chapter 7 array processing. objectives to introduce arrays and the uses of arrays to develop...
TRANSCRIPT
Chapter 7
Array processing
Objectives
• To introduce arrays and the uses of arrays
• To develop pseudocode algorithms for common operations on arrays
• To illustrate the manipulation of single- and two-dimensional arrays
7.1Array processing
Array processing• Arrays are one of the most powerful
programming tools available• Provide the programmer with a way of
organising a collection of homogeneous data items (items that have the same type and same length) into a single data structure
• An array is a data structure that is made up of a number of variables all of which have the same data type
Array processing
• The individual data items that make up the array are referred to as the element of the array
• Elements in the array are distinguished from one another by the use of an index or subscript, enclosed in parentheses, following the array name – for example: ‘scores (3)’
Array processing
– The most typical operations performed on arrays are:• Loading a set of initial values into the
element of an array• Processing the elements of an array• Searching an array, using a linear or
binary search, for a particular element• Writing out the contents of an array to a
report
Array processing
– The elements of an array are processed in sequence, starting with the first element. This can be accomplished easily in pseudocode with either a DO loop or a DOWHILE loop
Array processing• Simple algorithms that manipulate
arrays– The following algorithm involve the
simple manipulation of an array written in a DO loop
– In this example, each element of the array is accumulated into a variable called sum. When all elements have been added, the variable sum is printed
Array processing
– Example: Find the sum of the elements of an arrayFind_sum_of_elements
Set sum to zeroDO index = 1 to number_of_elements
sum = sum + array (index)ENDDOPrint sum
END
7.2Initialising the elements of an
array
Initialising the elements of an array
• Because an array is an internal data structure, initial values must be placed into the array before any information can be retrieved from it
• These initial values can be assigned to the elements of the array as constants, or they can be read into the array from a file
Initialising the elements of an array• Loading constant values into an array
– This method should only be used when the data in the array is unlikely to be changed – for example, the names of the 12 months of the yearInitialise_month_table
month_table(1) = ‘January’month_table(2) = ‘February’
::
month_table(12) = ‘December’END
Initialising the elements of an array• Loading initial values into an array from
an input file–Defining array elements as constants
in a program is not recommended if the values change frequently, as the program will need to be changed every time an array element changes
–A common procedure is to read the input values into the elements of an array from an input file
Initialising the elements of an array
– The following pseudocode algorithm, values are read from an input file and assigned to the elements if an array, starting with the first element, until there are no more input values or the array is full
– The array name is ‘array’, the subscript is ‘index’, and the maximum number of elements that the array can hold is max_num_elements
Initialising the elements of an array
– ExampleRead_values_into_array
Set 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 values exist) AND index =
max_num_elements THEN
Print ‘array size too small’ENDIF
END
Initialising the elements of an array
–Note that the processing will terminate when either the input file has reached EOF or the array is full
– Error message will be printed if there are more input data items than there are elements in the array
Initialising the elements of an array• Arrays of variable size
– Some programs, the number of entries in an array can vary
– In this case, a sentinel value (for example, 9999) is used to mark the last element of the array, both in the initialising file of data items and in the array itself
– Includes a check to ensure that no attempt is made to load more entries into the array than there are elements, as in the following example
Initialising the elements of an array
– ExampleRead_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 too small’
ENDIF
END
Initialising the elements of an array
• Paired arrays– Two arrays that have the same
number of elements– The arrays are paired because the
elements in the first array correspond to the elements in the same position in the second array
– The following example illustrates paired array
Initialising the elements of an array
– ExampleRead_values_into_paired_array
Set 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 too small’ENDIF
END
7.3Searching an array
Searching an array• A common operation on arrays is to search the
element of an array for a particular data item• Reason for searching an array:
– To edit an input value – that is, to check that is a valid element of an array
– To retrieve information from an array– To retrieve information from a
corresponding element in a paired array • An array can be searched using either a linear
search or a binary search
Searching an array
• A linear search of an array– Involves looking at each of the
elements of the array, one by one, starting with the first element
–A linear search is often used to validate data items
– The following example illustrates linear search of an array
Searching an array– Example
Linear_search_of_an_arraySet max_num_elements to required valueSet element_found to falseDOWHILE (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
Searching an array• A binary search of an array
– Number of elements > 25, the elements are sorted into ascending sequence and search using binary search
– A binary locates the middle element of the array first, and determines if the element being searched for is in the first or second half of the table
– The search then points to the middle element of the relevant half table, and the comparison is repeated
Searching an array– Example
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_element)
index= (low_element + high_element) / 2IF input_value = array (index) THEN
Set element_found to trueELSE
IF input_value < array (index) THENhigh_element = index – 1
ELSElow_element = index + 1
ENDIFENDIF
ENDDOIF element_found THEN
Print array (index)ELSE
Print ‘value not found’, input_value ENDIF
END
7.4Writing out the contents of an
array
Writing out the contents of an array
• The elements of an array can be used as accumulators of data, to be written to a report
• Writing out the contents of an array involves starting with the first element of the array and continuing until all elements have been written
Writing out the contents of an array
• This can be represented by a simple DO loopWrite_values_of_array
DO index = 1 to number_of_elementsPrint array (index)
ENDDOEND
7.5Programming examples using
arrays
Programming examples using arrays
• Example 7.6 Process exam scoresDesign 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
Programming examples using arrays
Input Processing Output
18 examscores
Prompt for scoresGet scoresCompute class averageDisplay scoresDisplay class average
18 exam scoresClass_average
A. Defining Diagram
Programming examples using arrays
B. Control structures required1. An array to store the exam scores –
that is, ‘scores’2. An index to identify each element in
the array3. A DO loop to accept the scores4. Another DO loop to display the
scores to the screen
Programming examples using arraysC. Solution algorithmProcess_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)
ENDDO
Display average_score
END
7.6Two-dimensional arrays
Two-dimensional arrays
• An element of a two-dimensional array is specified using the name of the array, followed by two subscript, enclosed in parentheses, separated by a comma
• The row subscript is specified first, followed by the column subscript
Two-dimensional arrays• Loading a two-dimensional array
– Two dimensional array is loaded in columns within row order
–All the columns for row one are loaded before moving to row two and loading the columns for that row, and so on
– The reading of a series of values from a file into a two-dimensional array can be represented by a DO loop within a DOWHILE loop
Two-dimensional arrays
• Writing out the contents of a two-dimensional array–Write out the elements in the column
within a row, before moving on to the next row
– This is represented in pseudocode by a DO loop within another DO loop
Summary
• An array is defined as a data structure made up of a number of variables or data item that all have the same data type and are accessed by the same name.
• The individual elements that make up the array are accessed by the use of an index or subscript beside the name of the array – for example, scores (3).
Summary• Algorithms were developed for the most
common operations on arrays, namely:– loading a set of initial values into the
elements of an array– processing the elements of an array– searching an array, using a linear or
binary search, for a particular element
–writing out the contents of an array to a report.