Array Processing

Lecture 7

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

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

Simple Algorithm to manipulate Array

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.

Find_sum_of_elements

Set sum to zero

DO index = 1 to number_of_elements

sum = sum + array(index)

ENDO

Print sum

END

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.

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

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.

Find_largest_elementSet largest_element to array(1)DO index = 2 to number_of_elements

IF array(index) > largest_element THENlargest_element = array(index)

ENDIFENDOPrint largest_element

END

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.

Find_smallest_elementSet smallest_element to array (1)DO index = 2 to number_of_elements

IF array(index) < smallest_element THEN

smallest_element = array(index)ENDIF

ENDOPrint smallest_element

END

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 THENsmallest_element = array(index)

ELSEIF array(index) > largest_element THEN

largest_element = array(index)ENDIF

ENDIFENDOPrint the range as smallest_element followed by largest_element

END

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.

1. Loading constant values into array (only be used for data which is unlikely to be changed)

Initialise_month_tablemonth_table(1) = `Januari`month_table(2) = `February`

.

.

.month_table(12) = `December`

END

2. Loading initial values into an array from an input file

Read_values_into_arraySet max_num_elements to required valueSet index to zeroRead first input valueDOWHILE (input value exist) AND (index<max_num_elements)

index = index + 1array(index) = input valueRead next input value

ENDDOIF (input value exist) AND index = max_num_elements THEN

Print `Array size is too small`ENDIF

END

Array of variable sizeRead_values_into_variable_array

Set max_num_elements to required valueSet index to zeroRead first input valueDOWHILE (input value NOT = 9999) AND (index<max_num_elements)

index = index + 1array(index) = input valueRead next input value

ENDDOIF index < max_num_elements THEN

index = index + 1array(index) = 9999

ELSEPrint `Array size is too small`

ENDIFEND

Sentinel value indicate the end of input records during initial processing and the last element of the array during further processing

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

Read_values_into_paired_arraySet max_num_elements to required valueSet index to zeroRead first input valueDOWHILE (NOT EOF input record) AND (index<max_num_elements)

index = index + 1product_codes(index) = input_product_codeselling_prices (index) = input_selling_priceRead next record

ENDDOIF (NOT EOF input record) AND index = max_num_elements THEN

Print `Array size is too small`ENDIF

END

Paired Arrays Example(Algorithm to read a file of product codes and corresponding selling

price and load them into corresponding arrays)

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.

Linear search array

Linear_search_of_an_arraySet max_num_elements to required valueSet element_found to falseSet index to 1DOWHILE (NOT element_found) AND (index <= max_num_elements)

IF array(index) = input_value THENSet element_found to true

ELSEindex = index + 1

ENDIFENDDOIF element_found THEN

Print array (index)ELSE

Print ´value not found´, input_valueENDIF

END

Binary Search Array(effective method for elements more than 25 and sorted into ascending sequence)

Binary_search_of_an_arraySet element_found to falseSet low_element to 1Set high_element to max_num_elementsDOWHILE (NOT element_found) AND (low_element <= high_elements)

index = (low_element + high_element)/2IF input_value = array(index) THEN

Set element_found to trueELSE IF input_value < array (index) THEN

high_element = index – 1 ELSE

low_element = index + 1 ENDIFENDIF

ENDDOIF element_found THEN

Print array (index)ELSE

Print ´value not found´, input_valueENDIF

END

Writing out the contents of an Array

Write_values_of_array

DO index = 1 to number_of_elements

Print array (index)

ENDDO

END

Programming Example Using Array

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.

• Defining diagram

Input Processing Output

18 exam scores Prompt the scoresGet scoresCompute class averageDisplay scoresDisplay class average

18 exam scoresClass_average

Control Structures required

1. An array to store the exam scores – called ´scores´

2. An index to identify each element in the array

3. A DO loop to accept the scores

4. Another DO loop to display the scores to the screen.

Solution AlgorithmProcess_exam_scores

Set total_score to zeroDO index = 1 to 18

Prompt operator for scoreGet scores(index)total_score = total_score + scores(index)

ENDDOCompute average_score = total_score / 18DO index = 1 to 18

Display scores(index)ENDDODisplay average_score

END

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.

• Defining diagram

Input Processing Output

100 integer values Read integer valuesCompute integer valuesCompute integer countDisplay integer averageDisplay integer count

Integer_averageinteger_count

Control Structures required

1. An array of integer values – called ´numbers´

2. A DO loop to calculate the average of the integers

3. Another DO loop to count the number of integers greater than the average.

Solution AlgorithmProcess_integer_array

Set integer_total to zeroSet integer_count to zeroDO index = 1 to 100

integer_total = integer_total + numbers(index)ENDDOinteger_average = integer_total / 100DO index = 1 to 100

IF numbers(index) > integer_average THENadd 1 to integer_count

ENDIFENDDODisplay integer_average, integer_count

END

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.

• Defining diagram

Input Processing Output

Sales_record• Sales_number

Read sales recordsValidate sales numbersPrint error message

Error_message

Control Structures required

1. A previously initialised array of sales numbers, called ´sales_numbers´

2. A DOWHILE loop to read the sales file

3. A DOWHILE loop to perform linear search

4. A variable element_found to stop the search

Solution AlgorithmValidate_sales_numbers

Set max_num_elements to 35Read sales recordDOWHILE sales_records exist

Set element_found to falseSet index to 1DOWHILE (NOT element_found) AND (index <= max_num_elements)

IF sales_numbers(index) = input sales number THENSet element_found to true

ELSEindex = index + 1

ENDIFENDDOIF NOT element_found THEN

Print `invalid sales numer`, input sales numberENDIFRead sales record

ENDDOEND

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:

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

5001 - 9999 35.00

• Defining diagram

Input Processing Output

Entry weight Prompt for entry weightGet entry weightSearch shipping weight arrayComputer shipping chargesDisplay shipping charge

Shipping_chargeerror_message

Control Structures required

1. Two arrays, called ´shipping_weigths´ and ´shipping_charges`

2. A DOWHILE loop to search the shipping_weigths array and then retrieve the shipping_charges

3. A variable element_found to stop the search when entry weight is found

Solution AlgorithmCalculate_shipping_charge

Set max_num_elements to 6Read index to 1Set element found to falsePrompt for entry weigthGet entry weightDOWHILE (NOT element_found) AND (index <= max_num_elements)

IF shipping_weights(index) < entry weight THENadd 1 to index

ELSEset element_found to true

ENDIFENDDOIF element_found THEN

shipping_charge = shipping charges(index)Display `shipping charge is`, shipping_charge

ELSEDisplay `invalid shipping weight`, entry weight

ENDIFEND

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)

One dimensional Array

Shipping weights (grams)

1 – 100

101 – 500

501 – 1000

1001 – 3000

3001 – 5000

5001 - 9999

Two dimensional Array

Shipping charges ($) (by shipping zone)

1 2 3 4

2.50 3.50 4.00 5.00

3.50 4.00 5.00 6.50

4.50 6.50 7.50 10.00

10.00 11.00 12.00 13.50

13.50 16.00 20.00 27.50

32.00 34.00 35.00 38.00

Loading a two-dimensional array(from previous table)

Read_values_into_arraySet max_num_elements to 24Set row_index to zeroRead input fileDOWHILE (input values exist) AND (row_index < 6)

row_index = row_index + 1DO column_index = 1 to 4

shipping_charges(row_index,column_index) = input value

read input fileENDDO

ENDDOIF (input values exist) AND row_index = 6 THEN

Print ´Array size to small`ENDIF

END

Searching Two dimensional Array

Calculate_shipping_ChargesSet row_index to 1Set element_found to falsePrompt for shipping_weight, zoneGet shipping_weight, zoneDOWHILE (NOT element_found) AND (row_index <= 6)

IF shipping_weights(row_index) < input shipping_weight THEN add 1 to row_indexELSE set element_found to trueENDIF

ENDDOIF 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_chargeELSE display `invalid zone`, zoneENDIF

ELSEDisplay `invalid shipping weight`, input shipping_weight

ENDIFEND

Writing out the contents of 2-d array

Write_values_of_arraySet number_of_rows to required valueSet number_of_columns to required valueDO row_index = 1 to number_of_rows

DO column_index = 1 to number_of_columns

Print array (row_index, column_index)

ENDDOENDDO

END