangles; each instance (object) will represent one rectangle
- Attributes of a rectangle:
  - Length
  - Width
- Methods that will use the rectangle’s attributes
  - Get length
  - Get width
  - Set length
  - Set width
  - Compute the rectangle’s area
- Note that the first four are a specific type of method called “getters” and “setters” because they allow other code to read (get) or write (set) the rectangle’s instance variables while respecting encapsulation

The Rectangle class:

class Rectangle
{
  private int length;
  private int width;
 
  public void SetLength(int lengthParameter)
  {
    length = lengthParameter;
  }
 
  public int GetLength()
  {
    return length;
  }
 
  public void SetWidth(int widthParameter)
  {
    width = widthParameter;
  }
 
  public int GetWidth()
  {
    return width;
  }
 
  public int ComputeArea()
  {
    return length * width;
  }
}

Let’s look at each part of this code in order.

Attributes
- Each attribute (length and width) is stored in an instance variable
- Instance variables are declared similarly to “regular” variables, but with one additional feature: the access modifier
- Syntax: [access modifier] [type] [variable name]
- The access modifier can have several values, the most common of which are public and private. (There are other access modifiers, such as protected and internal, but in this class we will only be using public and private).
- An access modifier of private is what enforces encapsulation: when you use this access modifier, it means the instance variable cannot be accessed by any code outside the Rectangle class
- The C# compiler will give you an error if you write code that attempts to use a private instance variable anywhere other than a method of that variable’s class
SetLength method, an example of a “setter” method
- This method will allow code outside the Rectangle class to modify a Rectangle object’s “length” attribute
- Note that the header of this method has an access modifier, just like the instance variable
- In this case the access modifier is public because we want to allow other code to call the SetLength method
- Syntax of a method declaration: [access modifier] [return type] [method name]([parameters])
- This method has one parameter, named lengthParameter, whose type is int. This means the method must be called with one argument that is int type.
  - Similar to how Console.WriteLine must be called with one argument that is string type — the Console.WriteLine declaration has one parameter that is string type.
  - Note that it is declared just like a variable, with a type and a name
- A parameter works like a variable: it has a type and a value, and you can use it in expressions and assignment
- When you call a method with a particular argument, like 15, the parameter is assigned this value, so within the method’s code you can assume the parameter value is “the argument to this method”
- The body of the SetLength method has one statement, which assigns the instance variable length to the value contained in the parameter lengthParameter. In other words, whatever argument SetLength is called with will get assigned to length
- This is why it is called a “setter”: SetLength(15) will set length to 15.
GetLength method, an example of a “getter” method
- This method will allow code outside the Rectangle class to read the current value of a Rectangle object’s “length” attribute
- The return type of this method is int, which means that the value it returns to the calling code is an int value
- Recall that Console.ReadLine() returns a string value to the caller, which is why you can write string userInput = Console.ReadLine(). The GetLength method will do the same thing, only with an int instead of a string
- This method has no parameters, so you do not provide any arguments when calling it. “Getter” methods never have parameters, since their purpose is to “get” (read) a value, not change anything
- The body of GetLength has one statement, which uses a new keyword: return. This keyword declares what will be returned by the method, i.e. what particular value will be given to the caller to use in an expression.
- In a “getter” method, the value we return is the instance variable that corresponds to the attribute named in the method. GetLength returns the length instance variable.
SetWidth method
- This is another “setter” method, so it looks very similar to SetLength
- It takes one parameter (widthParameter) and assigns it to the width instance variable
- Note that the return type of both setters is void. The return type void means “this method does not return a value.” Console.WriteLine is an example of a void method we’ve used already.
- Since the return type is void, there is no return statement in this method
GetWidth method
- This is the “getter” method for the width attribute
- It looks very similar to GetLength, except the instance variable in the return statement is width rather than length
The ComputeArea method
- This is not a getter or setter: its goal is not to read or write a single instance variable
- The goal of this method is to compute and return the rectangle’s area
- Since the area of the rectangle will be an int (it is the product of two ints), we declare the return type of the method to be int
- This method has no parameters, because it does not need any arguments. Its only “input” is the instance variables, and it will always do the same thing every time you call it.
- The body of the method has a return statement with an expression, rather than a single variable
- When you write return [expression], the expression will be evaluated first, then the resulting value will be used by the return command
- In this case, the expression length * width will be evaluated, which computes the area of the rectangle. Since both length and width are ints, the int version of the * operator executes, and it produces an int result. This resulting int is what the method returns.

Using Our Class

We’ve written a class, but it does not do anything yet
- The class is a blueprint for an object, not an object
- To make it “do something” (i.e. execute some methods), we need to instantiate an object using this class
- The code that does this should be in a separate file (e.g. Program.cs), not in Rectangle.cs
Here is a program that uses our Rectangle class:

using System;
 
class Program
{
  static void Main(string[] args)
  {
    Rectangle myRectangle = new Rectangle();
    myRectangle.SetLength(12);
    myRectangle.SetWidth(3);
    int area = myRectangle.ComputeArea();
    Console.WriteLine(
      "Your rectangle's length is "
        + $"{myRectangle.GetLength()}, and its width is "
        + $"{myRectangle.GetWidth()}, so its area is {area}."
    );
  }
}

Instantiating an object
- The first line of code creates a Rectangle object
- The left side of the = sign is a variable declaration — it declares a variable of type Rectangle
  - Classes we write become new data types in C#
- The right side of the = sign assigns this variable a value: a Rectangle object
- We instantiate an object by writing the keyword new followed by the name of the class (syntax: new [class name]()). The empty parentheses are required, but we will explain why later.
- This statement is really an initialization statement: It declares and assigns a variable in one line
- The value of the myRectangle variable is the Rectangle object that was created by new Rectangle()
Calling setters on the object
- The next two lines of code call the SetLength and SetWidth methods on the object
- Syntax: [object name].[method name]([argument]). Note the “dot operator” between the variable name and the method name.
- SetLength is called with an argument of 12, so lengthParameter gets the value 12, and the rectangle’s length instance variable is then assigned this value
- Similarly, SetWidth is called with an argument of 3, so the rectangle’s width instance variable is assigned the value 3
Calling ComputeArea
- The next line calls the ComputeArea method and assigns its result to a new variable named area
- The syntax is the same as the other method calls
- Since this method has a return value, we need to do something with the return value — we assign it to a variable
- Similar to how you must do something with the result (return value) of Console.ReadLine(), i.e. string userInput = Console.ReadLine()
Calling getters on the object
- The last line of code displays some information about the rectangle object using string interpolation
- One part of the string interpolation is the area variable, which we’ve seen before
- The other interpolated values are myRectangle.GetLength() and myRectangle.GetWidth()
- Looking at the first one: this will call the GetLength method, which has a return value that is an int. Instead of storing the return value in an int variable, we put it in the string interpolation brackets, which means it will be converted to a string using ToString. This means the rectangle’s length will be inserted into the string and displayed on the screen

Flow of Control with Objects

Consider what happens when you have multiple objects in the same program, like this:
```
class Program
{
  static void Main(string[] args)
  {
    Rectangle rect1;
    rect1 = new Rectangle();
    rect1.SetLength(12);
    rect1.SetWidth(3);
    Rectangle rect2 = new Rectangle();
    rect2.SetLength(7);
    rect2.SetWidth(15);
  }
}
```
- First, we declare a variable of type Rectangle
- Then we assign rect1 a value, a new Rectangle object that we instantiate
- We call the SetLength and SetWidth methods using rect1, and the Rectangle object that rect1 refers to gets its length and width instance variables set to 12 and 3
- Then we create another Rectangle object and assign it to the variable rect2 . This object has its own copy of the length and width instance variables, not 12 and 3
- We call the SetLength and SetWidth methods again, using rect2 on the left side of the dot instead of rect1. This means the Rectangle object that rect2 refers to gets its instance variables set to 7 and 15, while the other Rectangle remains unmodified
The same method code can modify different objects at different times
- Calling a method transfers control from the current line of code (i.e. in Program.cs) to the method code within the class (Rectangle.cs)
- The method code is always the same, but the specific object that gets modified can be different each time
- The variable on the left side of the dot operator determines which object gets modified
- In rect1.SetLength(12), rect1 is the calling object, so SetLength will modify rect1
  - SetLength begins executing with lengthParameter equal to 12
  - The instance variable length in length = lengthParameter refers to rect1’s length
- In rect2.SetLength(7), rect2 is the calling object, so SetLength will modify rect2
  - SetLength begins executing with lengthParameter equal to 7
  - The instance variable length in length = lengthParameter refers to rect2’s length

Accessing object members

The “dot operator” that we use to call methods is technically the member access operator
A member of an object is either a method or an instance variable
When we write objectName.methodName(), e.g. rect1.SetLength(12), we are using the dot operator to access the “SetLength” member of rect1, which is a method; this means we want to call (execute) the SetLength method of rect1
We can also use the dot operator to access instance variables, although we usually do not do that because of encapsulation

If we wrote the Rectangle class like this:

class Rectangle
{
    public int length;
    public int width;
}

Then we could write a Main method that uses the dot operator to access the length and width instance variables, like this:

static void Main(string[] args)
{
    Rectangle rect1 = new Rectangle();
    rect1.length = 12;
    rect1.width = 3;
}

But this code violates encapsulation, so we will not do this.

Method calls in more detail

Now that we know about the member access operator, we can explain how method calls work a little better
When we write rect1.SetLength(12), the SetLength method is executed with rect1 as the calling object — we are accessing the SetLength member of rect1 in particular (even though every Rectangle has the same SetLength method)
This means that when the code in SetLength uses an instance variable, i.e. length, it will automatically access rect1’s copy of the instance variable
You can imagine that the SetLength method “changes” to this when you call rect1.SetLength():
```
public void SetLength(int lengthParameter)
{
    rect1.length = lengthParameter;
}
```
Note that we use the “dot” (member access) operator on rect1 to access its length instance variable.
Similarly, you can imagine that the SetLength method “changes” to this when you call rect2.SetLength():
```
public void SetLength(int lengthParameter)
{
    rect2.length = lengthParameter;
}
```
The calling object is automatically “inserted” before any instance variables in a method
The keyword this is an explicit reference to “the calling object”
- Instead of imagining that the calling object’s name is inserted before each instance variable, you could write the SetLength method like this:
```
public void SetLength(int lengthParameter)
{
    this.length = lengthParameter;
}
```
- This is valid code (unlike our imaginary examples) and will work exactly the same as our previous way of writing SetLength
- When SetLength is called with rect1.SetLength(12), this becomes equal to rect1, just like lengthParameter becomes equal to 12
- When SetLength is called with rect2.SetLength(7), this becomes equal to rect2 and lengthParameter becomes equal to 7

Methods and instance variables

Using a variable in an expression means reading its value
A variable only changes when it is on the left side of an assignment statement; this is writing to the variable
A method that uses instance variables in an expression, but does not assign to them, will not modify the object
For example, consider the ComputeArea method:
```
public int ComputeArea()
{
    return length * width;
}
```
It reads the current values of length and width to compute their product, but the product is returned to the method’s caller. The instance variables are not changed.
After executing the following code:
```
Rectangle rect1 = new Rectangle();
rect1.SetLength(12);
rect1.SetWidth(3);
int area = rect1.ComputeArea();
```
rect1 has a length of 12 and a width of 3. The call to rect1.ComputeArea() computes $12 \cdot 3 = 36$ , and the area variable is assigned this return value, but it does not change rect1.

Methods and return values

Recall the basic structure of a program: receive input, compute something, produce output
A method has the same structure: it receives input from its parameters, computes by executing the statements in its body, then produces output by returning a value
- For example, consider this method defined in the Rectangle class:
```
public int LengthProduct(int factor)
{
    return length * factor;
}
```
  Its input is the parameter factor, which is an int. In the method body, it computes the product of the rectangle’s length and factor. The method’s output is the resulting product.
The return statement specifies the output of the method: a variable, expression, etc. that produces some value
A method call can be used in other code as if it were a value. The “value” of a method call is the method’s return value.
- In previous examples, we wrote int area = rect1.ComputeArea();, which assigns a variable (area) a value (the return value of ComputeArea())
- The LengthProduct method can be used like this:
```
Rectangle rect1 = new Rectangle();
rect1.SetLength(12);
int result = rect1.LengthProduct(2) + 1;
```
  When executing the third line of code, the computer first executes the LengthProduct method with argument (input) 2, which computes the product $12 \cdot 2 = 24$ . Then it uses the return value of LengthProduct, which is 24, to evaluate the expression rect1.LengthProduct(2) + 1, producing a result of 25. Finally, it assigns the value 25 to the variable result.
When writing a method that returns a value, the value in the return statement must be the same type as the method’s return type
- If the value returned by LengthProduct is not an int, we will get a compile error
- This will not work:
```
public int LengthProduct(double factor)
{
    return length * factor;
}
```
  Now that factor has type double, the expression length * factor will need to implicitly convert length from int to double in order to make the types match. Then the product will also be a double, so the return value does not match the return type (int).
- We could fix it by either changing the return type of the method to double, or adding a cast to int to the product so that the return value is still an int
Not all methods return a value, but all methods must have a return type
- The return type void means “nothing is returned”
- If your method does not return a value, its return type must be void. If the return type is not void, the method must return a value.
- This will cause a compile error because the method has a return type of int but no return statement:
```
public int SetLength(int lengthP)
{
    length = lengthP;
}
```
- This will cause a compile error because the method has a return type of void, but it attempts to return something anyway:
```
public void GetLength()
{
    return length;
}
```

Introduction to UML

UML is a specification language for software
- UML: Unified Modeling Language
- Describes design and structure of a program with graphics
- Does not include “implementation details,” such as code statements
- Can be used for any programming language, not just C#
- Used in planning/design phase of software creation, before you start writing code
- Process: Determine program requirements $\to$ Make UML diagrams $\to$ Write code based on UML $\to$ Test and debug program
UML Class Diagram elements
- Top box: Class name, centered
- Middle box: Attributes (i.e. instance variables)
  - On each line, one attribute, with its name and type
  - Syntax: [+/-] [name]: [type]
  - Note this is the opposite order from C# variable declaration: type comes after name
  - Minus sign at beginning of line indicates “private member”
- Bottom box: Operations (i.e. methods)
  - On each line, one method header, including name, parameters, and return type
  - Syntax: [+/-] [name]([parameter name]: [parameter type]): [return type]
  - Also backwards compared to C# order: parameter types come after parameter names, and return type comes after method name instead of before it
  - Plus sign at beginning of line indicates “public”, which is what we want for methods
UML Diagram for the Rectangle class
- Note that when the return type of a method is void, we can omit it in UML
- In general, attributes will be private (- sign) and methods will be public (+ sign), so you can expect most of your classes to follow this pattern (-s in the upper box, +s in the lower box)
- Note that there is no code or “implementation” described here: it does not say that ComputeArea will multiply length by width
Writing code based on a UML diagram
- Each diagram is one class, everything within the box is between the class’s header and its closing brace
- For each attribute in the attributes section, write an instance variable of the right name and type
  - See ”- width: int”, write private int width;
  - Remember to reverse the order of name and type
- For each method in the methods section, write a method header with the matching return type, name, and parameters
  - Parameter declarations are like the instance variables: in UML they have a name followed by a type, in C# you write the type name first
- Now the method bodies need to be filled in - UML just defined the interface, now you need to write the implementation

Variable Scope

Instance and local variables

Instance variables: Stored (in memory) with the object, shared by all methods of the object. Changes made within a method persist after method finishes executing.
Local variables: Visible to only one method, not shared. Disappear after method finishes executing. Variables we’ve created before in the Main method (they are local to the Main method!).
Example: In class Rectangle, we have these two methods:
```
public void SwapDimensions()
{
    int temp = length;
    length = width;
    width = temp;
}
public int GetLength()
{
    return length;
}
```
- temp is a local variable within SwapDimensions, while length and width are instance variables
- The GetLength method cannot use temp; it is visible only to SwapDimensions
- When SwapDimensions changes length, that change is persistent — it will still be different when GetLength executes, and the next call to GetLength after SwapDimensions will return the new length
- When SwapDimensions assigns a value to temp, it only has that value within the current call to SwapDimensions — after SwapDimensions finishes, temp disappears, and the next call to SwapDimensions creates a new temp

Definition of scope

Variables exist only in limited time and space within the program
Outside those limits, the variable cannot be accessed — e.g. local variables cannot be accessed outside their method
Scope of a variable: The region of the program where it is accessible/visible
- A variable is “in scope” when it is accessible
- A variable is “out of scope” when it does not exist or cannot be accessed
Time limits to scope: Scope begins after the variable has been declared
- This is why you cannot use a variable before declaring it
Space limits to scope: Scope is within the same code block where the variable is declared
- Code blocks are defined by curly braces: everything between matching { and } is in the same code block
- Instance variables are declared in the class’s code block (they are inside class Rectangle’s body, but not inside anything else), so their scope extends to the entire class
- Code blocks nest: A method’s code block is inside the class’s code block, so instance variables are also in scope within each method’s code block
- Local variables are declared inside a method’s code block, so their scope is limited to that single method
The scope of a parameter (which is a variable) is the method’s code block - it is the same as a local variable for that method
Scope example:
```
public void SwapDimensions()
{
    int temp = length;
    length = width;
    width = temp;
}
public void SetWidth(int widthParam)
{
    int temp = width;
    width = widthParam;
}
```
- The two variables named temp have different scopes: One has a scope limited to the SwapDimensions method’s body, while the other has a scope limited to the SetWidth method’s body
- This is why they can have the same name: variable names must be unique within the variable’s scope. You can have two variables with the same name if they are in different scopes.
- The scope of instance variables length and width is the body of class Rectangle, so they are in scope for both of these methods

Variables with overlapping scopes

This code is legal (compiles) but does not do what you want:

class Rectangle
{
    private int length;
    private int width;
    public void UpdateWidth(int newWidth)
    {
        int width = 5;
        width = newWidth;
    }
}

The instance variable width and the local variable width have different scopes, so they can have the same name
But the instance variable’s scope (the class Rectangle) overlaps with the local variable’s scope (the method UpdateWidth)
If two variables have the same name and overlapping scopes, the variable with the closer or smaller scope shadows the variable with the farther or wider scope: the name will refer only to the variable with the smaller scope
In this case, that means width inside UpdateWidth refers only to the local variable named width, whose scope is smaller because it is limited to the UpdateWidth method. The line width = newWidth actually changes the local variable, not the instance variable named width.
Since instance variables have a large scope (the whole class), they will always get shadowed by variables declared within methods
You can prevent shadowing by using the keyword this, like this:
```
class Rectangle
{
    private int length;
    private int width;
    public void UpdateWidth(int newWidth)
    {
        int width = 5;
        this.width = newWidth;
    }
}
```
Since this means “the calling object”, this.width means “access the width member of the calling object.” This can only mean the instance variable width, not the local variable with the same name
Incidentally, you can also use this to give your parameters the same name as the instance variables they are modifying:
```
class Rectangle
{
    private int length;
    private int width;
    public void SetWidth(int width)
    {
        this.width = width;
    }
}
```
Without this, the body of the SetWidth method would be width = width;, which does not do anything (it would assign the parameter width to itself).

Constants

Classes can also contain constants
Syntax: [public/private] const [type] [name] = [value];
This is a named value that never changes during program execution
Safe to make it public because it cannot change — no risk of violating encapsulation
Can only be built-in types (int, double, etc.), not objects
Can make your program more readable by giving names to “magic numbers” that have some significance
Convention: constants have names in ALL CAPS
Example:
```
class Calendar
{
    public const int MONTHS = 12;
    private int currentMonth;
    //...
}
```
The value “12” has a special meaning here, i.e. the number of months in a year, so we use a constant to name it.
Constants are accessed using the name of the class, not the name of an object — they are the same for every object of that class. For example:
```
Calendar myCal = new Calendar();
decimal yearlyPrice = 2000.0m;
decimal monthlyPrice = yearlyPrice / Calendar.MONTHS;
```

Reference Types: More Details

Data types in C# are either value types or reference types
- This difference was introduced in an earlier lecture (Datatypes and Variables)
- For a value type variable (int, long, float, double, decimal, char, bool) the named memory location stores the exact data value held by the variable
- For a reference type variable, such as string, the named memory location stores a reference to the value, not the value itself
- All objects you create from your own classes, like Rectangle, are reference types
Object variables are references
- When you have a variable for a reference type, or “reference variable,” you need to be careful with the assignment operation
- Consider this code:
```
using System;
 
class Program
{
  static void Main(string[] args)
  {
    Rectangle rect1 = new Rectangle();
    rect1.SetLength(8);
    rect1.SetWidth(10);
    Rectangle rect2 = rect1;
    rect2.SetLength(4);
    Console.WriteLine(
      $"Rectangle 1: {rect1.GetLength()} "
        + $"by {rect1.GetWidth()}"
    );
    Console.WriteLine(
      $"Rectangle 2: {rect2.GetLength()} "
        + $"by {rect2.GetWidth()}"
    );
  }
}
```
- The output is:
```
Rectangle 1: 4 by 10
Rectangle 2: 4 by 10
```
- The variables rect1 and rect2 actually refer to the same Rectangle object, so rect2.SetLength(4) seems to change the length of “both” rectangles
- The assignment operator copies the contents of the variable, but a reference variable contains a reference to an object — so that’s what gets copied (in Rectangle rect2 = rect1), not the object itself
- In more detail:
  - Rectangle rect1 = new Rectangle() creates a new Rectangle object somewhere in memory, then creates a reference variable named rect1 somewhere else in memory. The variable named rect1 is initialized with the memory address of the Rectangle object, i.e. a reference to the object
  - rect1.SetLength(8) reads the address of the Rectangle object from the rect1 variable, finds the object in memory, and executes the SetLength method on that object (changing its length to 8)
  - rect1.SetWidth(10) does the same thing, finds the same object, and sets its width to 10
  - Rectangle rect2 = rect1 creates a reference variable named rect2 in memory, but does not create a new Rectangle object. Instead, it initializes rect2 with the same memory address that is stored in rect1, referring to the same Rectangle object
  - rect2.SetLength(4) reads the address of a Rectangle object from the rect2 variable, finds that object in memory, and sets its length to 4 — but this is the exact same Rectangle object that rect1 refers to
Reference types can also appear in method parameters
- When you call a method, you provide an argument (a value) for each parameter in the method’s declaration
- Since the parameter is really a variable, the computer will then assign the argument to the parameter, just like variable assignment
  - For example, when you write rect1.SetLength(8), there is an implicit assignment lengthParameter = 8 that gets executed before executing the body of the SetLength method
- This means if the parameter is a reference type (like an object), the parameter will get a copy of the reference, not a copy of the object
- When you use the parameter to modify the object, you will modify the same object that the caller provided as an argument
- This means objects can change other objects!
- For example, imagine we added this method to the Rectangle class:
```
public void CopyToOther(Rectangle otherRect)
{
    otherRect.SetLength(length);
    otherRect.SetWidth(width);
}
```
  It uses the SetLength and SetWidth methods to modify its parameter, otherRect. Specifically, it sets the parameter’s length and width to its own length and width.
- The Main method of a program could do something like this:
```
Rectangle rect1 = new Rectangle();
Rectangle rect2 = new Rectangle();
rect1.SetLength(8);
rect1.SetWidth(10);
rect1.CopyToOther(rect2);
Console.WriteLine($"Rectangle 2: {rect2.GetLength()} "
    + $"by {rect2.GetWidth()}");
```
  - First it creates two different Rectangle objects (note the two calls to new), then it sets the length and width of one object, using rect1.SetLength and rect1.SetWidth
  - Then it calls the CopyToOther method with an argument of rect2. This transfers control to the method and (implicitly) makes the assignment otherRect = rect2
  - Since otherRect and rect2 are now reference variables referring to the same object, the calls to otherRect.SetLength and otherRect.SetWidth within the method will modify that object
  - After the call to CopyToOther, the object referred to by rect2 has a length of 8 and a width of 10, even though we never called rect2.SetLength or rect2.SetWidth

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