•One-Dimensional Array
•Two-Dimensional Array
•Three-Dimensional Array
•Some programming Language allows as
many as 7 dimension
\
Two-Dimensional Array
•A Two-Dimensional m x n array
A is a
collection of m
. n data elements such that each
element is specified by a pair of integer (such as J, K) called subscript with
property that
1
≤ J ≤ m and
1 ≤ K ≤ n
The
element of A
with
first subscript J
and second subscript K
will be denoted by AJ,K
or A[J][K]
2D Arrays
The elements of a
2-dimensional array a is shown as below
a[0][0] a[0][1]
a[0][2] a[0][3]
a[1][0] a[1][1] a[1][2]
a[1][3]
a[2][0] a[2][1] a[2][2]
a[2][3]
Columns Of A 2D Array
2D Array
•Let
A be a
two-dimensional array m
x n
•The array A will
be represented in the memory by a block of m
x n sequential memory location
•Programming
language will store array A
either
–Column by
Column (Called Column-Major Order) Ex:
Fortran, MATLAB
–Row by
Row (Called
Row-Major Order) Ex: C, C++ , Java
2D Array in Memory
•LOC(LA[K]) = Base(LA) + w(K -1)
•LOC(A[J,K])
of A[J,K]
Column-Major Order
LOC(A[J,K])
= Base(A) + w[m(K-1) + (J-1)]
Row-Major Order
LOC(A[J,K])
= Base(A) + w[n(J-1) + (K-1)]
2D Array Example
•Consider a 25 x 4 array A. Suppose
the Base(A) = 200 and w =4. Suppose the programming store 2D array using
row-major. Compute LOC(A[12,3])
•LOC(A[J,K]) = Base(A) + w[n(J-1) +
(K-1)]
•
•LOC(A[12,3]) = 200 + 4[4(12-1) + (3
-1)] = 384
•An
n-dimensional
m1
x m2
x …. X mn array B is a collection of m1.m2…mn
data elements in which each element is specified by a list of n
integers – such as K1,
K2,
…., Kn
– called subscript with the property that
1≤K1≤m1, 1≤K2≤m2, ….
1≤Kn≤mn
The
Element B
with subscript K1,
K2,
…,Kn
will be denoted by
BK1,K2, …,Kn or
B[K1,K2,….,Kn] .
•Let C
be a n-dimensional
array
•Length Li
of
dimension i
of C
is the number of elements in the index set
Li = UB – LB + 1
•For a given subscript Ki,
the effective index Ei
of Li is the number of indices preceding
Ki in the index set
Ei = Ki
– LB
•Address LOC(C[K1,K2,
…., Kn])
of an arbitrary element of C can be obtained as
Column-Major
Order
Base( C) + w[((( … (ENLN-1
+ EN-1)LN-2)
+ ….. +E3)L2+E2)L1+E1]
Row-Major
Order
Base( C) + w[(… ((E1L2
+ E2)L3
+ E3)L4
+ ….. +EN-1)LN
+EN] .
Example :
•MAZE(2:8, -4:1, 6:10)
•Calculate the address of MAZE[5,-1,8]
•Given: Base(MAZE) = 200, w = 4,
MAZE is stored in Row-Major order
•L1 = 8-2+1 = 7, L2 = 6, L3 = 5
•E1 = 5 -2 = 3, E2 = 3, E3 = 2
•Base( C) + w[(… ((E1L2
+ E2)L3
+ E3)L4
+ ….. +EN-1)LN
+EN]
•E1L2
= 3 . 6 = 18
•E1L2
+ E2
= 18 + 3 = 21
•(E1L2
+ E2)L3
= 21 . 5 = 105
•(E1L2+E2)L3
+ E3
= 105 + 2 = 107
•MAZE[5,-1,8] = 200 + 4(107) = 200 +
248 = 628
Pointer, Pointer Array :
•Let DATA
be any array
•A variable P is
called a pointer if P
points to an element in DATA
i.e
if P
contains the address of an element in DATA
•An array PTR
is called a pointer array if each element of PTR
is a pointer.
Two
Dimensional 4x9 or 9x4 array
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