sa07slide(singledimensionalarray)

8/7/2019 sa07slide(SingleDimensionalArray)

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Single-DimensionalArrays


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Introducing Arrays

Array is a data structure that represents a collection of thesame types of data.

5.6

4.5

3.3

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4.0

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99.993

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double myList [10];

myList[0]

myList[1]

myList[2]

myList[3]

myList[4]

myList[5]

myList[6]

myList[7]

myList[8]

myList[9]

Element value

Array element at

index 5


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Declaring Array Variablesdatatype arrayName[arraySize];

Example:

double myList[10];

C++ requires that the array size used to declare an array must be a

constant expression. For example, the following code is illegal:

int size = 4;

double myList[size]; // Wrong

But it would be OK, if size is a constant as follow:

const int size = 4;

double myList[size]; // Correct


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Arbitrary Initial Values

When an array is created, its elementsare assigned with arbitrary values.


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Indexed VariablesThe array elements are accessed through the index. Arrayindices are 0-based; that is, they start from 0 to arraySize-1.In the past example , myList holds ten double values andthe indices are from 0 to 9.

Each element in the array is represented using thefollowing syntax, known as an indexed variable:

arrayName[index];

For example, myList[9] represents the last element in thearray myList.


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UsingIndexed Variables

After an array is created, an indexed variable canbe used in the same way as a regular variable.

For example, the following code adds the value

in myList[0] and myList[1] to myList[2].

myList[2] = myList[0] + myList[1];


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No Bound Checking

C++ does not check arrays boundary. So, accessing

array elements using subscripts beyond the

boundary (e.g., myList[-1] and myList[11]) does

not cause syntax errors, but the operating systemmight report a memory access violation.


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Array Initializers

Declaring, creating, initializing in one step:

dataType arrayName[arraySize] = {value0, value1,

..., valuek};

double myList[4] = {1.9, 2.9, 3.4, 3.5};


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Declaring, creating, initializing

Using the Shorthand Notation

double myList[4] = {1.9, 2.9, 3.4, 3.5};

This shorthand notation is equivalent to thefollowing statements:

double myList[4];

myList[0] = 1.9;myList[1] = 2.9;

myList[2] = 3.4;

myList[3] = 3.5;


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Implicit Size

C++ allows you to omit the array size whendeclaring and creating an array using an initilizer.

For example, the following declaration is fine:

double myList[] = {1.9, 2.9, 3.4, 3.5};

C++ automatically figures out how many elementsare in the array.


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Partial Initialization

C++ allows you to initialize a part of the array. Forexample, the following statement assigns values

1.9, 2.9 to the first two elements of the array. The

other two elements will be set to zero. Note that ifan array is declared, but not initialized, all its

elements will contain garbage, like all other local

variables.

double myList[4] = {1.9, 2.9};


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Initializing Character Arrays

char city[] = {'D', 'a', 'l', 'l', 'a', 's'};

char city[] = "Dallas";

This statement is equivalent to the preceding statement,except that C++ adds the character '\0', called the nullterminator, to indicate the end of the string, as shown inFigure below.

city[0] city[1]

'D' 'a' 'l' 'l' 'a' 's' '\0'

city[2] city[3]city[4]city[5] city[6]


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Initializing arrays with random

values

The following loop initializes the array myList withrandom values between 0 and 99:

for (int i = 0; i < ARRAY_SIZE; i++){

myList[i] = rand() % 100;

}


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Trace Program with Arrays

int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){

values[i] = i + values[i-1];

}

values[0] = values[1] + values[4];

}

Declare array variable values, create an

array, and assign its reference to values

After the array is created

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animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){


}


}

i becomes 1

After the array is create

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animation


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int main()

{

int values[5];

for (int i = 1; i < 5; i++){

values[i] = values[i] + values[i-1];

}


}

i (=1) is less than 5

After the array is create

0

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0

0

0

0

0

animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){


}


}

After this line is executed, value[1] is 1

After the first iteration

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animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){


}

values[0] = values[1] +values[4];

}

After i++, i becomes 2

animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++)

{


}

values[0] = values[1] +

values[4];}

i (= 2) is less than 5

animation


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1

0

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0


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){


}


}

}

After this line is executed,

values[2] is 3 (2 + 1)

After the second iteration

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animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){


}


}

After this, i becomes 3.


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animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){


}


}

i (=3) is still less than 5.


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animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){


}


}

After this line, values[3] becomes 6 (3 + 3)

After the third iteration

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0

animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){


}


}

After this, i becomes 4


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animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){


}


}

i (=4) is still less than 5


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animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){


}


}

After this, values[4] becomes 10 (4 + 6)

After the fourth iteration

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animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++)

{

values[i] = i + values[i-1];}


}

After i++, i becomes 5

animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){


}


}

i ( =5) < 5 is false. Exit the loop

animation


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int main()

{

int values[5]={0};

for (int i = 1; i < 5; i++){


}


}

After this line, values[0] is 11 (1 + 10)

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11

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animation


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Printing arrays

To print an array, you have to print each element in thearray using a loop like the following:

for (int i = 0; i < ARRAY_SIZE; i++){

cout


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Printing Character Array

For a character array, it can be printed using one printstatement. For example, the following code displaysDallas:

char city[] = "Dallas";

cout


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Copying Arrays

Can you copy array using a syntax like this?

list = myList;

This is not allowed in C++. You have to copy individualelements from one array to the other as follows:

for (int i = 0; i < ARRAY_SIZE; i++)

{

list[i] = myList[i];

}


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Summing All Elements

Use a variable named total to store the sum. Initially totalis 0. Add each element in the array to total using a looplike this:

double total = 0;


{

total += myList[i];

}


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Finding the Largest Element

Use a variable named max to store the largest element.Initially max is myList[0]. To find the largest element inthe array myList, compare each element in myList withmax, update max if the element is greater than max.

double max = myList[0];


{if (myList[i] > max) max = myList[i];

}


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Finding the smallest index of the

largest element

double max = myList[0];

int indexOfMax = 0;


{if (myList[i] > max)

{

max = myList[i];

indexOfMax = i;

}

}


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Searching Arrays

Searching is the process of looking for a specific element inan array; for example, discovering whether a certain score isincluded in a list of scores. Searching is a common task incomputer programming. There are many algorithms anddata structures devoted to searching. In this section, two

commonly used approaches are discussed, linear search andbinary search.

int linearSearch(const int list[], int key, int arraySize)

{

for (int i = 0; i < arraySize; i++)

{if (key == list[i])

return i;

}

return-1;

}

list

key Compare key with list[i] for i = 0, 1,

[0] [1] [2]


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Linear Search

The linear search approach compares the key

element, key,sequentially with each element in

the array list. The method continues to do so

until the key matches an element in the list orthe list is exhausted without a match being

found. If a match is made, the linear search

returns the index of the element in the arraythat matches the key. If no match is found, the

search returns -1.


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Linear Search Animation

6 4 1 9 7 3 2 8

6 4 1 9 7 3 2 8

6 4 1 9 7 3 2 8

6 4 1 9 7 3 2 8

6 4 1 9 7 3 2 8

6 4 1 9 7 3 2 8

3

3

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3

3

animation

Key List


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Binary Search

For binary search to work, the elements in the

array must already be ordered. Without loss of

generality, assume that the array is in

ascending order.e.g., 2 4 7 10 11 45 50 59 60 66 69 70 79

The binary search first compares the key with

the element in the middle of the array.


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Binary Search, cont.

If the key is less than the middle element,

you only need to search the key in the firsthalf of the array.

If the key is equal to the middle element,the search ends with a match.

If the key is greater than the middleelement, you only need to search the key inthe second half of the array.

Consider the following three cases:


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Binary Search

1 2 3 4 6 7 8 9

1 2 3 4 6 7 8 9

1 2 3 4 6 7 8 9

8

8

8

Key List

animation


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[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

2 4 7 10 11 45 50 59 60 66 69 70 79

key is 11

key < 50

list

mid

[0] [1] [2] [3] [4] [5]

key > 7

key == 11

highlow

mid highlow

list

[3] [4] [5]

mid highlow

list

2 4 7 10 11 45

10 11 45


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Binary Search, cont.[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

2 4 7 10 11 45 50 59 60 66 69 70 79

key is 54

key > 50

list

mid

[0] [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

key < 66

key < 59

highlow

mid highlow

list

[7] [8]

mid highlow

list

59 60 66 69 70 79

59 60

[6] [7] [8]

highlow

59 60


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The binarySearch method returns the index of the

search key if it is contained in the list. Otherwise,

it returns insertion point - 1. The insertion point is

the point at which the key would be inserted into

the list.


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From Idea to Solutionint binarySearch(const int list[], int key, int arraySize)

{

int low = 0;

int high = arraySize - 1;

while (high >= low)

{

int mid = (low + high) / 2;

if (key < list[mid])high = mid - 1;

else if (key == list[mid])

return mid;

else

low = mid + 1;

}

return low - 1;

}


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Sorting Arrays

Sorting, like searching, is also a common task incomputer programming. It would be used, for

instance, if you wanted to display the grades from

Listing 6.2, AssignGrade.cpp, in alphabetical order.Many different algorithms have been developed for

sorting. This section introduces two simple, intuitive

sorting algorithms: selection sort and insertion sort.


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Selection sort finds the largest number in the list and places it last. It then finds the largestnumber remaining and places it next to last, and so on until the list contains only a singlenumber. Figure 6.17 shows how to sort the list {2, 9, 5, 4, 8, 1, 6} using selection sort.

Selection Sort

2 9 5 4 8 1 6

swap

Select 1 (the smallest) and swap it

with 2 (the first) in the list

1 9 5 4 8 2 6

swap

The number 1 is now in thecorrect position and thus no

longer needs to beconsidered.

1 2 5 4 8 9 6

swap

1 2 4 5 8 9 6


with 9 (the first) in the remaining

list

The number 2 is now in thecorrect position and thus no

longer needs to beconsidered.Select 4 (the smallest) and swap itwith 5 (the first) in the remaining

list

The number 6 is now in the

correct position and thus no


1 2 4 5 8 9 6Select 6 (the smallest) and swap itwith 8 (the first) in the remaining

list

1 2 4 5 6 9 8

swap




1 2 4 5 6 8 9


with 9 (the first) in the remaininglist


correct position and thus nolonger needs to beconsidered.

Since there is only one element

remaining in the list, sort is

completed

5 is the smallest and in the right

position. No swap is necessary




swap

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