CS212: DATASTRUCTURES

Lecture 3: Searching

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Lecture Contents

searching Sequential search algorithm. Binary search algorithm.

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Search Algorithms

Searching , the process used to find the location of a target among a list of objects.

In this chapter, we will study searches that work with arrays Search

Algorithms

Sequential

Search

Binary Search

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Search Algorithms

1. Sequential search.

1. It works on the ordered list or the unordered.

2. Binary search.

It requires an ordered list.

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1/ Sequential (Linear) Search

Search an array or list by checking items one at a time.

Sequential search is usually very simple to implement, and is practical when the list has only a few elements, or when performing a single search in an unordered list. Look at every element : This is a very

straightforward loop comparing every element in the array with the target(key).

Eighter we find it,

or we reach the end of the list! Sequential search works the same for both array-

based and linked lists

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Sequential Search

public int linearSearch (int target)

{

for (int n = 0; n < a.length ; n++)

{if (a[n] == target)

return n;

{

return –1;

}

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Locating data in unordered list.

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2/ Binary search algorithm

Search a sorted array by repeatedly dividing the search interval in half.

A fast way to search a sorted array is to use a binary search.

Can’t use binary search algorithm with linked list No physical relationship between the nodes

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Binary search algorithm

Test the data in the element at the middle of the array.

it is in the first half before middle

it is in the second half after middle

Test the data in the element at the middle of the array.

Test the data in the element at the middle of the array.

it is in the second

half!

it is in the second half!

it is in the first half!

it is in the first half!

.. .... ..

Calculate the middle element

Calculate the middle element

If the middle element equals to the Target , the algorithm stops

Target < middle element Target > middle element

Target < middle Target < middle Target > middleTarget > middle

Calculate the middle element

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target > A[mid]first = mid +1

target == A[mid]

target < A[mid]last = mid -1

mid=(first+last)/2

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target < A[mid]last = mid -1

target > A[mid]first = mid +1

target < A[mid]last = first not found stop

target > A[mid]first = mid +1

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Recursive Binary search algorithm

algorithm RecBinarySearch (First, last , target)INPUT

First is index to first element in the list. last is index to last element in the list. target contains the data to be located.

OUTPUT if found – return the index

if not found – return (-1)

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Recursive search algorithm

mid = if target = a[mid] then

Location= midelse if (first=last) then

Location= -1else if (target < a[mid]) then

Location =binarySearch(first, mid-1, target)else if (target > a[mid]) then

Location=binarySearch(mid+1, last, target ) Return Location

2/)( lastfirst

base cases

recursive calls

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Example

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

20 11 7 5 3

BinarySearch (0,4,20)M=0+4/2=220 >7 then binarySearch(3 , 4,20)

BinarySearch (3,4,20)M=3+4/2=320 >11 then binarySearch(4 , 4,20)

BinarySearch (4,4,20)M=4+4/2=220 == 20

Return 4

Return 4

Return 4

Recursive call

Recursive call

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