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Data Structures & Algorithms

Lecture # 6


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Searching Algorithms

Sequential Search

Binary Search

Sorting Algorithms

Bubble Sort

Selection Sort

Insertion Sort Merge Sort

Today Topics


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What is Searching?

The process of finding a specific data item or record froma list is called searching.

Main task is efficient storage of data to facilitate fast

searching.

Other operations like inserting and deletion aredependent on this operation. For example, to delete a data item from a list, its position is first

located in the list and then the deletion operation is performed.


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What is Searching?

If specified data is found, Search is successful

Search operation is terminates when it is successful

If specified data is not found, search is unsuccessful

Commonly used searching methods are:

Sequential Search Binary Search


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Sequential Search It is simple and straightforward technique to

search a specified item in an unordered list

Specified value is searched in the listsequentially i.e. starting from the first elementto the last element in the list in a sequence.

When the required value is found, searchoperation stops.


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Sequential Search It is slow process

It is used for small amounts of data

It is not recommended for large

amount of data


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Algorithm Sequential SearchSearchItem (Item, ABC, LOC)

Find a value ITEM from an array ABC consisting of Nelements

1. start

2. Set Loc = -1

3. Repeat step-4 FOR I = 1 to N

4. If Item = ABC[I] then

Loc = IPrint Item found at location , Loc

End if


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Algorithm Sequential Search5. If Loc = -1 then

Print Item not Found

End if

6. Exit


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void main(){int arr[25];int n,item;coutn;for(int i=0;I


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int main(void){

int array[10]cout> key;

int flag = 0; // set flag to off

for(int i=0; i


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Algorithm Sequential SearchReplaceSearchItem (Value1, Value2)

Find a Value1 from an array ABC consisting of Nelements and replace with Value2

1. start

2. Set Loc = -1


4. If Item = ABC[I] then

ABC [I] = Value2Loc = I

Print Item modified at location , Loc

End if


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Algorithm Sequential Search5. If Loc = -1 then

Print Item not Found

End if

6. Exit


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Algorithm Sequential SearchFindLargeValue ()

Find and print the largest value in an array ABCconsisting of N elements

1. start

2. Set Max = ABC[0]


4. If Max < ABC[I] then

Max = ABC [I]End if

5. Print Max

6. Exit


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(Largest Element in Array) A nonempty arrayDATA with N numerical values is given. Thisalgorithm finds the location LOC and the value

MAX of the largest element ofDATA. Thevariable K is used as a counter.

Step 1. [Initialize] Set K:= 1, LOC := 1 and

MAX:= DATA[K].

Step 2. [increment counter]. Set K:= K + 1. Step 3. [Test counter] if K > N , than

write: LOC, MAX, and exit.

Step 4. [compare and update] if MAX < DATA[K],

than,

Set LOC:=K and MAX:= DATA[K]. Step 5. [Repeat loop]. Go to step 2.


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Binary Search It is a more efficient technique to

search a specific item from list of

items.

It is mostly used for relatively largelists or table of records that aresorted in ascending or descendingorder


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Binary Search It begins by searching the required value from the

middle of the list.

If the required value is in the middle of the list thensearch process terminates at that point.

If the list is sorted in ascending order and the requiredvalue is greater than the value at middle, the controlgoes to the higher value to search.

If the list is sorted in ascending order and the requiredvalue is lesser than the value at middle, the control goesto the lesser value to search.


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Algorithm Binary SearchBinarySearch(Item)

To find a value in an array ABC consisting of N elementssorted in ascending order

1. Start, LOC:=NULL

2. Set BEG:= LB, END:=UB and MID:= INT((BEG+END)/2)

3. Repeat step 3 and 4 while ABC[MID] != ITEM


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Algorithm Binary Search5. If Item < ABC [Mid] then

SET END:= MID-1.

else:

SET BEG: MID +1.

[end of if structure]

6. Set MID:= INT ((BEG+END)/2).

[end of step 2 loop]

7. If ABC[MID]=ITEM, then

SET LOC:=MID.

else:

SET LOC: NULL

8. [end of if structure]

9.exit


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performance The advantage of a binary search over a linear search is

outstanding for large numbers.

For an array of a million elements, binary search, O(logN), will find the target element with a worst case of only20 comparisons.

Linear search, O(N), on average will take 500,000comparisons to find the element.


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// binary search of an integer array, this search isefficient for large arrays

int main()

{

int a[20] = {0};

int n, i, j, temp;

int *beg, *end, *mid, target;

printf(" enter the total integers you want to enter (make it lessthen 20):\n");

scanf("%d", &n);

if (n >= 20) return 0;

printf(" enter the integer array elements:\n" );

for(i = 0; i < n; i++)

{

scanf("%d", &a[i]);

}


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// sort the loaded array, a must for binary search!

// you can apply qsort or other algorithms here

for(i = 0; i < n-1; i++)

{

for(j = 0; j < n-i-1; j++)

{

if (a[j+1] < a[j])

{

temp = a[j];

a[j] = a[j+1];

a[j+1] = temp;

}

}

} printf(" the sorted numbers are:");

for(i = 0; i < n; i++)

{

printf("%d ", a[i]);

}


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point to beginning and end of the array

beg = &a[0]; end = &a[n]; // use n = one element past the loaded

array!

printf("\n beg points to address %d and end to %d",beg,end); // test

mid should point somewhere in the middle ofthese addresses

mid = beg += n/2;

printf("\n mid points to address %d", mid); // test

printf("\n enter the number to be searched:");

scanf("%d",&target);


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binary search, there is an AND in the middle of while()!!!

while((beg


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// did you find the target?

if (*mid == target)

{

printf("\n %d found!", target);

}

else

{

printf("\n %d not found!", target);

}

getchar(); // trap enter

getchar(); // wait

return 0;

}


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Sorting The process of arranging data in a specified

order according to a given criteria is calledsorting.

The numeric type data may be arranged eitherin ascending or in descending order.

Character type data may be arranged inalphabetical order.


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Sorting Sorting methods can be divided into two types basedupon the complexity of their algorithms.

One type of sorting algorithms includes

Bubble Sort

Insertion Sort

Selection Sort

Other type consists is

Merge Sort

Choice of a method depends upon the type and size ofdata to be sorted.

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