1. Introduction to Searching techniques and
Matrices
Objectives
In this lesson, you will learn to:
State the algorithm for linear search
Perform operations on matrices
State the applications of matrices
Implement Recursion
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2. Introduction to Searching techniques and
Matrices
Searching
Searching is an operation that returns either:
The location of a given item of information
A message that the given information is not found
Searching algorithm depends on the type of data
structure used to store data
For example, there can be a data structure with:
Faster search operation (sorted array)
Faster modification operation (linked list)
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3. Introduction to Searching techniques and
Matrices
Searching (Contd..)
There is a trade-off in these data structures
Sorted array insertion and deletion is time
consuming
Linked list traversal is time-consuming
The different searching techniques are:
Linear search
Binary search
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4. Introduction to Searching techniques and
Matrices
Linear Search
Is the simplest search technique
In this technique begin at one end and scan until:
The item is found
The end of the list is reached
Benefits:
Can be used on any data structure
No restrictions on the way data is arranged
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5. Introduction to Searching techniques and
Matrices
Linear Search (Contd..)
Drawbacks:
Performance is dependant on the length of the
array
Average number of comparisons 1/2(n+1)
Even if required data is not present the complete
array is searched
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6. Introduction to Searching techniques and
Matrices
Binary Search
Binary search technique is faster than linear search
technique
After every search the number of items to be
searched is reduced by half
In this search technique:
Start by comparing the middle element
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7. Introduction to Searching techniques and
Matrices
Binary Search (Contd..)
Then the next quarter and so on until
The required item is found
No more data is left for searching
Benefits:
Faster search
After each step number of items to be searched
reduces by half
More efficient for searching large volume of data
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8. Introduction to Searching techniques and
Matrices
Binary Search (Contd..)
Average number of comparisons for 1 million items is
only 20
Drawbacks:
Data has to be sorted
Cannot be used on all data structures
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9. Introduction to Searching techniques and
Matrices
Problem Statement 4.D.1
Write a program to accept 20 numbers and store it in
an array. Now accept a number and search it in an
array, make sure that, before searching a number you
perform bubble sort it in.
Note: Implement using arrays
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10. Introduction to Searching techniques and
Matrices
Just A Minute
In a sorted array insertion and deletion are less time
consuming than searching.(True/False)
In a binary tree searching is more time consuming than
linked list ( True/False)
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11. Introduction to Searching techniques and
Matrices
Matrices
A rectangular arrangement of rows and columns is a
matrix
COLUMNS
A B C D
E F G H
ROWS
E F G H
I J K L
I J K L
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12. Introduction to Searching techniques and
Matrices
Matrices (Contd..)
The size of the matrix is called the dimensions of the
matrix
The sum of rows and columns of a matrix identify the
size
Each number in a matrix is called an element
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13. Introduction to Searching techniques and
Matrices
Matrices (Contd..)
A matrix with the same number of rows and columns
is called a square matrix
A B C
E F
E F G
I J
I J K
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14. Introduction to Searching techniques and
Matrices
Matrices (Contd..)
A X D
X Z
D
Z
E
The above figure shows another type of matrix that is,
a sparse matrix
A matrix with lot of blank elements is called a sparse
matrix
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15. Introduction to Searching techniques and
Matrices
Operations on Matrices
The basic operations on a matrix can be listed as:
Create
Store
Delete
Retrieve
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16. Introduction to Searching techniques and
Matrices
Multi-dimensional Matrix
4 Pages
2 Rows
3 Columns
The syntax for declaring a three-dimensional matrix is
same as that of two-dimensional array
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17. Introduction to Searching techniques and
Matrices
Multi-dimensional Matrix (Contd..)
Example:
int Newone[2][3][4];
The array Newone[2][3][4] contains 2*3*4=24
elements
The subscripts of the array are called:
row
column
page
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18. Introduction to Searching techniques and
Matrices
Multi-dimensional Matrix (Contd..)
In this array, we can store 8 different set of details.
Sum of row and page gives the number of different
sets of information that can be stored
Example: 4*2 = 8 for the array Newone
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19. Introduction to Searching techniques and
Matrices
Applications
Matrices can be applied in:
Finding the shortest route
Map coloring
Search engines for the WEB when combined with
queues and hash tables
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20. Introduction to Searching techniques and
Matrices
Problem Statement 4.D.2
Write a program to store the details of a student
( Student name, Registration number, and the Subject
marks) in a three-dimensional array. Also, give an option
to the user to query and print the details for a specific
student requested by the user by entering the
registration number of the student. Accept the student
data from the user?
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21. Introduction to Searching techniques and
Matrices
Recursion
Whenever a function invokes itself, it is called
recursion.
Every time a recursive function calls itself, it must call
itself with different values.
A recursive procedure or function must satisfy the
following two conditions:
There must be certain values called base values
for which the function will not call back itself.
Each time the function refers to itself, the
arguments passed must be closer to its base
value.
It is useful in writing clear, short, and simple programs
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22. Introduction to Searching techniques and
Matrices
Practice Statement 4.P.1
Identify the erroneous step(s) in the following Table
A.2
Step 1 0!=1
Step 2 1! =1*1=1
Step 3 2!=2*1=2
Step 4 3! =3x2 =6
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23. Introduction to Searching techniques and
Matrices
Just a Minute…
The factorial() function will repeatedly invoke itself until
the parameter passed to it is _____.
When the above function is invoked with a parameter of
5, the factorial() function is invoked ____ times in all.
State whether True or False.
With large values (say,100) of the parameter passed to
the factorial() function, there is a danger of the program
crashing.
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24. Introduction to Searching techniques and
Matrices
Summary
In this lesson, you learned that:
Information retrieval is one of the most important
applications of computers
Searching is an operation, which:
Returns the location in memory of some given
item of information
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25. Introduction to Searching techniques and
Matrices
Summary (Contd..)
The search algorithm depends mainly on the type of
data structure we use to store the data in memory
In a sorted array the search time can be greatly
reduced by using a search technique called binary
search
In sorted array, there is an overhead-involved that is,
insertion and deletion of data is a time-consuming
process
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26. Introduction to Searching techniques and
Matrices
Summary (Contd..)
In a linked List:
Search time will be high
Only sequential search is possible
Insertion and deletion will be fast
Binary Tree combines the advantage of sorted array
and a linked list
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27. Introduction to Searching techniques and
Matrices
Summary (Contd..)
Linear search is also referred to as sequential search
is the simplest search technique
In Linear Search, to search an item begin at one end
of the list and scan down the list until:
The desired item is found
The end of the list is reached
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28. Introduction to Searching techniques and
Matrices
Summary (Contd..)
The average number of comparison for a linear
search can be worked out by applying the formula
1/2(n+1)
Linear search technique has some drawbacks:
Even if there is no match for the item in the list, the
complete list is searched
The search time is directly proportional to the
length of the list
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29. Introduction to Searching techniques and
Matrices
Summary (Contd..)
Binary search is faster than linear search technique
In Binary Search, to search an item begin at the
middle of the list and scan one half of the list , then
the quarter and so on until:
the desired item is found or
there is no more data to search
In a binary search, after every comparison, the data to
be searched reduces by half.
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30. Introduction to Searching techniques and
Matrices
Summary (Contd..)
The drawbacks of binary search are:
The list has to be sorted
There should be a method to access the middle
element of the list
A rectangular arrangement of rows and columns is
called a matrix
A matrix with the same number of rows and columns
is called a square matrix
A matrix with a lot of zero or unused elements is
generally called a sparse matrix
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31. Introduction to Searching techniques and
Matrices
Summary (Contd..)
The basic operations on a matrix can be listed as:
Create
Store
Delete
Retrieve
The subscripts of a three-dimensional array are called:
Row
Column
Page
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32. Introduction to Searching techniques and
Matrices
Summary (Contd..)
Matrices can be applied for:
Finding a shortest route
Map coloring
Recursion can be defined as defining something in
terms of itself. A function is recursive if it makes a call
to itself, i.e. invokes itself.
Advantage of recursion is that it is useful in writing
clear, short, and simple programs.
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