11542_2-dimensional arrays and searching

8/3/2019 11542_2-Dimensional Arrays and Searching

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Two Dimensional arrays

And searching


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Two Dimensional Array:

A two dimensional m X n array A is a collection ofm . N data elements such that each element isspecified by a pair of integers.

Two dimensional arrays are called matrices in

mathematics and tables in business applications.

There is a standard way of drawing 2-dimensionalm X n array A where the elements of A form arectangular array with m rows and n columns and

where the element A[j,k] appears in row j andcolumn k.

A row is a horizontal list and column is a vertical listof elements.


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A[0,0] A[0,1]

A[1,0] A[1,1]

A[2,2]

Suppose a is a 2-dimensional array. The firstdimension of A Contains the index set 1---m, withLB=1 and UB=m and second with LB=1 and UB=n.the length of a dimension is the number of integers

in its index set. The pair of lengths m x n is calledthe size of the array

Student Test1 Test2

1 56 44

2 55 78

3 44 34


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0,1

2,1

3,1

1,2

2,2

3,2

1,3

2,3

3,3

Representation of 2-Dimensional Arrays

in Memory 1,11,2

1,3

2,1

2,2

2,3

3,1

3,2

3,3

Column Major

order

Row Major

order


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Searching

Searching refers to the operation of finding thelocation LOC of ITEM in DATA, or printing somemessage that item does not appear there. Thesearch is said to be successful if item does

appear in DATA and unsuccessful otherwise

Two techniques for searching the data.

Linear Search

Binary Search


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Linear Search: Algo(Linear Search)1) Set i=0

2) Repeat steps 3 and 4 while i


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In the best case the item may occur atfirst position. In this case the searchoperation terminates in success with just

one comparison. In worst case i.e either the item is

present at last position or missing fromthe array the search terminates in afailure or either n comparisons.


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Binary Search

Prerequisite for applying this technique

is that the data should be in sorted orderi.e in increasing numerical order forexample telephone directory .


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Binary Search: Algorithm(this algorithmfinds the location of item in data or setsloc=null)

1) [Initialize segment variables]

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

2) Repeat Steps 3 and 4 while BEG


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EXAMPLE:

Data given 22,44,40,11,30,55,66,77,60,3

Search :30

3,11,22,30,40,44,55,60,66,77,

Mid=INT((1+10)/2)=5

A[5]=40Item


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11542_2-dimensional arrays and searching

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