(chapter 4) A Concise and Practical Introduction to Programming Algorithms in Java

1A Concise and Practical Introduction to Programming Algorithms in Java © 2009 Frank Nielsen
Frank NIELSEN
nielsen@lix.polytechnique.fr
A Concise and
Practical
Introduction to
Programming
Algorithms in Java
Chapter 4: Arrays and strings

Why do we need arrays?
● To handle many variables at once
● Processing many data or generating many results
● In mathematics, we are familiar with variables
with indices:
In most languages, indices start at zero
(and not one).
...Just a convention

Declaring arrays in Java
For a given type, TYPE[ ] is the type of arrays
storing elements of type TYPE.
● For arrays declared within the scope of functions:
● int [ ] x;
● boolean [ ] prime;
● double [ ] coordinates;
● float [ ] [ ] matrix;
● For arrays declared in the body of a class, use the keyword static:
(array variables can be used by any function of the class)
● static int [ ] x;
● static boolean [ ] prime;

Building and initializing arrays
Observe:
static boolean prime[ ]={ false, true, true, true, false, true, false, true, false, false };
but not
static boolean prime[10]={ false, true, true, true, false, true, false, true, false, false };

Building and initializing arrays
● Declare array with the reserved keyword new
● Specify the size of the array at built time
● Arrays can be declared and initialized at once too:
● int [ ] x;
● x=new int [32];
● boolean [ ] prime = new boolean[16];
● Arrays initialized by enumerating all its values:
int [ ] prime={2, 3, 5, 7, 11, 13, 17, 19};

Size of arrays
Size of arrays is given by the member function length:
prime.length;
System.out.println(prime.length);
Size of arrays fixed for once, cannot be changed:
array.length=23; // Generate an error

Size of arrays

Index range of arrays and exceptions
Powerful mechanism of modern languages (Java, C++)
If index is out of range, an exception is raised on the fly:
ArrayIndexOutOfBounds
Out of range accesses may not be detected by the compiler:
Bug that yields termination or system crash
... However, fortunately, Java can catch exceptions too.

Size of arrays cannot be modified

Index range of arrays and exceptions
Observe the correct parsing

The concept of references
An array is allocated as a single contiguous memory block
Java is managing memory so you do not have to free it
once the array is not used anymore: garbage collector
An array variable is, in fact, a reference to the array
This reference of the array is the symbolic address of
the first element (index 0)
Thus, when we write...
int [ ] v = {0, 1, 2, 3, 4};
int [ ] t =v;
t[2]++;
System.out.println(t[2]++);
... the elements of the array v are not copied verbatim to t. Only the reference!!!

Arrays & references

Functions & arrays
Functions and procedures can have arrays as arguments.
(remember that array types are: TypeElement[ ])
Example: Function that returns the minimum of an array of integers

Functions & arrays
Example: Function that returns the inner product of 2 vectors
(produit scalaire)

Array arguments in functions
A variable that has a type array is a reference to the array
(the memory address of the first element)
Therefore an argument of type array does not copy
all array elements in the memory allocated for the function,
but rather allocate a single memory reference:
a machine word.
static void MyFunction(int [ ] x)
MyFunction(v);
Only the reference of v is copied to the memory allocated for
the function MyFunction.

Array arguments in functions
Thus we can modify the inside a function the contents of
the array: the values of the elements of the array.

Functions returning an array

Arrays of arrays...
So far, we described linear array (1D).
What about matrices (2D arrays)?
A bidimensional array (n,m) consists of n lines,
each of which is an array of m elements
int [ ] [ ] matrix;
matrix=new int[n][m];
By default, at initialization, the array is filled up with zero
Change the contents of 2D arrays using 2 nested loops:
for(int i=0; i<n; i++)
for(int j=0; j<m;j++)
matrix[i][j]=i*j+1;

2D Arrays: Matrix x vector product

Dichotomic search
Also called binary search algorithm
Assume we are given a sorted array of size n:
array[0] < array[1] < ... < array[n-1]
and a query key p
Seek whether there is an element in the array that has value p
That is, give a function that return the index of the element in
the array with value p, or that returns -1 otherwise.

Dichotomic search: Think recursion!
● Start with a search interval [left, right] with left=0 and right=n-1
● Let m denote the middle of this interval: m=(left+right)/2
● If array[m]=p then we are done, and we return m;
● If array[m] <a, then if the solution exists it is in [m+1,right]
● If array[m]>a, then if the solution exists it is in [left,m+1]
● The search algorithm terminates if left>right, we return -1;

Dichotomic search: Recursion

Strings: Basic objects in Java
● A string of character is an object with type String
● A variable of type String is a reference on that object:
String school= ''Ecole Polytechnique'';
String vars=school;
● Once built, a string object cannot be modified
● Beware: use only for moderate length strings,
otherwise use the class StringBuffer

Class String: Some methods
A method is a function or procedure on an object class
Method Length() : gives the number of characters
String s= ''anticonstitutionnellement'';
System.out.println(s.length());
Method equals():
s1.equals(s2): Predicate that returns true if and only if the
two strings s1 and s2 are made of the same sequence of characters.
String s1=''Poincare'';
String s2=TC.lireMotSuivant();
System.out.println(s1.equals(s2));
Beware: s1==s2 is different!
It compares the reference of the strings.
(Physical versus logical equality test)

Class String in action...

Class String: More methods
Method charAt():
s.charAt(i) gives the character at the (i+1)th position in string s.
String s= ''3.14159265'';
System.out.println(s.charAt(1));
Method compareTo():
u.compareTo(v) compares lexicographically the strings u with v.
String u=''lien'', v=''lit'', w=''litterie'';
System.out.println(u.compareTo(v));
System.out.println(v.compareTo(w));

Class String: More methods

Demystifying the main function
class ClassName
{
public static void main(String[ ] args)
{
...
}
}
Function main has an array of string of characters as arguments
These strings are stored in args[0], args[1], ...
... when calling java main s0 s1 s2 s3
Use Integer.parseInt() to convert a string into an integer

Parsing arguments in the main function

(chapter 4) A Concise and Practical Introduction to Programming Algorithms in Java

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(chapter 4) A Concise and Practical Introduction to Programming Algorithms in Java