Transcript sorting algorithms in Java

Arrays
● Java programming language provides a data structure
called the array ( ‫) מערך‬, which can store a fixed-size
sequential collection of elements of the same type.
● Arrays are widely used within Java programming
for different purposes such as sorting, searching
and etc.
1
Problems with simple variables
• Hard to give up values high number of variables.
• Complex to sort a high number of variables by value.
• Impossible to use loops .
Example problem:
Read one hundred numbers, compute their average, and find
out how many numbers are above the average.
We can use an array instead of a variables.
2
Array definition
•
•
•
•
•
An array ) ‫ ( מערך‬is a collection of variables of the same data type, and
the collection is assigned a name.
Array can be declared for any type.
In Java an array is an object ) ‫( עצם‬.
Each variable within the collection is called an array element.
An array element is identified by combining the array name and a
unique index ) ‫( אינדקס‬. An index is an integer from zero to 1 minus the
maximum number of elements in the array.
An array of size N is indexed from 0 to N – 1.
•
Array examples:
–
–
–
–
list of students’ marks
series of numbers entered by user
vectors
matrices
3
Array indexing
In Java ,array indexes always begin at zero.
The array myList has 10 values, indexed from 0 to 9.
The i-th element of array myList is specified by myList[i-1].
double[] myList = new double[10];
myList
reference
Array reference
variable
Array element at
index 5
myList[0]
5.6
myList[1]
4.5
myList[2]
3.3
myList[3]
13.2
myList[4]
4
myList[5]
34.33
myList[6]
34
myList[7]
45.45
myList[8]
99.993
myList[9]
11123
Element value
4
Declaring array variables
● In Java arrays are objects ( ‫) עצם‬. To create an array, the reference
( ‫ )הפניה‬to the array must be declared.
● The array can be created using the new operator, which
allocates memory space to store values.
Examples:
double [ ] myList = new double [ 10 ];
The variable myList is declared to be an array of 10 real numbers whose
type is written as double[ ].
int [ ] studGrades = new int [ 85 ];
The variable studGrades is declared to be an array of 85 integer numbers
whose type is written as int[ ].
Note: once an array is declared to be a certain size, the number of values it
can hold cannot be changed.
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Default values and initialization
● When an array is created, its elements are
assigned the default value of :
0
for the numeric primitive data types
'\u0000' for char data types
False
for boolean data types.
● Declaring, creating, initializing in one step:
double [ ] myList1 = { 1.9, 2.9, 3.4, 3.5 };
Note: Don’t use new operator if you plan to initialize the
array.
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Accessing array elements
● To access a value in an array, we use the name of array followed
by the index in square brackets.
int [ ] arr = { 69,61,73,19,37 };
arr[ 2 ] = 95; // initial value was 73
● Array indexes are integers and we can use integer expression to specify
the index.
int a = 7, b = 2,c = -3;
arr[ a/b ] = 71; // initial value was 19
System.out.println( arr[a + c] ); // output value is 37
NOTE :when accessing array elements, be careful to ensure
that the index stays within the array bounds.
7
The length of an array
• In order to get the number of elements in an array,
you can use the length attribute of an array.
• The length attribute of an array returns the size of
the array ( number of elements).
• It can be used by writing arrayName.length
For example :
int a = myList.length; // a = 10
int b = studGrade.length; // b = 85
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Array as Java object
● Java array is a container object that holds a fixed number of values of a
single type.
● The array declaration allocates only enough space for a reference to an
array but doesn't create the actual array object.
For example:
reference
int[ ] num = new int[5];
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The Assignment Operators and Arrays
int[ ] listA = { 5, 10, 15, 20, 25, 30, 35 };
int[ ] listB = new int[7];
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The Assignment Operators and Arrays
Arrays after assignment statement ListB = ListA;
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Array example 1
The next program section reads N integers into
an array and then reverses them and prints.
N value reads during the program execution.
5
15
103
-2
71
Before revers
71
-2
103
15
5
After revers
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Example 1 - solution
System.out.print( "Enter the number of array elements : “ );
int [ ] arr = new int [reader.nextInt()];
number of array elements
reads during the program running
for (int i = 0; i < arr.length; i++)
{
System.out.print("Enter number "+ (i+1) + " integer : “ );
arr[i] = reader.nextInt();
} // for
It is often convenient to use for loops
for (int i = 0; i < arr.length/2; i++)
when handling array, because
{
the number of its elements is constant.
int temp = arr[i];
arr[i] = arr[arr.length – i - 1];
arr[arr.length-i-1] = temp;
} // for
System.out.println(" The numbers in revers order : ");
for (int i = 0; i <arr.length; i++)
System.out.println(arr[i]);
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Array example 2
This program reads N integer number sequence and builds an array.
The program builds an array from a sequence ( some numbers can appear
twice or more in the sequence but appears only once in the array ).
For example:
N = 9 and input sequence is 9, 9, 5, 4, 4, 4, 1, 1, 7
arr
0
1
2
3
4
5
6
7
8
9
5
4
1
7
0
0
0
0
Note: maximum array’s elements is N , because each number can appears
only once in the sequence.
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Example 2 - solution
static final int N = 9;
public static void main (String[] args)
{
int [ ] arr = new int[N];
int j = 1; // array index
int num; // input variable
arr[0] = reader.nextInt();
for (int i = 0; i < N - 1; i++)
{
num = reader.nextInt();
if(num != arr[j-1])
{
arr[j] = num;
j++;
} //if
} // for
for(int i = 0; i < j; i++)
System.out.println(arr[i]);
} // main
final keyword when used with a
variable makes it a constant.
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Array example 3
This program section reads 10 integers into an array, finds the max and
min values of array elements and prints them.
If a variable is marked as final then the value
of that variable cannot be changed i.e
final keyword when used with a variable
makes it a constant.
static final int N=10;
public static void main (String[] args) {
int [] arr = new int[N];
for (int i = 0; i < N; i++)
arr[i] = reader.nextInt();
int max = arr[0],min = arr[0];
for (int i = 1; i < N; i++)
{
max = (arr[i]>max) ? arr[i] : max;
min = (arr[i]<min) ? arr[i] : min;
} //for
System.out.println(" The max element is : "+max);
System.out.println(" The min element is : "+min);
} //void main
if (arr[i]) > max
max = arr[i];
else
max = max;
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Array example 4
This program calculates the number of different values in array of integers.
public static void main (String[] args)
{
int a[ ] = { 5, 5, 2, 9, 3, 2, 5, 9, 3, 5 }; // array of integers
int i, j; // loop counters
int count = 1; // accumulator
for(i =1; i < a.length; i++)
{
for(j = 0; j < i; j++)
if(a[j] == a[i])
break;
if(j == i)
count++;
} // for
System.out.println(“The number of different values is : “ + count);
} // main
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Array example 4
Trace table ( i < 3 only )
count
i
i<3
1
T
j
j<i
a[ j ] == a[ i ]
0
T
T
0
T
F
1
T
F
2
F
1
2
T
public static void main (String[] args)
{
int a[ ] = { 5, 5, 2 }; // array of integers
int i, j; // loop counters
int count = 1; // accumulator
for(i =1; i < a.length; i++)
{
j == i
for(j = 0; j < i; j++)
if(a[j] == a[i])
break;
if(j == i)
count++;
F
} // for
System.out.println(count);
} // main
T
2
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Array example 5
static final int N = 26;
public static void main (String[] args)
{
int [] arr = new int[N];
int m = 0; // help variable
This program reads 100 letters and …?
for (int i = 0; i < N; i++)
arr[i] = 0;
for (int i = 0; i < 100; i++)
{
System.out.println(" Enter a letter: ");
char ch = reader.next().charAt(0);
arr[ch – ‘a’] ++;
} // for
for (int i = 1; i < N; i++)
if(arr[i] > arr[m])
m = i;
char mch = (char)(m + ’a’);
System.out.println(" mch : “ + mch);
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} // main
Sorting ( ‫)מיון‬
• Sorting is the process of arranging a list of items in
well – defined order.
• Sorting values of array elements is one of the basic
array manipulations.
• Many sorting algorithms have been developed
over the years.
In this course we examine two sorting algorithms:
selection sort (‫ )מיון בחירה‬and insertion sort ( ‫מיון‬
‫)הכנסה‬.
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Selection sort algorithm
The selection sort algorithm selects for each position
in the list the value, that should go in this position, and puts it there.
23
15
6
7
30
Scan starting with 23.
6 is smallest. Exchange 6 and 23
6
15
23
7
30
Scan starting with 15.
7 is smallest. Exchange 7 and 15
6
7
23
15
30
Scan starting with 23.
15 is smallest. Exchange 15 and 23
6
7
15
23
30
Scan starting with 23.
23 is smallest. Exchange 23 and 23
6
7
15
23
30
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Selection sort implementation
This program section uses a selection sort to arrange a list of integer
values into ascending order ( ‫) סדר עלה‬.
int [ ] arr = { 23,15,6,7,20 };
The outer loop controls the position where
for(int i = 0; i < arr.length; i++) the next smallest value will be stored.
{
int min_pos = i;
for(int j = i+1; j < arr.length; j++)
{
The inner loop finds the smallest value in
if ( arr[j] < arr[min_pos] )
min_pos = j; the rest of the list .
When the smallest value is determined, it is
int temp = arr[i]; // help variable
exchanged with the value stored at the
arr[i] = arr[min_pos];
index.
arr[min_pos] = temp;
} // inner for
} // outer for
The algorithm can easily be changed to put values in descending order ( ‫) סדר יורד‬
by finding the largest value each time.
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Insertion sort algorithm
The insertion sort algorithm works by inserting each value into a previously
sorted subset of the list.
3
9
6
1
2
3 is sorted.
Shift nothing. Insert 9.
3
9
6
1
2
3 and 9 are sorted.
Shift 9 to the right. Insert 6.
3
6
9
1
2
3 ,6 and 9 are sorted.
Shift 9,6 and 3 to the right.
Insert 1.
1
3
6
9
2
1,3 ,6 and 9 are sorted.
Shift 9,6 and 3 to the right.
Insert 2.
1
2
3
6
9
All values are sorted
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Insertion sort implementation
int [ ] arr = { 3,9,6,1,2 };
for (int i = 1; i < arr.length; i++)
{
The outer loop controls the
index in the array of the next
int j = i;
value to be inserted.
int a = arr[i];
while ( j > 0 && arr[ j-1] > a)
{
arr[ j ] = arr[ j-1];
j--;
} // block while The inner loop compares the current insert
values with values stored with lower indexes.
arr[ j ] = a;
If the current insert value is less then the value
at j position, that value is shifted to the right.
} // block for
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Java searching ( ‫(חיפוש‬
• Searching (‫ )חיפוש‬is an operation which finds the location of
a given element in an array.
• The search is said to be successful or unsuccessful
depending on whether the element that is to be searched is
found or not.
• Definition: A key is a value that you are looking for in an
array. If found, the index of the first location of the key will be
returned. If not found, a value of -1 will be returned.
• In this course we examine two searching algorithms:
- linear search (‫)חיפוש סדרתי‬
- binary search (‫)חיפוש בינארי‬.
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Linear search
• The simplest type of search is the liner (sequential) search.
• In the liner search, each element of the array is compared to the key, in
the order it appears in the array, until the desired element is found.
System.out.println( “enter search key”);
int num = reader.nextInt(); // input key value
boolean flag = false;
This searching type can be applied
for( int i = 0; i < arr.length; i++)
to a sorted or an unsorted list.
{
if (arr [i] == num)
{
Searching in case of unsorted list
flag = true;
starts from the 0th element and continues
break;
until the element is found or the end of list is
} // if
reached.
} // for
if (flag )
System.out.println(num + " is at position “ + i);
else
System.out.println(num + " not found ");
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Linear search in sorted array
int i; // loop counter
System.out.println( “enter search key” );
int num = reader.nextInt(); // input key value
for(i=0; i< arr.length && num > = arr[i]; i++)
{
if (arr [i] == num)
{
System.out.println(num + " is at position "+i);
break;
In case of sorted list we breaks the loop if
}
the key value founded.
} //for
if (i==0 || i==arr.length || num>arr[i] )
System.out.println(num + " not found ");
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Binary search example 1
Index
0
1
2
3
4
5
6
7
8
9
Find 6 in {-1, 5, 6, 18, 19, 25, 46, 78, 102, 114 }.
low index = 0, high index = 9.
•
Step 1 (middle element is 19 > 6): middle index = ( 0 + 9 ) / 2 = 4
low index = 0, high index = 4 - 1=3
•
Step 2 (middle element is 5 < 6):
middle index = (0 + 3 ) / 2 = 1
low index =0 +1, high index = 3
•
Step 3 (middle element is 6 == 6):
middle index= (1 + 3 ) / 2 = 2
searched element is found !
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Binary search example 2
index
0
1
2
3
4
5
6
7
8
9
Find 103 in {-1, 5, 6, 18, 19, 25, 46, 78, 102, 114}.
•
low index = 0, high index = 9.
Step 1 (middle element is 19 <103): middle index = ( 0 + 9 ) / 2 = 4
low index =4+1, high index = 9
•
Step 2 (middle element is 78 < 103): middle index = (5 + 9 ) / 2 = 7
low index =7 +1, high index = 9
•
Step 3 (middle element is 102 <103): middle index= (8 + 9 ) / 2 = 8
low index =8 +1, high index = 9
•
Step 4 (middle element is 114 >103): middle index= (9 + 9 ) / 2 = 9
low index =9, high index = 9 – 1 = 8
low index > high index : searched value is absent !
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Binary search algorithm
1. Get the middle element;
2. If the middle element equals to the searched value,
the algorithm stops;
3. Otherwise, two cases are possible:
– searched value is less, than the middle element. In
this case, go to the step 1 for the part of the array,
before middle element.
– searched value is greater, than the middle element. In
this case, go to the step 1 for the part of the array,
after middle element.
Now we should define, when iterations should stop.
First case is when searched element is found.
Second one is when sub-array has no elements. In this
case, we can conclude, that searched value isn't present
in the array.
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Binary search implementation
int [ ] arr = { -1,5,6,18,19,25,46,78,102,114 };
int i = 0,h = arr.length; // low and high array indexes
System.out.pirnt ("enter search key => ");
int num = reader.nextInt(); // input key value
while (i < h)
{
int mid = (i + h) / 2; // Compute mid point.
if (num < arr[mid])
h = mid;
else
if (num > arr[mid])
i = mid+1;
else
{
System.out.println( "found in "+mid+" position“ );
break;
}
} //while
if ( i >= h )
System.out.println(num + " not found “ );
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32
Strings
) ‫(מחרוזות‬
• Java string is a sequence of characters.
• They are objects of type String.
• Once a String object is created it cannot be changed.
Basic string operations:
String st = “Hello,word”;
Note: double quotations
String c1 = “color red”, c2, c3 =“color green”;
String bl = “ ”; // one character string
String day = reader.next();
System.out.println(“ The day is : “ + day);
String[ ] days ={ “Sunday”, “Monday”, “Thursday” };
0
1
2
3
4
c
o
l
o
r
5
6
7
8
r
e
d
Like array, every character in the string has its index,
but we can’t access it directly !.
index
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String methods 1
1.string.length(); returns the length of this string.
String palindrome = "Dot saw I was Tod";
int len = palindrome.length();
System.out.println( "String Length is : " + len );
This would produce
String Length is : 17
2.Concatenating Strings ( + ) returns a new string that
is string1 with string2 added to it at the end.
String string1 = "saw I was ";
System.out.println( "Dot " + string1 + "Tod“ );
This would produce
Dot saw I was Tod
3.string.charAt(index); returns the character located at the
String's specified index.
String st = “Welcome to Java";
char result = st.charAt(11);
System.out.println(result);
This would produce
following result : J
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String methods 2
4. string1.compareTo(sryring2) - Compares two strings lexicographically:
- The result is zero if the strings are equal.
- The result is a negative integer if string1
lexicographically precedes the string2 string.
- The result is a positive integer if string1 lexicographically
follows the string2 string.
We cannot just compare strings contents by simple if statement :
String st1 = “Hello”;
String st2 = “Hello”;
if(st1==st2) {
…
}
st1
H
e
l
l
o
st2
H
e
l
l
o
because st1 and st2 are memory addresses of st1 and st2.
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compareTo method - cont.
• Characters in Java are based on Unicode character set,
which defines an ordering of all possible characters that can
be used.
• The compareTo method can be used to determine the relative
( lexicographic ) order of strings.
For example:
String st1 = “AARBNML”, st2 = “AARZK”;
st1
st2
0
1
2
3
4
5
6
A
A
R
B
N
M
L
0
1
2
3
4
A
A
R
Z
K
• int x=st1.compareTo(st2); // x = - 24: 0066 - 0090
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compareTo method - examples
For example:
String str1 = "Strings are immutable";
String str2 = "Strings are immutable";
String str3 = "Integers are not immutable";
int result = str1.compareTo( str2 );
System.out.println(result);
result = str2.compareTo( str3 );
System.out.println(result);
result = str3.compareTo( str1 );
System.out.println(result);
This produces following
result:
0
10
-10
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String methods 3
5. string.substring ( index ) returns a new string that is a substring of the
string. The substring begins with the character at the specified index and
extends to the end of this string.
String st1 = “abcdefg”;
String st2 = st1.substring(3); // st2 = “defg”
String st3 = st1.substring(6); // st3 = “g”
6. string1.indexOf(string2) returns the index within string1 of the first
occurrence of the substring2.
If it does not occur as a substring, -1 is returned.
String st1 = “abcdefg”, st2 = “cd”,st3 = “abc”;
int p1 = st1.indexOf(st2); // p1= 2
int p2 = st1.indexOf(st3); // p2 = 0
int p3 = st1.indexOf(“xy”); // p3 = -1
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String methods 4
7. string1.indexOf(string2, ind) returns the index within string1 of the first
occurrence of the substring2 from the ind place .
If it does not occur as a substring from ind place, -1 is returned.
String st1 = “abcdefg”;
int p1 = st1.indexOf(“cd”,5); // p1= -1
int p2 = st1.indexOf (“cd”,1); // p2 = 2
int p3 = st1.indexOf(“ab”,3); // p3 = -1
8. string.substring ( startIndex,endIndex ) returns a new string that is a
substring of the string. The substring begins with the character at the
specified startIndex and extends to the endIndex (but not including).
String st1 = “abcdefg”;
String st2 = st1.substring(3,6); // st2 = “def”
String st3 = st1.substring(2,5); // st3 = “cde”
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String methods 5
9. string1.lastIndexOf(string2) returns the index within string1 of the last
occurrence of the substring2.
If it does not occur as as substring, -1 is returned.
String st1 = “abcdeabfg”;
int p1 = st1.lastIndexOf(“ab”); // p1= 5
int p2 = st1.lastIndexOf (“abc”); // p2 = 0
int p3 = st1.lastIndexOf(“xyz”); // p3 = -1
10. string.replace(oldChar, newChar) returns new string resulting from
replacing all occurrences of oldChar in this string with newChar.
String s1 = “abaabcas”;
String s2 = s1.replace(‘a’, ‘*’); // s2 = “*b**bc*s”
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Empty string
String in Java is considered empty if its length is zero.
Empty String is represented by String literal “”.
For example:
String str1 = “”; // empty string
String with white space are not considered as empty String in Java.
String str2 = “ “; // five characters string
We often needs to check if String is empty or not.
There are two ways to find if String is empty or not.
1. Checking if String is empty by using length() Java method :
if(str1.length() == 0) ….
2. Checking if String is empty by using boolean type isEmpty() Java
method :
if( str1.isEmpty() ) …
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Empty string - example
public class EmptyStringDemo
{
public static void main(String[ ] args)
{
String str = "tutorialspoint";
/* prints length of string str */
System.out.println("length of string = " + str.length());
/* checks if the string str is empty or not */
System.out.println("is this string empty? = " + str.isEmpty());
} // main
} // EmptyStringDemo
This will produce the following result :
length of string = 14
is this string empty? = false
42
String methods - example 1
This program section reads the sentences ,calculates and prints
it word’s numbers.
int words = 0; // words counter
int i = 0; // loop counter
String snc = "Welcome to Java course.";
do
{
This would produce 4
if( snc.charAt(i) == ' ')
words++;
?
i++;
} while( i< snc.length( ) );
System.out.println( "The number of words is: "+ (++words));
43
String methods - example 2
This program section reads the string and tests it.
If the string is palindrome, the program prints “YES”, otherwise “NO”.
public static void main(String[] args)
{
boolean flag = true; // help variable
String str; // input string
System.out.println(“Enter the string”);
str = reader.next();
0
int size = str.length();
a
for(int i = 0; i <size/2 && flag; i++)
if(str.charAt(i) != str.charAt( size – 1 – i)
flag = false;
if(flag)
System.out.println(“YES”);
else
System.out.println(“NO”);
}
Size = 5
1
2
3
4
b
c
b
a
44
String methods - example 3
This program reads the string and builds the array of all
characters from the input string which appears only one time.
For example:
b - 2 times
f - 4 times
input string = "abcbdefdfffgh"
d - 2 times
output array is :
a c e g h
45
example 3
solution
public static void main(String[] args) {
String st = reader.next();
int i, j, k; // loop counters
boolean flag; // help variable
int len = str.length();
char[] helpArray = new char[len]; // help array
for(i = 0;i < len;i++)
helpArray[i] = str.charAt(i);
for(i = 0; i < len-1; i++)
{
for(j = i+1 ,flag = false; j < len; j++)
if(helpArray[i] == helpArray[j])
{
for(k = j ;k < len-1; k++)
helpArray[k] = helpArray[k+1];
flag = true;
j--;
len--;
} // if
46
example 3
solution, cont.
if( flag )
{
for(k = i ;k <len-1; k++)
helpArray[k] = helpArray[k+1];
i--;
len--;
} // if(flag)
} // outer for
char[ ] finArr = new char[len]; // creating output array
for(i = 0;i< len;i++)
finArr[i] = helpArray[i];
/* printing output array */
for(i = 0;i< len;i++)
System.out.print (helpArray[i]);
System.out.println();
} // main
47
‫‪Exam question example‬‬
‫כתוב תכנית הקולטת מחרוזת של טקסט ומדפיסה מחרוזת חדשה המכילה את אותו טקסט‬
‫כאשר‪:‬‬
‫‪48‬‬
Exam question - solution
String s = reader.next();
String fixStr = "";
for(int i = 0; i < s.length(); i++) {
if (s.charAt(i) == '.' || s.charAt(i) == ',') {
/* Remove spaces before point or comma */
for (int j = i-1; j >= 0 && s.charAt(j) == ' '; j--)
fixStr = fixStr.substring(0,fixStr.length() - 1);
fixStr += s.charAt(i) + " ";
/* Remove redundant spaces after point or comma */
while ( i+1 < s.length() && s.charAt(i+1) == ' ')
i++;
} // if
else
fixStr += s.charAt(i);
} // for
/* Remove redundant characters after the last point */
for (int i = fixStr.length() - 1; i >= 0 && fixStr.charAt(i) == ' '; i--)
fixStr = fixStr.substring(0,fixStr.length() - 1);
System.out.println( “ The new string is :” + fixStr);
49
Two - dimensional arrays
• Java, as with most languages, supports multi-dimensional arrays 1-dimensional, 2-dimensional, 3-dimensional, ... In practice most
arrays are one-dimensional, and two-dimensional.
• 2-dimensional arrays ( 2D array) are usually represented with a
row-column "spreadsheet" style.
• Two-dimensional arrays are usually visualized as a matrix, with rows
and columns.
• Assume we have an array, arr, with two rows and four columns.
int [][] arr = new int[2][4]; // Two rows and four columns
Row index
0
1
2
3
0
34
15
105
-43
1
345
-73
88
66
Column index
50
Two - dimensional arrays
A 2D Array in JAVA is really an Array of Arrays:
Assume we have an array :
int [ ][ ] nums = new int[5][4];
The above is really equivalent to a 3step process:
1. create the single reference nums (yellow square)
int [ ][ ] nums;
2. create the array of references (blue squares)
nums = new int[5][ ];
3. this create the second level of arrays (red squares)
for (int i = 0; i < 5 ; i++)
nums[ i ] = new int[4]; // create arrays of integers
51
Two - dimensional arrays
● A 2 - dimensional array in Java can have different numbers of
elements in different rows.
In other words: a 2-dimensional array in Java is made up with many rows
of 1- dimensional arrays.
For example:
NOTE : We will only discuss and use rectangular 2-dimensional arrays
in this course.
52
Declaring, Creating and Initializing
You can also use an array initializer to declare, create and
initialize a two-dimensional array. For example :
int [ ][ ] array = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9},
{10, 11, 12}
};
Same as
int [ ][ ] array = new int[4][3];
array[0][0] = 1; array[0][1] = 2; array[0][2] = 3;
array[1][0] = 4; array[1][1] = 5; array[1][2] = 6;
array[2][0] = 7; array[2][1] = 8; array[2][2] = 9;
array[3][0] = 10; array[3][1] = 11; array[3][2] = 12;
static final int ROW = 4;
static final int COL = 3;
int array = new int [ ROW ][ COL ];
for (int i = 0; i < ROW; i++)
for (int j = 0; j < COL; j++)
arr[i][ j ] = reader.nextInt();
Two-dimensional arrays are almost
always processed with nested for
loops. The two index variables are
often called i and j.
53
Lengths of Two-dimensional arrays
int[ ][ ] x = new int[3][4];
x
x[0][0] x[0][1] x[0][2] x[0][3]
x[0].length is 4
x[1][0] x[1][1] x[1][2] x[1][3]
x[1].length is 4
x[2][0] x[2][1] x[2][2] x[2][3]
x[2].length is 4
x[0]
x[1]
x[2]
x.length is 3
for (int i = 0; i < x.length; i++)
{
for (int j = 0; j < x[ i ].length; j++)
System.out.print ( “ “+x[ i ][ j ]);
System.out.println ( “ “);
} // for
You can get the size of each dimension
with the length attribute.
This is the most general style.
54
Lengths of Two-dimensional arrays
● If a is a 2- dimensional array then: a[i] is a 1- dimensional array.
In other words: a 2- dimensional array in Java is made up with many rows
of 1-dimensional arrays.
● The variable a[i].length contains the number of columns in row i.
55
Lengths of Two-dimensional arrays, example.
This program section calculates and prints the sum of each
column of a 2D rectangular matrix.
int sum; // sum of column elements
for (int col = 0; col < matrix[0].length; col++)
{
sum = 0;
for (int row = 0; row < matrix.length; row++)
sum = sum + matrix[row][col];
System.out.println("Sum of column " + (col + 1)
+ " = " + sum);
{ // outer for
56
Lengths of Two-dimensional arrays, example.
public static void main(String[ ] args)
{
String[ ][ ] strarray = {
{"this" ,"is","the","first","row"},
{"this","is","the","second","row"},
{"this","is","the","third","row"}
};
This would produce :
for(int i = 0; i < strarray.length; i++)
{
for(int j = 0; j < strarray[ i ].length; j++)
System.out.print(strarray[ i ][ j ]+" ");
System.out.println();
this is the first row
} // outer for
this is the second row
} // main
this is the third row
57
Lengths of Two-dimensional arrays, example.
This program section calculates and prints the maximum
element of each row in a 2D matrix .
for ( int row = 0; row < matrix.length; row++)
{
largest = matrix[row][0];
for (int col = 1; col < matrix[row].length col++)
if (largest < matrix[row][col])
largest = matrix[row][col];
System.out.println("The largest element of row "
+ (row + 1) + " = " + largest);
{ // outer for
58
Two - dimensional array example 1
This program section checks if the diagonal’s elements of square matrix
are equal.
mat.length = 4
Minor
diagonal
3
0
9
-1
7
7
10
6
6
4
8
5
i
mat[i][i]
0
3
1
7
2
6
3
4
int [][] mat = {{3,0,9,3},{-1,7,7,2},
{10,6,6,-15},{4,8,5,4}};
2
boolean flag = true; // help variable
-15
int i = 0; // loop counter
while ( i < mat.length && flag)
4
Main
{
diagonal
if ( mat[ i ][ i ] != mat[ i ][mat.length - i - 1] )
flag = false;
i++;
mat[i][4-i-1]
} // while
3
if ( flag )
System.out.println(“Yes");
7
else
6
System.out.println(“No");
4
3
59
Two - dimensional array example 2
This program section transposes the integer square matrix.
public static void main(String[ ] args)
{
System.out.print ("Enter array size: ");
int size = reader.nextInt(); // size=3
int[ ][ ] a = new int[size][size];
for (int r = 0; r < a.length; r++)
for (int c = 0; c < a[0].length; c++)
a[r][c] = reader.nextInt();
int startc = 1;
for (int r = 0; r < a.length; r++)
{
for (int c = startc; c < a[0].length; c++)
{
int temp = a[r][c];
a[r][c] = a[c][r];
a[c][r] = temp;
} // inner loop
startc++;
} // outer loop
} // main
Original array:
678
431
295
Transposed array:
642
739
815
60
Matrix multiplication
Typical applications in science and engineering involve implementing various
mathematical operations with matrix ,for example matrix multiplication:
C
i, j
Note: the number of columns in the A matrix m equals
the number of rows in the matrix B.
Square matrix
61
Matrix multiplication , cont.
static final int N = 3; // square matrix
double[ ][ ] c = new double[N][N];
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
for (int k = 0; k < N; k++)
c[i][j] + = a[i][k] * b[k][j];
} // for j
} // for i
62
Puzzle
63