1. Array Processing
Lecture 7

2. Motivation One of the most powerful programming tools available
Help to organize a collection of homogeneous data items (same type and lenght). The individual data items that make up the array are called as Element of the array
Example: Scores[3]  indicated the third exam score

3. Operation on Arrays Loading initial value into the element of array
Processing the elements of the array
Searching an array (linear or binary search)
Writing out the array content to the report

4. Simple Algorithm to manipulate Array

5. Example 7.1 Find the sum of the elements of an array
Each elemen of the array is accumulated into a variable called sum. When all elements have been added, the variable sum is printed.

6. Find_sum_of_elements
Set sum to zero
DO index = 1 to number_of_elements
sum = sum + array(index)
ENDO
Print sum
END

7. Example 7.2 Find the average of the elements of an array
Each element of the array is accumulated into a variable called sum. When all elements have been added, the average of the elements is found and printed.

8. Find_element_average
Set sum to zero
DO index = 1 to number_of_elements
sum = sum + array(index)
ENDO
Average = sum / number_of_elements
Print average
END

9. Example 7.3 Find the largest elements of an array
The elements of an array are searched to determine which element is the largest. The algorithm starts by putting the first element of the array into the variable largest_element, and then looks at the other elements of the array to see if a larger value exists. The largest value is then printed.

10. Find_largest_element
Set largest_element to array(1)
DO index = 2 to number_of_elements
IF array(index) > largest_element THEN
largest_element = array(index)
ENDIF
ENDO
Print largest_element
END

11. Example 7.4 Find the smallest of the elements of an array
The elements of an array are searched to determine the smallest element. The algorithm starts by putting the first element of the array into the variable smallest_element, and then looks at the other elements of the array to see if a smaller value exists. The smallest value is then printed.

12. Find_smallest_element
Set smallest_element to array (1)
DO index = 2 to number_of_elements
IF array(index) < smallest_element THEN
smallest_element = array(index)
ENDIF
ENDO
Print smallest_element
END

13. Example 7.5 Find the range of the elements of an array
The elements of an array are searched to determine the smallest and the largest elements. The algorithm starts by putting the first element of the array into the variables smallest_element and largest_element, and then looks at the other elements to see if a smaller or larger value exists. The two values are then printed.

14. Find_range_of_element Set smallest_element to array(1)
Set largest_element to array(1)
DO index = 2 to number_of_elements
IF array(index) < smallest_element THEN
smallest_element = array(index)
ELSE
IF array(index) > largest_element THEN
largest_element = array(index)
ENDIF
ENDO
Print the range as smallest_element followed by largest_element
END

15. Initialising the elements of an array
Because an array is an iternal data structure, initial values must be placed into the array before any information can be retrieved from it.
The initial values can be assigned to the element as constant or be read from file.

16. Loading constant values into array (only be used for data which is unlikely to be changed)
Initialise_month_table
month_table(1) = `Januari`
month_table(2) = `February` .
month_table(12) = `December`
END

17. 2. Loading initial values into an array from an input file
Read_values_into_array
Set max_num_elements to required value
Set index to zero
Read first input value
DOWHILE (input value exist) AND (index<max_num_elements)
index = index + 1
array(index) = input value
Read next input value
ENDDO
IF (input value exist) AND index = max_num_elements THEN
Print `Array size is too small`
ENDIF
END

18. Array of variable size Read_values_into_variable_array
Set max_num_elements to required value
Set index to zero
Read first input value
DOWHILE (input value NOT = 9999) AND (index<max_num_elements)
index = index + 1
array(index) = input value
Read next input value
ENDDO
IF index < max_num_elements THEN
array(index) = 9999
ELSE
Print `Array size is too small`
ENDIF
END
Sentinel value  indicate the end of input records during initial processing and the last element of the array during further processing

19. Paired Arrays
Two array with the same number of elements are paired because they correspond each other.
Example:
A student number ID array and student name array

20. Paired Arrays Example (Algorithm to read a file of product codes and corresponding selling price and load them into corresponding arrays)
Read_values_into_paired_array
Set max_num_elements to required value
Set index to zero
Read first input value
DOWHILE (NOT EOF input record) AND (index<max_num_elements)
index = index + 1
product_codes(index) = input_product_code
selling_prices (index) = input_selling_price
Read next record
ENDDO
IF (NOT EOF input record) AND index = max_num_elements THEN
Print `Array size is too small`
ENDIF
END

21. Searching an Array The reason:
To edit an input value (ie. Valid element or not)
To retrieve information from array
To retrieve information from corresponding element in a paired array.

22. Linear search array Linear_search_of_an_array
Set max_num_elements to required value
Set element_found to false
Set index to 1
DOWHILE (NOT element_found) AND (index <= max_num_elements)
IF array(index) = input_value THEN
Set element_found to true
ELSE
index = index + 1
ENDIF
ENDDO
IF element_found THEN
Print array (index)
Print ´value not found´, input_value
END

23. Binary Search Array (effective method for elements more than 25 and sorted into ascending sequence)
Binary_search_of_an_array
Set element_found to false
Set low_element to 1
Set high_element to max_num_elements
DOWHILE (NOT element_found) AND (low_element <= high_elements)
index = (low_element + high_element)/2
IF input_value = array(index) THEN
Set element_found to true
ELSE
IF input_value < array (index) THEN
high_element = index – 1
low_element = index + 1
ENDIF
ENDDO
IF element_found THEN
Print array (index)
Print ´value not found´, input_value
END

24. Writing out the contents of an Array
Write_values_of_array
DO index = 1 to number_of_elements
Print array (index)
ENDDO
END

25. Programming Example Using Array

26. Example 7.6 Process exam scores
Design a program that will prompt for and receive 18 examination scores from a mathematics test, compute the class average, and display all the scores and the class average to the screen.

27. Defining diagram Input Processing Output 18 exam scores
Prompt the scores
Get scores
Compute class average
Display scores
Display class average
Class_average

28. Control Structures required
An array to store the exam scores – called ´scores´
An index to identify each element in the array
A DO loop to accept the scores
Another DO loop to display the scores to the screen.

29. Solution Algorithm Process_exam_scores Set total_score to zero
DO index = 1 to 18
Prompt operator for score
Get scores(index)
total_score = total_score + scores(index)
ENDDO
Compute average_score = total_score / 18
DO index = 1 to 18
Display scores(index)
Display average_score
END

30. Example 7.7 Process integer array
Design an algorithm that will read an array of 100 integer values, calculate the average integer value, and count the number of integers in the array that are greater than the average integer value. The algorithm is to display the average integer value and the count of integers greater than average.

31. Defining diagram Input Processing Output Read integer values
Compute integer values
Compute integer count
Display integer average
Display integer count
Integer_average
integer_count

32. Control Structures required
An array of integer values – called ´numbers´
A DO loop to calculate the average of the integers
Another DO loop to count the number of integers greater than the average.

33. Solution Algorithm Process_integer_array Set integer_total to zero
Set integer_count to zero
DO index = 1 to 100
integer_total = integer_total + numbers(index)
ENDDO
integer_average = integer_total / 100
DO index = 1 to 100
IF numbers(index) > integer_average THEN
add 1 to integer_count
ENDIF
Display integer_average, integer_count
END

34. Example 7.8 Validate sales number
Design an algorithm that will read a file of sales transactions and validate the sales numbers on each record. As each sales record is read, the sales number on the record is to be verifief against an array of 35 sales numbers. Any sales number not found in the array is to be flagged as an error.

35. Defining diagram Input Processing Output Sales_record
Sales_number
Read sales records
Validate sales numbers
Print error message
Error_message

36. Control Structures required
A previously initialised array of sales numbers, called ´sales_numbers´
A DOWHILE loop to read the sales file
A DOWHILE loop to perform linear search
A variable element_found to stop the search

37. Solution Algorithm Validate_sales_numbers Set max_num_elements to 35
Read sales record
DOWHILE sales_records exist
Set element_found to false
Set index to 1
DOWHILE (NOT element_found) AND (index <= max_num_elements)
IF sales_numbers(index) = input sales number THEN
Set element_found to true
ELSE
index = index + 1
ENDIF
ENDDO
IF NOT element_found THEN
Print `invalid sales numer`, input sales number
END

38. Example 7.9 Calculate shipping Charge
Design an algorithm that will read an input weight for an item to be shipped, search an array of shipping weigths and retrieve a corresponding shipping charge. In this algorithm, two paired arrays, each containing six elements, have been established and initialised. The array, shipping_weights, contains a range of shipping weights in grams, and the array, shipping_charges, contains a corresponding array of shipping charges in dollars, as follows:

39. Shipping weights (grams)
Shipping charges
1 – 100
3.00
101 – 500
5.00
501 – 1000
7.50
1001 – 3000
12.00
3001 – 5000
16.00
35.00

40. Defining diagram Input Processing Output Entry weight
Prompt for entry weight
Get entry weight
Search shipping weight array
Computer shipping charges
Display shipping charge
Shipping_charge
error_message

41. Control Structures required
Two arrays, called ´shipping_weigths´ and ´shipping_charges`
A DOWHILE loop to search the shipping_weigths array and then retrieve the shipping_charges
A variable element_found to stop the search when entry weight is found

42. Solution Algorithm Calculate_shipping_charge Set max_num_elements to 6
Read index to 1
Set element found to false
Prompt for entry weigth
Get entry weight
DOWHILE (NOT element_found) AND (index <= max_num_elements)
IF shipping_weights(index) < entry weight THEN
add 1 to index
ELSE
set element_found to true
ENDIF
ENDDO
IF element_found THEN
shipping_charge = shipping charges(index)
Display `shipping charge is`, shipping_charge
Display `invalid shipping weight`, entry weight
END

43. Two-dimensional Arrays
Where two subscripts are required to locate an element in an array.
The number of elements is calculated as the product of the number of rows and the number of columns
Specified by: array(row_index,column_index)

44. Shipping weights (grams)
One dimensional Array
Shipping weights (grams)
1 – 100
101 – 500
501 – 1000
1001 – 3000
3001 – 5000

45. Shipping charges ($) (by shipping zone)
Two dimensional Array
Shipping charges ($) (by shipping zone) 1 2 3 4
2.50
3.50
4.00
5.00
6.50
4.50
7.50
10.00
11.00
12.00
13.50
16.00
20.00
27.50
32.00
34.00
35.00
38.00

46. Loading a two-dimensional array (from previous table)
Read_values_into_array
Set max_num_elements to 24
Set row_index to zero
Read input file
DOWHILE (input values exist) AND (row_index < 6)
row_index = row_index + 1
DO column_index = 1 to 4
shipping_charges(row_index,column_index) = input value
read input file
ENDDO
IF (input values exist) AND row_index = 6 THEN
Print ´Array size to small`
ENDIF
END

47. Searching Two dimensional Array
Calculate_shipping_Charges
Set row_index to 1
Set element_found to false
Prompt for shipping_weight, zone
Get shipping_weight, zone
DOWHILE (NOT element_found) AND (row_index <= 6)
IF shipping_weights(row_index) < input shipping_weight THEN
add 1 to row_index
ELSE
set element_found to true
ENDIF
ENDDO
IF element_found THEN
IF zone = (1 or 2 or 3 or 4) THEN
shipping_charge = shipping_charges(row_index, zone)
display ´shipping charge is`, shipping_charge
display `invalid zone`, zone
Display `invalid shipping weight`, input shipping_weight
END

48. Writing out the contents of 2-d array
Write_values_of_array
Set number_of_rows to required value
Set number_of_columns to required value
DO row_index = 1 to number_of_rows
DO column_index = 1 to number_of_columns
Print array (row_index, column_index)
ENDDO
END