1 arrays … the sequel applications and extensions chapter 10

1

Arrays … The SequelApplications and Extensions

Chapter 10

2

Applying What You Learn

Searching through arrays efficiently

Sorting arrays

Using character arrays as "STRINGS"

strings … get it? hahahaha

3

Lists• Defn => A collection of homogeneous

components– linear collection– variable length collection

• Length <=> the actual number of values stored in the list

• Example -- a file of time card information

Joe, 40, Clyde, 38.5, Sniudly, 42.75 ...

4

Lists

• Arrays can be used to implement a list– declare the array large– keep track of how many elements used

• We often do operations on the lists– create a list, add an item, delete an item– print the list, search the list for a value– sort the list

• A list of numbersscores : 85 79 92 57 68 80 . . . scores : 85 79 92 57 68 80 . . .

0 1 2 3 4 5 98 99

5

Sequential Search

• Consider the list unordered (not sorted)

• For a function to search for a targert we must specify– name of the array to be searched– length of the list (number of array elements)– a flag parameter which tells whether or

not the search was successful– an index value to be returned which tells where in the list

the item was found

scores

scores : 85 79 92 57 68 80 . . . scores : 85 79 92 57 68 80 . . . 0 1 2 3 4 5 98 99

5

boolean & found

int & location

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Sequential Search

• Algorithm example

• Note use of reference parameters for the found flag and the location

void search (int list[ ], int length, int target, boolean & found, int &location) { location = 0; while ((location < length) && (target != list[location])) location++; found = (index < length); } // if found == TRUE, location OK . . . search (scores, 5, 92, found_it, where_its_at);

void search (int list[ ], int length, int target, boolean & found, int &location) { location = 0; while ((location < length) && (target != list[location])) location++; found = (index < length); } // if found == TRUE, location OK . . . search (scores, 5, 92, found_it, where_its_at);

scores : 85 79 92 57 68 80 . . . scores : 85 79 92 57 68 80 . . . 0 1 2 3 4 5 98 99

7

Sorted List -- Faster Search

• Sorted list => components arranged in order– alphabetical– numerically ascending or descending

• Advantage of a sorted list– need to search only until the value found is larger

than target value

8

Sorting

• Means arranging the list elements into some order (for instance, strings into alphabetical order, or numbers into ascending or descending order).

Dale NellWeems ChipHeadington MarkCooper SoniaHuang Jeff

Cooper Sonia Dale NellHeadington MarkHuang Jeff Weems Chip

sorting

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Sorting Algorithm

• Make a pass through the list, look for smallest number

list 1 : 85 79 92 57 68 80 . . . list 1 : 85 79 92 57 68 80 . . .

list 2 :list 2 :

10

Sorting Algorithm


• Write that number in another list, cross it off first list

list 1 : 85 79 92 57 68 80 . . . list 1 : 85 79 92 57 68 80 . . .

list 2 : 57list 2 : 57

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Sorting Algorithm


• Write that number in another list, cross it off first list

• Repeat process, always look for smallest number remaining

list 1 : 85 79 92 57 68 80 . . . list 1 : 85 79 92 57 68 80 . . .

list 2 : 57 68 list 2 : 57 68

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Sorting Algorithm


• Write that number in another column, cross it off first list

• Repeat process, always look for smallest number remaining

• Stop when all numbers have been crossed off

13

Sequential Search in a Sorted List

• Note difference from previous search

void search_ord ( int list[ ], int target, int length, int & index, boolean & found)

{ index = 0;list [length] = target; // store an item beyond end while (target > list [index])

index++;found = (index < length && ltem = = list[index]; )

Explain how the last statement worksExplain how the last statement works

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Inserting into an Ordered List

• We wish to insert a new number into the list in the right position– find where it goes -- look until you find a number

bigger than the new number

list 2 : 14 22 45 61 87 list 2 : 14 22 45 61 87

length : 5length : 5

5959

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list 2 : 14 22 45 61 87 list 2 : 14 22 45 61 87



bigger than the new number– shift that number all the rest of the elements down

list 2 : 14 22 45 61 87 list 2 : 14 22 45 61 87


5959

16

list 2 : 14 22 45 61 87 list 2 : 14 22 45 61 87



bigger than the new number– shift that number all the rest of the elements down– insert the new number in the vacated spot

list 2 : 14 22 45 59 61 87 list 2 : 14 22 45 59 61 87


5959

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bigger than the new number– shift that number all the rest of the elements down– insert the new number in the vacated spot– be sure to increment the length


list 2 : 14 22 45 59 61 87 list 2 : 14 22 45 59 61 87

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Binary Search in an Ordered List• Examines the element in the middle of the array. • Is it the sought item?

– If so, stop searching.

– Is the middle element too small? • Then start looking in second half of array.

– Is the middle element too large? • Then begin looking in first half of the array.

• Repeat the process in the half of the list that should be examined next.

• Stop when – item is found, or when

– there is nowhere else to look and it has not been located.

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String Library Routines

String comparison:returns -1 if s1 < s2

returns 0 if they are equalreturns +1 if s1 > s2

String comparison:returns -1 if s1 < s2

returns 0 if they are equalreturns +1 if s1 > s2

• String assignment• String assignment

Returns length of the string

Returns length of the string

20

Using typedef with Arrays

• Specify an array type– this can be used throughout program– helps program self document

• Example :

typedef char default_string [80]; . . .

defalt_string fname, descrip;void reverse (default_string s);

typedef char default_string [80]; . . .

defalt_string fname, descrip;void reverse (default_string s);

21

Two dimensional Arrays

• A collection of components– all of the same type– structured in TWO dimensions– each component accessed by a PAIR of indices

representing the component’s position in each dimension

7 2 13 6 -40 6 3 -9 5

12 4 3 1 -15 2 -2 8 10

0 1 2 3 4

0

1

2

3

Which cell isLocation (2,3) ?

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Declaring Two Dimensional Arrays

• Syntax: data_type array_name [row_dim][col_dim];

• Example:

• First element isint_table[0][0]

• Last element isint_table[4][3]

7 2 13 6 -40 6 3 -9 5

12 4 3 1 -15 2 -2 8 10

0 1 2 3 4

0

1

2

3

int int_table [5][4];int int_table [5][4];

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Processing Two-D Arrays

• Arrays processed in some pattern– random– along rows– along columns– whole array

• We will use the declaration shown below:

int int_table [5][4];int row, col;

int int_table [5][4];int row, col;

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• What does the routine below do with the array? What should we name the function?

0

total_a_row

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• What does this routine below do with the array? What should we name the function?

0

total_column

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• This function initializes an array.

• Fill in the blanks with the correct identifiers

3

col

table value

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Printing a Table

• We must process each row, item by item

• Which will be the inner loop?Which will be the outer loop?

• The LCV of the inner loop must be the one which changes the most often

What goeshere?

row row rowcol col col

endl

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Passing Arrays as Parameters

• Recall declaration for 1-D array

• we didn’t specify the size in the brackets– we sent the size as a separate parameter

• Recall name of the array is a pointer constant– tells where the array starts in memory– this is what is passed to the function

void whatever ( float num_list [ ], int size);void whatever ( float num_list [ ], int size);

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Passing 2-D Arrays as Parameters

• For a 2-D array, declare

• We are sending the starting address– also how many elements it takes to jump us to the next row– that is -- the number of columns

• Note that this could be for an array for ANY number of rows, but exactly 4 columns

• As with 1-D, we also send another parameter for the function as a limiting value

void whatever ( float num_table [ ][4], int num_rows);void whatever ( float num_table [ ][4], int num_rows);

30

Alternate 2-D Array Definition

• Think of the 2-D array as an array of arrays

• Example

• Each element of renters is an array of rent_pmts

typedef float rent_pmts [12];rent_pmts renters [6];

typedef float rent_pmts [12];rent_pmts renters [6];

50 50 … 50 50

50 50 … 50 50

… … …

50 50 … 50 50

0

1

…

5

0 1 … 10 11

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Multidimensional Arrays

• C++ arrays not limited to two dimensions– limitation is amount of memory

50 50 … 50 50

50 50 … 50 50

… … …

50 50 … 50 50

const int NUM_BLDGS = 10;const int APTS_PER_BLDG = 12;float apt_pmts [NUM_BLDGS][6][APTS_PER_BLDG];


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Multidimensional Arrays

• C++ arrays not limited to two dimensions

– limitation is amount of memory

50 50 … 50 50

50 50 … 50 50

… … …

50 50 … 50 50



This gives a 3-D array with 720 items

apt_pmt [bldg][tennant][apt]

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Testing and Debugging

• Initialize all components of an array

– no guarantee of what is there to start with

• Use the same number of indeces as the declaration of array

• Make sure indeces are in order

– don’t reverse row and column references

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• Use meaningful identifiers for the array name and indeces

• Double check upper and lower bounds on indeces

– don’t walk off the edge of the array

• When declaring multidimensional array as a formal parameter

– must state sizes of all but first dimension

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• When calling function with array as parameter

– sizes of multi-dim actual parameter must match exactly sizes of formal

• Use typedef statement to define multi-dimensional array type

– use this for actual and formal parameter declaration

1 arrays … the sequel applications and extensions chapter 10

Documents

list list

list length

new number list

smallest number list

list elements

ordered list

list example

list unordered