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Basic Building BlocksArray
Structure
Classes
Arrays, structures, and classes are collection of data items
with thefollowing differences:
Arrays Structures/Classes
Elements are of the same type. Elements may be of different
type.
Elements are accessed through an
index
Elements are accessed through
name.
Arrays, structures, and classes are stored using consecutive
memory
locations for the whole array or structure/class.
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Ordered Lists
One of the most common data object is an orderedlist.
An ordered list has elements with definite ordering.The simplest
example of an ordered list is an ordered
pair which has only two elements. Examples of ordered lists:
1. Months of the years (Jan, Feb, Mar, Apr, May,.,Dec)
2. English Alphabets (A, B, C, , Z)3. Words in a sentence (This
is a book on data
structures.)
4. Names of the students in a class stored in the order
of their roll numbers.
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Operations Defined on an Ordered List
or Vector
1. Find the length of list.
2. Check if the list is empty.
3. Traverse the list in some order.
4. Get the ith elements in the list.
5. Change the value of the ith element.
6. Insert a new element at the ith position.7. Delete the ith
element.
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Representation of an Ordered List
The easiest way to represent an orderedlist is by an
one-dimensional array where
we store the ith element of the list in thearray element with
index i.
This is called sequential or linear
mapping mapping a one-dimensionalvector onto a one-dimensional
space.
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class LinearList {public:
LinearList(int s); // constructor~ LinearList () {delete [ ]
ListArray; } // destructorbool add (int value);
bool remove (int index);bool change(int index, int value);bool
get(int index, int & value);void printAll();
bool isFull() {return MaxSize == size;}
bool isEmpty() {return size == 0; }int length() {return
size;}private:
int MaxSize; // max List sizeint *ListArray;int size; // no. of
elements in the List
};
Linear List Using Arrays
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LinearList :: LinearList(int s){
MaxSize = s;ListArray = new int[MaxSize];size = 0;
}
void LinearList :: printALL(){
for (i = 0; i < size; i++)cout
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bool LinearList :: change(int index, int value) {if (index <
size && index >= 0) {
ListArray[index] = value;return true;
}else
return false;
}
bool LinearList :: get(int index, int & value) {if (index
< size && index >= 0) {
value = ListArray[index];return true;}else
return false;
}
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bool LinearList::add(int value){
if (! isFull() ) {for (int i = size; i >= 1; i--) {
if (ListArray[i-1] > value)ListArray[i] = ListArray[i
-1];
elsebreak;
}ListArray[i] = value;size++;
return true;}else return false;
}
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bool LinearList::remove(int index){
if (index < size && index >= 0) {for (int i =
index; i < size - 1; i++)
ListArray[i] = ListArray[i +1];size--;
return true;}else return false;
}
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Representation of SingleDimensional Arrays
Whole array is stored in a single contiguous memoryblock.
Address of the first element is called the base addressand it is
also the start address of array.
The address of the ith element is given by thefollowing
formula:
Addressi = base_address + i * size_of_element
Arrays are very efficient way of organizing data sinceaccessing
array elements requires O(1).
elem0 elem1 elem2 elemi elemn-1
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float sum (float list [], int n){
float temp = 0;
int i;for (i = 0; i < n; i++)
temp = temp + list[i];
return temp;
}
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void add (int a[][], int b[][],
int c[][],int rows, int cols)
{
int i, j;for (i=0; i
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const int N = 100;
void add (int a[][N], int b[][N],
int c[][N],int rows, int cols)
{
int i, j;for (i=0; i
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Two Dimensional Array
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99827622
643823
6351
Users view (abstraction)
543451060998276226438236351
Systems view
(implementation)
Offset of a[i][j]?
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Two Dimensional Array
543451060
99827622
643823
6351
Users view (abstraction)
Offset of a[i][j]?Number of elements in each row?
ith
rowtotal elements in the previous rows?
jth element in ith row
Offset (in units)
N
i * N
i * N + j
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Row major C, Pascal, C++, etc.
Column Major FORTRAN
Ada - indefinite
Two Dimensional Array
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Row Major
Slice along the 1st dimension to get an
array of N-1 dimensions
Continue until you are left with onedimension only.
Offset of a[d0] [d1] [dn-1]
Multi-Dimensional Arrays
A[D0] [D1][Dn-1]
(((d0*D1 + d1)*D2 + d2)*D3 + ) + dn-1
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Symmetric Matrices
