1. Data Structures and Algorithms
Processing
Arrays
Arrays
@ Often advantageous for a user to store several
values for the same variable in the internal
memory of the computer because it decreases
processing time.
@ This multiple storage means there has to be
more than one memory location in the
computer for each variable name.
@ When more than one memory location is
designated for a single variable, it is called
an array.
Static Arrays
@ This means that once the computer is told
how many locations to save, that number
cannot be changed unless the instruction is
changed.
Processing Arrays *Property of STI
Page 1 of 17

2. Data Structures and Algorithms
Processing
Arrays
Dynamic Arrays
@ When using dynamic arrays, the programmer
designates the number of array locations as a
variable, which can be expanded or contracted
during the execution of the solution.
Base-Zero System
@ Because computers are zero-based, for
counting purposes, many programming
languages are also zero-based.
@ This means that the first array element is
numbered zero and not one.
Base-One System
@ Base one is easier for the programmer to
understand since the first element will have
an index of 1.
Processing Arrays *Property of STI
Page 2 of 17

3. Data Structures and Algorithms
Processing
Arrays
Base-Zero Versus Base-One Arrays
Processing Arrays *Property of STI
Page 3 of 17

4. Data Structures and Algorithms
Processing
Arrays
One-Dimensional Arrays
Processing Arrays *Property of STI
Page 4 of 17

5. Data Structures and Algorithms
Processing
Arrays
Parallel Arrays
Processing Arrays *Property of STI
Page 5 of 17

6. Data Structures and Algorithms
Processing
Arrays
Entering Data into an Array
Algorithm Flowchart
A
LOOP:R = 1 TO N STEP 1
R
1 N
ENTER A(R)
1
LOOP-END:R
ENTER
A(R)
R = Counter
R
N = Number of elements in
the array
A(R) = Element R B
in the A array
Processing Arrays *Property of STI
Page 6 of 17

7. Data Structures and Algorithms
Processing
Arrays
Algorithm Flowchart
A
R=0
1. R = 0
2. REPEAT REPEAT
R = R+1 R=R+1
ENTER A(R)
UNTIL A(R) = -1 ENTER
A(R)
*3. N = R-1
F UNTIL
A(R) = -1
T
*
N=R-1
B
Processing Arrays *Property of STI
Page 7 of 17

8. Data Structures and Algorithms
Processing
Arrays
Algorithm Flowchart
A
1. R = 1 R=1
2. ENTER A(R)
3. WHILE A(R) <> -1
ENTER
A(R)
R = R+1
ENTER A(R)
WHILE F
A(R) <> -1
WHILE - END
*4. N = R-1
R=R+1
ENTER
A(R)
*
N=R+1
B
Processing Arrays *Property of STI
Page 8 of 17

9. Data Structures and Algorithms
Processing
Arrays
Printing an Array
Algorithm Flowchart
A
LOOP: R=1 TO N STEP 1
PRINT A(R) R
1 N
1
LOOP-END: R
PRINT
R = Element number A(R)
N = Total number
of elements
R
A(R) = Rth element of
the A array
B
Processing Arrays *Property of STI
Page 9 of 17

10. Data Structures and Algorithms
Processing
Arrays
Accumulating the Elements of an Array
Algorithm Flowchart
A
LOOP:R = 1 TO N STEP 1
SUM = SUM + A(R)
R
1 N
LOOP-END: R 1
N = Number of elements SUM = SUM
+ A(R)
R = Element number
SUM = Sum of the R
elements of A
A(R) = Rth element of the
array B
TEST: R SUM
A
1 2 1 2 3 2 6 12
4 5 6 7 20 30 42
2 4
3 6
4 8 N
5 10
6
6 12
Processing Arrays *Property of STI
Page 10 of 17

11. Data Structures and Algorithms
Processing
Arrays
Two-Dimensional Arrays
@ A two-dimensional array is a block of memory
locations associated with a single memory variable
name and designated by row and column numbers.
Processing Arrays *Property of STI
Page 11 of 17

12. Data Structures and Algorithms
Processing
Arrays
Loading a Two-Dimensional Array
Row by Row
@ You load a two- Data Block
A
dimensional array 1
Array
with nested loops. 2 R A
3 1 3
The data are
C
1 2 3 4
4 1 R
normally loaded 5 1 1 2 3 4
6 2 5 6 7 8
row by row. When 7 C 3 9 10 11 12
you load the data 8
9
1
1
4
The row remains
row by row, the 10 constant as the
column varies.
11
outer loop 12
ENTER
represents the row, A(R, C)
and the inner loop
represents the
C
column. C = Column
R R = Row
B
Processing Arrays *Property of STI
Page 12 of 17

13. Data Structures and Algorithms
Processing
Arrays
Printing a Two-Dimensional Array
A
PRINT
COLUMN
HEADINGS
R
1 NR
1
PRINT ROW
HEADING (R)
C
1 NC
1
PRINT A(R,C)
W/O CURSOR
R = Row RETURN
NR = Number of rows C
C = Column RETURN
CURSOR
NC = Number of columns R
B
Processing Arrays *Property of STI
Page 13 of 17

14. Data Structures and Algorithms
Processing
Arrays
Accumulating the Rows and Columns of a Two-
Dimensional Array
@ Column 5 holds the sum of each of the rows
@ Row 4 holds the sum of each of the columns
@ A (4,5) holds the grand total
Processing Arrays *Property of STI
Page 14 of 17

15. Data Structures and Algorithms
Processing
Arrays
Algorithm Flowchart
A
LOOP:R = 1 TO NR STEP 1 R
1 NR
1
LOOP: C = 1 TO NC STEP 1
A(R,NC + 1) = A(R,NC + 1) C
1 NC
+ A(R,C) 1
A(NR + 1,C) = A(NR + 1,C)
+ A(R,C) A(R, NC + 1) =
A(R, NC + 1) +
A(R,C)
LOOP-END: C
A(NR + 1,C)=
A(NR + 1,NC + 1) = A(NR + 1,C) +
A(R,C)
A(NR + 1, NC + 1)
+A(R, NC + 1)
C
LOOP-END: R
A(NR + 1,NC + 1)
=A(NR + 1, NC + 1)
+A(R, NC + 1)
R
B
Processing Arrays *Property of STI
Page 15 of 17

16. Data Structures and Algorithms
Processing
Arrays
Multidimensional Arrays
In some cases there is a need for arrays with a third or
even a fourth dimension. These arrays are called
multidimensional arrays.
Advantages :
@ Facilitate an
understanding
of the data
@ Improve the
readability of
algorithms
@ Facilitate
processing
Processing Arrays *Property of STI
Page 16 of 17

17. Data Structures and Algorithms
Processing
Arrays
Table Look-up Technique
@ A common application for arrays is using a value to look up another
value in a table. A one-dimensional array would be used if the
element number can be utilized as the given value. A two-
dimensional array with two columns would be used if the element
number cannot be utilized.
element DAYS Algorithm FLOWCHART:
1 31 1. ENTER MONTH
2. DAYS_OF_THE_MONTH = START
DAYS(MONTH)
2 28
3. PRINT DAYS_OF_MONTH
4. END
3 31
ENTER
4 30 MONTH
5 31
6 30 DAYS_OF_THE_
MONTH =
DAYS(MONTH)
7 31
8 31
PRINT
DAYS_OF_
9 30 MONTH
10 31
11 30
END
12 31
Processing Arrays *Property of STI
Page 17 of 17