DATA STRUCTURE
CSC 212
REEM ALMOTIRI
Information Technology Department
Majmaah University
1
Lecture 2
Searching and Sorting Arrays
2
Topics
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What is Searching
Linear Searching Algorithms
Binary Search Algorithm
What is Sorting
Types of Sorting Algorithms
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What is Searching
Search: locate an item in a list (array, vector, etc.)
of information
Searching :-is the process of determining whether
or not a given value exists in a data structure or a
storage media.
We discuss two searching methods on one - dimensional
arrays:-
– Linear search
– Binary search
4
Linear Searching Algorithms
Suppose that you want to determine whether 27 is in the list
First compare 27 with list[0]; that is, compare 27 with 35
Because list[0] ≠ 27, you then compare 27 with
list[1]
Because list[1] ≠ 27, you compare 27 with the next
element in the list
Because list[2] = 27, the search stops
This search is successful!
Figure 1: Array list with seven (07) elements
5
Linear Searching Algorithms
int linearSearch(const int integerArray[],int SIZE,int value)
{ int index = 0;
int position1 = -1;
bool foundNum = false;
while(index < SIZE)
{
if(integerArray[index] == value)
{
foundNum = true;
position1 = index;
}
index++;
}
return position1;
}
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Linear Search Algorithm
Set found to false
Set position to –1
Set index to 0
While index < number of elts and found is false
If list [index] is equal to search value
found = true
position = index
End If
Add 1 to index
End While
Return position
9-7
Linear Search Example
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Array numlist contains
17
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23
5
11
2
29
3
Searching for the value 11, linear search examines 17,
23, 5, and 11
Searching for the the value 7, linear
search examines 17, 23, 5, 11, 2, 29, and 3
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Linear Search Tradeoffs
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Benefits
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Easy algorithm to understand
Array can be in any order
Disadvantage
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Inefficient (slow): for array of N elements, examines
N/2 elements on average for value that is found in
the array, N elements for value that is not in the
array
Binary Search Algorithm
 Can
only be performed on a sorted list !!!
 Uses divide and conquer technique to search list
Divide a sorted array into three sections:
1.
middle element
elements on one side of the middle element
elements on the other side of the middle element
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2.
3.
If the middle element is the correct value, done.
Otherwise, go to step 1, using only the half of the
array that may contain the correct value.
Continue steps 1 and 2 until either the value is found
or there are no more elements to examine.
9-10
Binary Search Algorithm
Search item is compared with middle element
of list
1. If search item < middle element of list, search
is restricted to first half of the list
2. If search item > middle element of list, search
second half of the list
3. If search item = middle element, search is
complete
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9-11
Binary Search Example
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Array numlist2 contains
2
3
5
11
17
23
29
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Searching for the the value 11, binary search examines
11 and stops
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Searching for the the value 7, binary
search examines 11, 3, 5, and stops
9-12
Binary Search Tradeoffs
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Benefit
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Much more efficient than linear search
(For array of N elements, performs at most
log2N comparisons)
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Disadvantage
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9-13
Requires that array elements be sorted
Binary Search Algorithm example
• Determine whether 75 is in the list
Figure 2: Array list with twelve (12) elements
Figure 3: Search list, list[0] … list[11]
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Binary Search Algorithm example
Figure 4: Search list, list[6] … list[11]
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Binary Search Algorithm
int binarySearch(const int integerArray[],int size,int value)
{ int first = 0;
int last = size-1;
int midpoint = (first+last)/2;
int position2 = -1;
bool foundNum = false;
while(!foundNum && first<=last) {
if(integerArray[midpoint] == value) {
foundNum = true;
position2++;
return position2; }
else if(integerArray[midpoint] > value) {
last = midpoint-1; position2++;
}
else last = midpoint+1;
position2++; } return position2;
}
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Searching an Array of Objects
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9-17
Search algorithms are not limited to arrays of
integers
When searching an array of objects or structures,
the value being searched for is a member of an
object or structure, not the entire object or
structure
Member in object/structure: key field
Value used in search: search key
What is Sorting
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Sort: arrange values into an order
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Given a set (container) of n elements
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E.g. array, set of words, etc.
Goal Arrange the elements in ascending order
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Alphabetical
Ascending numeric
Descending numeric
Start  1 23 2 56 9 8 10 100
End  1 2 8 9 10 23 56 100
Types of Sorting Algorithms
There are many, many different types of sorting algorithms, but
the primary ones are:
Bubble Sort
 Selection Sort
 Insertion Sort
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Bubble Sort Algorithm
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Algorithm :1.
2.
3.
4.
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Compare 1st two elements and exchange them if they are
out of order.
Move down one element and compare 2nd and 3rd
elements. Exchange if necessary. Continue until end of
array.
Pass through array again, repeating process and exchanging
as necessary.
Repeat until a pass is made with no exchanges.
Bubble Sort Example
Array numlist3 contains
17
Compare values 17 and
23. In correct order, so
no exchange.
23
5
11
Compare values 23 and
11. Not in correct order,
so exchange them.
Compare values 23 and
5. Not in correct order,
so exchange them.
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Bubble Sort Example (continued)
After first pass, array numlist3 contains
In order from
previous pass
17
Compare values 17 and
5. Not in correct order,
so exchange them.
5
11
23
Compare values 17 and
23. In correct order, so
no exchange.
Compare values 17 and
11. Not in correct order,
so exchange them.
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Bubble Sort Example (continued)
After second pass, array numlist3 contains
In order from
previous passes
5
Compare values 5 and
11. In correct order, so
no exchange.
11
17
23
Compare values 17 and
23. In correct order, so
no exchange.
Compare values 11 and
17. In correct order, so
no exchange.
9-23
No exchanges, so
array is in order
Bubble Sort Tradeoffs
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Benefit
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Easy to understand and implement
Disadvantage
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Inefficiency makes it slow for large arrays
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Bubble Sort
7 2 8 5 4
2 7 5 4 8
2 5 4 7 8
2 4 5 7 8
2 7 8 5 4
2 7 5 4 8
2 5 4 7 8
2 4 5 7 8
2 7 8 5 4
2 5 7 4 8
2 4 5 7 8
2 7 5 8 4
2 5 4 7 8
2 7 5 4 8
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(done)
Bubble Sort
void bubbleSort(int arr[], int n) {
bool swapped = true;
int j = 0;
int tmp;
while (swapped) {
swapped = false;
j++;
for (int i = 0; i < n - j; i++) {
if (arr[i] > arr[i + 1]) {
tmp = arr[i];
arr[i] = arr[i + 1];
arr[i + 1] = tmp;
swapped = true;
}
}
} }
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Selection sort
The idea of algorithm is quite simple.
Array is imaginary divided into two parts:
- sorted one and unsorted one.
At the beginning, sorted part is empty, while unsorted
one contains whole array.
At every step, algorithm finds minimal element in
the unsorted part and adds it to the end of the sorted
one.
When unsorted part becomes empty, algorithm stops.
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Selection Sort Algorithm
1.
Locate smallest element in array and exchange it
with element in position 0.
2.
Locate next smallest element in array and exchange
it with element in position 1.
3.
Continue until all elements are in order.
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Selection Sort Example
Array numlist contains
11
2
29
3
Smallest element is 2. Exchange 2 with
element in 1st array position (i.e. element 0).
Now in order
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2
11
29
3
Selection Sort – Example (continued)
Next smallest element is 3. Exchange
3 with element in 2nd array position.
Now in order
2
3
29
11
Next smallest element is 11. Exchange
11 with element in 3rd array position.
Now in order
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2
3
11
29
Selection sort
Given an array of length n,
Search elements 0 through n-1 and select the smallest
Swap it with the element in location 0
Search elements 1 through n-1 and select the smallest
Swap it with the element in location 1
Search elements 2 through n-1 and select the smallest
Swap it with the element in location 2
Search elements 3 through n-1 and select the smallest
Swap it with the element in location 3
Continue in this fashion until there’s nothing left to search
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Selection sort
7 2 8 5 4
2 7 8 5 4
2 4 8 5 7
2 4 5 8 7
2 4 5 7 8
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Selection sort
void selectionSort(int arr[], int n) {
int i, j, minIndex, tmp;
for (i = 0; i < n - 1; i++) {
minIndex = i;
for (j = i + 1; j < n; j++)
if (arr[j] < arr[minIndex])
minIndex = j;
if (minIndex != i) {
tmp = arr[i];
arr[i] = arr[minIndex];
arr[minIndex] = tmp;
}
}
} 33
Selection Sort Tradeoffs
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Benefit
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More efficient than Bubble Sort, due to fewer
exchanges
Disadvantage
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Considered harder than Bubble Sort to understand
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Insertion sort
Insertion sort algorithm resembles selection sort. Array is
imaginary divided into two parts - sorted
one and unsorted one.
At the beginning, sorted part contains first element of
the array and unsorted one contains the rest.
At every step, algorithm takes first element in
the unsorted part and inserts it to the right place of
the sorted one.
When unsorted part becomes empty, algorithm stops.
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Insertion sort
:
36
Insertion sort
:
void insertionSort(int arr[], int length) {
int i, j, tmp;
for (i = 1; i < length; i++) {
j = i;
while (j > 0 && arr[j - 1] > arr[j]) {
tmp = arr[j];
arr[j] = arr[j - 1];
arr[j - 1] = tmp;
j--;
}
}
}
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Sorting an Array of Objects
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As with searching, arrays to be sorted can contain objects
or structures
The key field determines how the structures or objects
will be ordered
When exchanging contents of array elements, entire
structures or objects must be exchanged, not just the key
fields in the structures or objects
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HOMEWORK!
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