(2) collections algorithms

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Nico Ludwig (@ersatzteilchen)
Collections – Part II

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2
●
Collections – Part II
– Arrays revisited
– Value and Reference Semantics of Elements
– A Way to categorize Collections
– Indexed Collections
●
Lists
●
Basic Features and Examples
●
Size and Capacity
TOC

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The Collection Story
● A very important topic in programming besides algorithms arecollections of data.
– Virtually data collections were present before algorithms: computing dealt with mass data from the beginning (business data).
– The so called "data processing" was applied to predict the results of the US presidential elections in 1952 for the first time basically.
● Terminology alert: Collections are called containers in C++.
● Nowadays we have to deal with huge amounts of data in databases.
● Back to programming with data:
– Data is held in objects. - "Object" is not a term dedicated to oo-languages, it could be a Pascal RECORD instance as well.
– Understanding and using collections is key for the art and craft of programming apart from algorithms.
– In most programming languages (languages) we already have a first class citizen to deal with collections of data: arrays!
● Let's begin our discussion of collections with arrays.
● Terminology alert for German programmers: Stick to calling an arrayarray, not "Feld", even though German literature does!
– A Feld is a field of a UDT! This is an example where translation is really inappropriate, leading to ridiculous misunderstandings.
● In 1952 the UNIVAC I (UNIVersal Automatic
Computer I) was used for the prediction for the
presidential election.
● Mind that compiler and run time usually also
always use the term "array". Either they are
themselves only printing English messages, or
they print German messages, but stick to special
terms. - The word "array" is a special term, not a
word that needs to be translated!

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Arrays – Part I
● Generally, we call a collection an array if following statements hold true:
– The collection has the semantics of a table.
– The "rows" of that table, the elements or "slots", can be accessed with a numeric "row number", the so called index.
● Array indexes usually start at 0 (0-based indexing), the index referencing the last element boils down to length – 1. In Basic arrays have 1-based indexing.
– The elements of an array can be accessed randomly with O(1) complexity. - This is very fast!
– (The elements of an array usually have the same static type, C++ calls this the element type.)
● In many languages arrays have integrated syntactical support, e.g. in Java, C++, C#, VB, JavaScript etc.
– Creation of arrays with initializer lists and the []-notation:
● Many languages support an initialization syntax for arrays.
●
In C++ automatic arrays require to be created with a constant length known at compile time.
●
Other languages like Java and C# create arrays only on the heap, and therefor these languages also accept non-constant lengths for arrays.
– Accessing and manipulating array elements by accessing them with the index/subscript/[]-operator (C++, Java, C#):
● The array number2 contains only elements of value 0 with the exception of the element at index 3. Arrays having "gaps" are called sparse arrays.
// C++
int numbers[] = {1, 2, 3, 4, 5};
// Java
int[] numbers = {1, 2, 3, 4, 5};
int[] numbers2 = new int[5];
1 2 3 4 5
numbers[0]
numbers (C/C++)
numbers[length - 1]
// Reading the element at index 3:
int aNumber = numbers[3];
// Writing the value 12 to the element at index 3:
numbers2[3] = 12;
0 0 0 12 0 numbers2
a sparse array

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Support of arrays in various languages:
– Arrays are often the only collection that is integrated into a language, i.e. no extra library imports are required to use them.
●
In C/C++ the array elements reside in a contiguous block of memory, which enables the fundamental concept of pointer arithmetics in C/C++
●
Therefor C++ requires array elements to be of the same static type because then all elements have the same size to make pointer arithmetics work!
– Arrays have a fixed length (i.e. the count of elements) after creation that can't be changed. - We can not add or remove elements.
●
This is not the case for JavaScript arrays. In JavaScript, arrays, also called "array-like objects", are the only type of collections existing!
– Arrays can manage objects of dynamic or static types depending on the support of the language.
●
Statically typed languages allow only array elements of the same static type.
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Dynamically typed languages allow individual array elements to be of any type.
– Arrays are a primary construct of imperative languages. In opposite to immutable lists used in functional programming
languages.
1 2 3 4 5
lower address
numbers (C/C++)
higher address
contiguous block of memory
// C++
int numbers[5]; // numbers can only store five ints
Car parkingBay[100]; // parkingBay can only store 100 Car instances
// JavaScript
var objects = [5, "five", {x: 34, y: 4.4}]; // objects contains an integer, a string and an object
Arrays – Part II
● E.g. F# as a functional programming language
does have an extra ugly syntax for array-creation,
-accessing and -manipulation; F#'s arrays are
mutable! So, F# clearly states immutable
collections (i.e. F# lists) being more primary than
arrays!

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Arrays can be n-dimensional (multidimensional) in many programming languages.
– N-dimensional arrays can be used to build matrix data structures.
– 2-dimensional arrays can be seen as an abstraction of tables
having more than one column. 3-dimensional arrays are cubes!
– Terminology alert: sometimes one-dimensional arrays are called vectors! Not to be confused with spatial vectors!
●
Languages may support two kinds of n-dimensional arrays:
– Rectangular n-dimensional arrays. Here a 2-dimensional 3x3 matrix (one big object):
– Jagged n-dimensional arrays are typically build as arrays of arrays (some individual arrays):
// C#
int[,] retangularArray = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}; // Represents a 3x3 matrix.
// C#
int[][] jaggedArray = new int[3][];
// Set the values of the sub-arrays in the jagged array structure:
jaggedArray[0] = new[] {1, 2, 3, 4};
jaggedArray[1] = new[] {6, 7};
jaggedArray[2] = new[] {8, 9, 0};
1 2 3 4
8 9 0
6 7 jaggedArray (.Net)
jaggedArray[0]
jaggedArray[1]
jaggedArray[2]
C# - leaving away the type name on creating anonymous
arrays with array initializers
// Assume we have a method with a string-array parameter:
private void AwaitsAStringArray(string[] strings);
// Pass a newly created array with an array initializer:
AwaitsAStringArray(new string[]{ "Monica", "Rebecca", "Lydia" });
// Alternatively leave the type name away on the new keyword:
AwaitsAStringArray(new[]{ "Monica", "Rebecca", "Lydia" });
A=
(
a11 a12 a13
a21 a22 a23
a31 a32 a33
)
rectangularArray=
(
1 2 3
4 5 6
7 8 9)
Arrays – Part III
● The mathematical numeration of matrix elements
is row-major, i.e. the first index is the row's index
and second index is the column's index.
● .Net's framework design guidelines suggest using
jagged arrays instead of rectangular arrays. The
reasoning behind this is the low propability of
wasted space, when arrays get sparse and the
CLR is able to optimize index access to jagged
arrays better than for rectangular arrays.
● Rectangular arrays can consume very much
memory if it has many dimensions (even if the
array is not filled).
● Jagged arrays can also be defined in Java and
Groovy.

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C/C++ allow the definition of arrays that act like "n-dimensional" arrays.
– "N-dimensional" arrays are equivalent to "normal" arrays in C/C++.
●
I. e. the memory layout is equivalent for both. N-dimensional arrays have no genuine concept in C/C++!
– C/C++ provide alternative syntaxes for defining and accessing "mimicked" n-dimensional arrays.
– The definition/initialization syntax differs, however.
●
Creation and memory layout:
●
The memory layout of C/C++ arrays is done by row-major order, in which the rows are laid down in linear memory after another.
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The elements of multidimensional arrays in C/C++ are accessed with multiple applications of the []-operator:
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The way C/C++ arrange n-dimensional arrays is critical for optimizations in the CPU's cache and vectorization.
– (But to gain maximum performance, developers have to access elements in a special order.)
– Closely related is the performance gain when using the GPU to process large amounts of data to relief the CPU.
– You should notice that n-dimensional arrays are no topic for application programming, but for high performance computing.
// Creates an "n-dimensional" 2x3 array in C++:
int mArray[2][3] = {{1, 2, 3}, {4, 5, 6}};
// Creates a "normal" 6 array in C++:
int array[6] = {1, 2, 3, 4, 5, 6};
1 2 3 4 5 6 array
mArray
1 2 3 4 5 6
for (int i = 0; i < 2; ++i) { // 1. "dimension" (columns)
for (int j = 0; j < 3; ++j) { // 2. "dimension" (rows)
mArray[i][j] = 0; // Uses i and j as "coordinates".
}
}
for (int i = 0; i < 6; ++i) {
array[i] = 0; // Uses i as index.
}
Multidimensional Arrays in C/C++
● Data vectorization means that blocks of data, such
as arrays, are not manipulated element-wise in
loops, but manipulated as a whole. CPUs provide
special instructions to apply vectorization.

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Car{ Power = 120 }
Car{ Power = 180 }
●
An important point we've to clarify, is, whether collections hold copies or references to "contained" objects.
– We have to understand, how the language we use handles this.
– Do the collection and the contained elements share the same lifetime or not?
●
If a language defines value semantics for contents of variables, arrays will hold copies.
– E.g. an array of int in C/C++:
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If a language defines reference semantics for contents of variables, arrays will hold references.
– E.g. an array of reference type (the class Car in this example) in C#:
// C++
int value = 42;
int numbers[5];
numbers[3] = value; // Copies the content of value. ? ? ? 42 ? numbers
42 value
numbers[3] = 80; // Doesn't modify value.
80
C# - automatically implemented properties
public class Car {
// Power's backing field will be created automatically!
public int Power {get; set;}
}
// C#
Car myCar = new Car{ Power = 120 };
Car[] parkingLot = new Car[5];
parkingLot[3] = myCar; // Copy a reference to myCar.
parkingLot[3].Power = 180; // Will also modify myCar!
null null null null parkingLot
myCar
C# - object initializers
// Create a Car object and set the property
// Power:
Car car = new Car();
car.Power = 180;
// Alternatively create a Car object and set
// the property Power within one expression
// as object initializer:
Car car2 = new Car{ Power = 180 };
Value and Reference Semantics of Elements

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Some languages allow holding references to objects as array elements, we can exploit this "layer of indirection".
– E.g. we can create arrays with elements whose static type is the type of a base type and whose dynamic type is any object of
derived type.
●
In C++ we can add this extra layer of indirection with pointers to objects of a base type.
– It allows to use the elements of an array polymorphically:
●
The array parkingLot holds elements of the static type Vehicle*.
●
The pointers can point/indirect to any subtype of Vehicle (in this case Car and Bike).
●
Through the pointers held in parkingLot, the overridden method Drive() can be called dynamically.
– The application of polymorphism in arrays (and also other collections) is a very
important feature that is also present in other oo-languages. => It is the basis for
object-based collections.
// C++11:
Car car;
Bike bike;
Vehicle* parkingLot[] = {&car, &bike};
for(Vehicle* vehicle : parkingLot) {
vehicle->Drive();
}
// > zooming off...
// > woosh...
// C++:
class Vehicle {
public:
virtual void Drive() const = 0;
};
// C++:
class Car : public Vehicle {
public:
void Drive() const {
std::cout<<"zooming off..."<<std::endl;
}
};
// C++:
class Bike : public Vehicle {
public:
void Drive() const {
std::cout<<"woosh..."<<std::endl;
}
};
[0] [1]
(Car)
(Bike)
parkingLot (Vehicle*[2])
Homogeneous and Heterogeneous Arrays – dynamic and
static Type of Elements
● In most languages the array elements need to be
of the same static type. JavaScript arrays can be
really heterogeneous, but JavaScript does only
have dynamic types altogether...

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Most languages have arrays that don't expose their length.So programmers have to pass the array's length separately.
– More modern languages/platforms do have arrays that expose their length, e.g. Java, .Net and JavaScript, but not C/C++!.
– (C++11 provides an STL wrapper type for c-arrays: std::array. It exposes the array's length!)
– This is a major source of problems and bugs while working with arrays.
●
Esp. in C/C++ arrays are directly associated to physical memory. This is a further source of potential bugs and problems.
– Therefor higher level C++ STL container types should be used.
●
The length (i.e. the count of elements) of an array is fixed.
– Not so in JavaScript.
●
.Net's framework design guidelines suggest using "genuine" collections instead of arrays in public interfaces.
Shortcomings of Arrays

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Object-based vs. generic
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Indexed, sequential vs. associative
– Terminology alert: The C++ STL tells sequential (those are indexed and sequential containers) from associative containers.
– Terminology alert: Java tells Collections (sequential collections (and "somehow" indexed collections also)) from Maps.
●
Ordered or unordered
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Mutable or readonly
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Synchronized or unsynchronized
Platform-agnostic Categorization of Collections

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We start with discussing indexed, sequential and associative collections, beginning with indexed collections.
●
Indexed collections have following basic features:
– Elements can be accessed and modified via an index number (0-based or not).
– Elements have a defined order.
– Elements can be randomly accessed (usuallay with O(1) complexity – this is very fast).
●
Ok, these basic features do just describe arrays as collections, but indexed collections have more features:
– The collection exposes the count of elements it holds, (i.e. length; with 0-based indexes the last index would be length - 1).
– Elements can be added or removed after creation of an indexed collection.
●
The length of an indexed collection can grow or shrink during run time!
●
Esp. in C/C++, arrays are a major source of problems, indexed collections help, because they expose their length.
Indexed Collections – Part I
● Java provides the marker interface
RandomAccess, which indicates collections that
provide random access.

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In modern languages we can find following indexed collectionsbeyond arrays:
– "Genuine" lists or vectors
– deques
●
Strings are a special kind of indexed collection in many languages.In C/C++ c-strings are just arrays.
– On some platforms (Java, .Net) strings act as readonly indexed collections.
●
I.e. the elements of strings (the characters) can't be modified and elements can't be added or removed to strings.
●
String operations will not modify the original string, but a new string with a content different from the original string will be created. This is called the
"defense copy pattern".
– The above mentioned platforms do also define mutable string types.
●
Those encapsulate an original string object and allow accessing it with an interface providing mutating operations.
●
Examples: StringBuilder (.Net/Java), StringBuffer (Java), NSMutableString (Cocoa), std::string (C++).
●
(To make working with string-like types simpler in Java, String, StringBuffer and StringBuilder implement the interface CharSequence.)
Indexed Collections – Part II

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An important shortcoming of arrays in C/C++ is their undefined behavior, if indexes exceed array bounds.
●
Modern platforms (Java/.Net) introduce bounds checking of array-access via indexes during run time with exceptions
:
●
Indexed collections beyond arrays (e.g. lists) usually support bounds checking with exceptions as well.
// C#:
int numbers = new int[5];
numbers[10] = 10; // Well defined! Will throw ArgumentOutOfRangeException.
// We could also handle ArgumentOutOfRangeException (not recommended):
try
{
int value = numbers[-3]; // Well defined! Will throw ArgumentOutOfRangeException.
}
catch(ArgumentOutOfRangeException)
{
Console.WriteLine("ArgumentOutOfRangeException thrown.");
}
// C++
int numbers[5];
numbers[10] = 10; // Undefined! Above number's bounds.
int value = numbers[-3]; // Undefined! Below number's bounds.
Indexed Collections and "Bounds checked Arrays"

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Now its time to introduce our first collection "beyond" arrays: the list.
– Java/.Net provide a implementation of list: ArrayList. ArrayList is an object-based collection, let's understand what that means for us.
●
Terminology alert: in Lisp and C++ lists are linked lists and no indexed collections!
●
ArrayLists can only store objects of the static .Net type Object! Therefor ArrayList is said to be an object-based collection.
– That's no problem! - The dynamic type stored in ArrayList can be any type derived from Object.
– Each .Net type is derived from Object, therefor any .Net type can be stored in ArrayList as dynamic type.
●
There is just one quirk with object-based collections: we have to use downcasts to get the formerly stored values back!
– This means: we as programmers have to remember the types of the stored values, i.e. their dynamic types!
// C#:
// Create an ArrayList of two elements (passing an int[] to the ctor):
ArrayList aList = new ArrayList(new[]{42, 18});
// 42 and 18 are then stored on the indexes 0 and 1 (ArrayList's index is 0-based).
// When we fetch the values back, we just get objects of the static type Object back:
object the42 = aList[0];
object the18 = aList[1];
// We have to use cast contact lenses to get the dynamic types out of the objects:
int the42AsInt = (int)the42;
// We can also cast directly from the indexer notation:
int the18AsInt = (int)aList[1];
// .Net System.Collections.ArrayList (C#)
public class ArrayList { // (Details hidden)
// The "operator[]":
public object this[int index] {
get { /*pass*/ }
set { /*pass*/ }
}
}
[0] [1]
(int)
(int)
aList (Object[2])
(logical representation)
Indexed Object-based Collections
● Mind how C#'s indexer (i.e. the "operator[]")
makes using ArrayLists look like arrays.

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Creating the empty list names:
●
Then we can add two elements like so:
●
We can access the elements of a list like so (bounds checked):
●
We can set the elements of a list to new values like so (bounds checked):
●
We can get the current count of elements stored in the list:
// C#:
ArrayList names = new ArrayList();
names.Add("James");
names.Add("Miranda");
// Java:
names.add("James");
names.add("Miranda");
// Get the values back (object-based collection):
object name1 = names[0]; // "James" (static type Object)
object name2 = names[1]; // "Miranda"
// Cast the strings out of the objects:
string name1AsString = (string)name1;
// We can also cast directly from the index notation:
string name2As = (string)names[1];
// Get the values back (object-based collection):
Object name1 = names.get(0); // "James" (static type Object)
Object name2 = names.get(1); // "Miranda"
// Cast the strings out of the objects:
String name1AsString = (String)name1;
// We can also cast directly from the getter-call:
String name2As = (String)names.get(1);
names.set(1, "Meredith");
System.out.println(names.get(1));
// >Meredith
names[1] = "Meredith";
Console.WriteLine(names[1]);
// >Meredith
names.add("Christie"); // Adding one more element.
System.out.println(names.size());
// >3
names.Add("Christie"); // Adding one more element.
Console.WriteLine(names.Count);
// >3
C# - collection initializers
// Alternatively create and initialize with a collection
// initializer:
ArrayList names2 = new ArrayList{ "James", "Miranda" };
List – Basic Operations
● As can be seen, in Java expressions like array[i]
just need to be replaced by list.get(i)/list.set(i).
● Groovy's syntax (Groovy is based on the Java
platform) for creating arrays does directly create
ArrayLists instead of bare arrays. (But Groovy
permits the []-operator to access ArrayLists!)

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Removing elements (bounds checked):
●
Inserting elements (bounds checked):
●
Find an element:
●
Other operations (selection):
// Removes the first occurrence of "James" from names.
// - If the specified value is not in the list, nothing will be removed.
names.Remove("James");
// - If the specified index is out of bounds of the list, an
// ArgumentOutOfRangeException will be thrown.
names.RemoveAt(0);
// Inserts "Karl" into names at the specified index.
// ArgumentOutOfRangeException will be thrown.
names.Insert(0, "Karl");
// Returns the index where "Karl" resides in names or -1.
int foundIndex = names.IndexOf(value);
names.Clear();
names.AddRange(new[]{"Mary", "Jane"});
names.Reverse();
// Removes the first occurrence of "James" from names.
// - If the specified value is not in the list, nothing will be removed.
names.remove("James");
// IndexOutOfBoundsException will be thrown.
names.removeAt(0);
// Inserts "Karl" into names at the specified index.
// IndexOutOfBoundsException will be thrown.
names.add(0, "Karl");
// Returns the index where "Karl" resides in names or -1.
int foundIndex = names.indexOf(value);
names.clear();
names.addAll(Arrays.asList("Mary", "Jane"));
boolean listIsEmpty = names.isEmpty();
List – Other important Operations

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(Yes, it can be done simpler. This is only an example.)
●
We don't know the count of lines in advance: a list seems to be a good collection, because it can grow! Solve it with list!
// C#:
// Begin with an empty list:
ArrayList allLines = new ArrayList();
string line = null;
StreamReader file = new StreamReader("/Library/Logs/Software Update.log");
// Read the file line by line:
while(null != (line = file.ReadLine()))
{
// Add each line to the list as String:
allLines.Add(line);
}
// Output all the read lines to the console:
for (int i = 0; i < allLines.Count; ++i)
{
// As ArrayList is object-based, we've to cast the element back to String:
string storedLine = (string)allLines[i];
Console.WriteLine(storedLine);
}
List – Practical Example:
Reading a File Line by Line into a List

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We could iterate over the list to search a specific entry ("2008-11-24 23:02:24 +0100: Installed "Safari" (3.2.1)"):
●
Often collections provide more clever operations to check containment of objects directly, e.g. with .Net's method Contains():
– This code does effectively the same as the snippet above, but this time we delegate the search procedure to the list itself!
– As can be seen no loop or comparison is required, list's method Contains() does everything for us!
bool containsSafari = false;
// Iterate over all entries of the list:
for (int i = 0; i < allLines.Count; ++i)
{
// Find a certain element in the list:
string entry = (string)allLines[i];
if (entry.Equals("2008-11-24 23:02:24 +0100: Installed "Safari" (3.2.1)"))
{
containsSafari = true;
break;
}
}
Console.WriteLine("Contains 'Safari': {0}", containsSafari);
// > Contains 'Safari': True
// Let's ask the list to find the contained element:
bool containsSafari = allLines.Contains("2008-11-24 23:02:24 +0100: Installed "Safari" (3.2.1)");
Console.WriteLine("Contains 'Safari': {0}", containsSafari);
// > Contains 'Safari': True
List – Practical Example:
Does the List contain a certain element?
● Java's interfaces List/Collection provide the
method contains().

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Esp. in functional programming (fp) languages there exist very sophisticated ways tocreate filled lists w/o loops.
– This is required, because lists can usually not be modified after creation in fp languages. For example in Lisp and Haskell:
– What we see here in action is called list comprehension, it means to create collections with complex content in one expression.
●
Non-fp languages have been updated to provide list comprehensions in order to get compact expressiveness:
// F#
let numbers = [1..9]
// >[0; 1; 2; 3; 4; 5; 6; 7; 8; 9]
let numbersSquaredList = [ for n in 1 .. 9 -> n * n ]
// > [1; 4; 9; 16; 25; 36; 49; 64; 81]
let numbersSquaredArray = [| for n in 1 .. 9 -> n * n |]
// > [|1; 4; 9; 16; 25; 36; 49; 64; 81|]
List – List Comprehensions
– Haskell
numbers = [1..9]
-- >[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
numbersSquared = [n * n | n <- [0..9]]
-- >[1, 4, 9, 16, 25, 36, 49, 64, 81]
; Common Lisp (loop macro)
(loop for n from 1 to 9 collect n)
; >(1 2 3 4 5 6 7 8 9)
(loop for n from 1 to 9 collect (* n n))
; >(1 4 9 16 25 36 49 64 81)
// C# (version >= 3 provides query expressions)
var numbers = Enumerable.Range(1, 9).ToList();
// > 1, 2, 3, 4, 5, 6, 7, 8, 9
var numbersSquared = (from n in Enumerable.Range(1, 9)
select n * n).ToList();
// > 1, 4, 9, 16, 25, 36, 49, 64, 81
// Java (version >= 8 provides streams)
List<Integer> numbers = IntStream.range(1, 10).boxed().collect(Collectors.toList());
List<Integer> numbersSquared = IntStream.range(1, 10)
.map(n -> n * n)
.boxed()
.collect(Collectors.toList());
// > 1, 4, 9, 16, 25, 36, 49, 64, 81
// Groovy
def numbers = (1 .. 9).toList()
// >[0; 1; 2; 3; 4; 5; 6; 7; 8; 9]
def numbersSquared = (1 .. 9).collect{it * it}
// >[1, 4, 9, 16, 25, 36, 49, 64, 81]
numbers={n | n∈N , n<10}
numbersSquared={n
2
| n∈N , n<10}
Mathematical set builder notation

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When we think about the implementation of an indexed collection we can assume that it isbacked by an array.
– This means that indexed collections encapsulate or simulate arrays of varying size. - That's straight forward!
– Now we'll clarify how managing of indexed collections' internal space for contained elements works.
●
Most interesting are obviously methods like ArrayList's method add() in Java. It could be implemented like so:
●
But the assumed implementation of add() has a serious problem: it is very inefficient!
– Every time a new element is added two operations are going on basically:
●
(1) enlarge: the encapsulated array elementData is copied to a new array having the old length + 1
●
(2) append: and then the new element is set as last element in the new array.
// Java: (fictive implementation of ArrayList.add())
public boolean add(Object element) {
// Enlarge and append:
elementData = Arrays.copyOf(elementData, elementData.length + 1);
elementData[elementData.length - 1] = element;
}
ArrayList names = new ArrayList(); // Creates an ArrayList of zero elements.
names.add("James"); // Create a new internal array of size one.
names.add("Miranda"); // Create a new internal array of size two.
names.add("Helen"); // Create a new internal array of size three.
ArrayList
- elementData : Object[]
+ add(Object element)
Indexed Collections – Size and Capacity – Part I

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Indeed the real implementation of ArrayList is more clever! ArrayList uses the idea of capacity for more efficiency.
●
Let's create another empty ArrayList in Java:
– The real representation of names looks not very empty!
●
The actual memory representation:
– As can be seen names is not really empty.
– names' field elementData (this is the encapsulated Object-array) has an initial length of ten.
– All elements of elementData have the initial value null.
– But names exposes a size of zero! - What the heck is going on?
●
ArrayList has an initial size of zero and an initial capacity of ten!
– In modern collection APIs, collections maintain capacity and size separately, let's understand why this is a good idea ...
names (ArrayList)
elementData (Object[10])
size
0
null null null null null null null null null null
// Java:
Indexed Collections – Size and Capacity – Part II

23
23
●
With ArrayList's initial capacity of ten we can add ten elements, before a new elementData-array needs to be created:
– Let's begin with adding three Strings to names:
– Add another seven Strings to names:
– Then we add another, the eleventh String to names...
●
...when the capacity of the ArrayList is
exhausted, the encapsulated array
(elementData) needs to be enlarged.
– (1) A new bigger array is created and
– (2) the content of the old array is copied to the new array.
●
(In this implementation, elementData is enlarged for five elements, so the new capacity is 15.)
– (3) The last element (the eleventh element) will be set to the added element.
names (ArrayList)
size
3
"James" "Miranda""Helen"
names.add("James");
names.add("Miranda");
names.add("Helen");
null null null null null null null
names.addAll(Arrays.asList("Gil", "Trish", "Simon"));
names.addAll(Arrays.asList("Clark", "Jeff", "Sam", "Ed"));
names (ArrayList)
size
10
"James" "Miranda""Helen""Gil""Trish""Simon""Clark""Jeff""Sam""Ed"
names.add("Joe");
names (ArrayList)
size
11
"James" "Miranda""Helen""Gil""Trish""Simon""Clark""Jeff""Sam""Ed""Joe"null null null null
Indexed Collections – Capacity Control – Part I
● The values of the initial capacity as well the
amount of growth/increment of the capacity should
be taken from the spec. of the platform in
question. Tip: In practice programmers should not
rely on these specs, but rather control the capacity
themselves.

24
24
●
We just learned that when the required space of an ArrayList exceeds its capacity, the internal memory is "re-capacitized".
●
Of course it is! The idea of the encapsulated array's capacity apart from the collection's size is todefer the need to
"re-capacitize" the encapsulated array to the latest thinkable occasion: When size gets greater than capacity.
– But there is a problem: if we constantly exceed the capacity of a collection, it will often be re-capacitized.
●
Yes, we can solve this problem with capacity control!
– One idea of capacity control is to set the required capacity of a collection, before elements are added, e.g. like so:
– Add ten elements; the size will be below the capacity:
– Then we add the eleventh element...
– ...this just meets the capacity of names
– => With capacity control there was no need for "re-capacitation"!
names.addAll(Arrays.asList("James", "Miranda", "Helen", "Gil", "Trish", "Simon", "Clark", "Jeff", "Sam", "Ed"));
int initialCapacity = 11; // Ok, we know in advance that we're going to add eleven elements to names. So we can set the required capacity early!
ArrayList names = new ArrayList(initialCapacity); // E.g. we can specify the capacity right in the ctor.
names (ArrayList)
size
0
null null null
"James" null null
"Miranda" null null
"Helen" null null null null
"Gil""Trish""Simon"
names.add("Joe");
"Clark""Jeff""Sam""Ed"null
"Joe"
10
11
Indexed Collections – Capacity Control – Part II

25
25
●
Collections (not only indexed collections) often provide a set ofmethods/properties to manage capacity.
– The capacity is the number of elements a collection can store; the size is the actual number of elements a collection contains.
– => This must always be true: capacity >= size.
●
Collections may have ctors to set the initial capacity overriding the default capacity, e.g. initializing it w/ a capacity of eleven:
●
Some collections allow setting a certain minimum capacity, or to set the capacity directly:
●
But names' size is still eleven!
// Java:
ArrayList names = new ArrayList(11);
names.addAll(Arrays.asList("James", "Miranda", "Helen", "Gil",
"Trish", "Simon", "Clark", "Jeff", "Sam", "Ed", "Joe"));
// C#:
ArrayList names = new ArrayList(11);
names.AddRange(new []{"James", "Miranda", "Helen", "Gil",
"Trish", "Simon", "Clark", "Jeff", "Sam", "Ed", "Joe"});
names.ensureCapacity(20); names.Capacity = 20;
boolean hasEleven = names.size() == 11;
// hasEleven evaluates to true.
bool hasEleven = names.Count == 11;
// hasEleven evaluates to true.
Performance guideline
● If the effective size of a collection to be created is known ahead,
set the capacity as soon as possible, e.g. in the ctor.
● If memory is low, it can be helpful to set a small capacity for a new
collection or to trim the capacity of existing collections to size.
Indexed Collections – Capacity Control – Part III
● Some IDEs allow enabling a warning during code
inspection, if a collection w/o explicitly specified
capacity is filled.

26
26
●
Collections can also be created along with a bulk of data, which can yield performance benefits due to efficient capacitation:
– (Not all platforms apply capacity control on bulk operations!)
●
Often collections can also be filled with items in bulk after creation:
Indexed Collections – Capacity Control – Part IV
// Java; instead of adding items to a list with a loop...
List<Integer> numbers = new ArrayList<>();
for (int item : new int[]{1, 2, 3, 4}) {
numbers.add(item);
}
// … the list could be initialized with another "ad hoc" collection like an array:
List<Integer> numbers2 = new ArrayList<>(Arrays.asList(1, 2, 3, 4));
// C#; instead of adding items to a list with a collection initializer or loop...
IList<int> numbers = new List<int>{1, 2, 3, 4};
IList<int> numbers2 = new List<int>();
foreach (int item in new []{1, 2, 3, 4}) {
numbers2.Add(item);
}
// … the list could be initialized with another "ad hoc" collection like an array:
IList<int> numbers3 = new List<int>(new []{1, 2, 3, 4});
// Java; adding a couple of items to a list in bulk:
List<Integer> numbers = new ArrayList<>();
numbers.addAll(Arrays.asList(1, 2, 3, 4))
// Alternatively Collections.addAll() can be used (its usually faster):
Collections.addAll(numbers, 1, 2, 3, 4);
// C#; adding a couple of items to a list in bulk:
List<int> numbers = new List<int>();
// (Mind that AddRange() isn't available via the interface IList!)
numbers.AddRange(new []{1,2,3,4});
● Java's Collections.addAll() is faster than
Collection.addAll() because the latter creates a
redundant array.

(2) collections algorithms

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