Searching in Arrays

Mar 27, 2017Download as PPSX, PDF0 likes723 views

This document discusses two algorithms for searching arrays: linear search and binary search. Linear search simply checks each element of the array sequentially to find a target value, while binary search relies on the array being sorted and checks elements in a divide-and-conquer manner by repeatedly dividing the search space in half. The document provides pseudocode to illustrate how binary search works and compares the advantages of each approach.

Searching in Arrays
1
Instructor
Dhiviya Rose J , AP-Sr. Scale | SoCSE

INFO 106 – Computer Programming
Searching Arrays: Linear Search and
Binary Search
• Search an array for a key value
• Linear search
▫ Simple
▫ Compare each element of array with key value
▫ Useful for small and unsorted arrays
2

INFO 106 – Computer Programming
Linear Search
• Step through array of records, one at a time.
• Look for record with matching key.
• Search stops when
▫ record with matching key is found
▫ or when search has examined all records without
success.

INFO 106 – Computer Programming
How Linear Search works
4

INFO 106 – Computer Programming
7
Program
#include<stdio.h>
void main()
{
int a[10],i,target;
printf("Enter array value n");
for(i=0;i<n;i++)
scanf("%d",&a[i]);
printf("Which value to be search ->");
scanf("%d",&target);
/* Linear Search logic */
for(i=0;i<n;i++)
if(target==a[i])
{
printf(“Value found at %d”,i);
}
}

INFO 106 – Computer Programming
Advantages of Linear Search
• Don't have to sort the data we search.
• Works well if only search operation is minimum
• Not optimal in case of large amount of data
8

INFO 106 – Computer Programming
Binary Search
• Assume that we are give an array of records that
is sorted. For instance:
▫ an array of records with integer keys sorted from
smallest to largest (e.g., ID numbers), or
▫ an array of records with string keys sorted in
alphabetical order (e.g., names).

Binary Search
[ 0 ] [ 1 ]
Example: sorted array of integer keys. Target=7.
3 6 7 11 32 33 53
[ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ]

INFO 106 – Computer Programming
Binary Search Pseudocode
…
if(size == 0)
found = false;
else {
middle = index of approximate midpoint of array segment;
if(target == a[middle])
target has been found!
else if(target < a[middle])
search for target in area before midpoint;
else
search for target in area after midpoint;
}
…

INFO 106 – Computer Programming
Program
int result=-1;
int low=0;
int high=length-1;
int mid;
while( result==-1 && low<=high )
{ mid= low + ((high - low) / 2);
if( list[mid] == target )
result = mid;
else if( list[mid] < target)
low = mid + 1;
else
high = mid - 1;
}
13

INFO 106 – Computer Programming
Other Searching Algorithms
• Interpolation Search
• Indexed Searching
• Binary Search Trees
• Hash Table Searching
• Grover's Algorithm
• Best-first
• A*
14

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Introduction All the materials around us are made up of elements. These elements can be broadly divided into two major groups: Metals Non-Metals Each group has its own unique physical and chemical properties. Let's understand them one by one. Physical Properties 1. Appearance Metals: Shiny (lustrous). Example: gold, silver, copper. Non-metals: Dull appearance (except iodine, which is shiny). 2. Hardness Metals: Generally hard. Example: iron. Non-metals: Usually soft (except diamond, a form of carbon, which is very hard). 3. State Metals: Mostly solids at room temperature (except mercury, which is a liquid). Non-metals: Can be solids, liquids, or gases. Example: oxygen (gas), bromine (liquid), sulphur (solid). 4. Malleability Metals: Can be hammered into thin sheets (malleable). Non-metals: Not malleable. They break when hammered (brittle). 5. Ductility Metals: Can be drawn into wires (ductile). Non-metals: Not ductile. 6. Conductivity Metals: Good conductors of heat and electricity. Non-metals: Poor conductors (except graphite, which is a good conductor). 7. Sonorous Nature Metals: Produce a ringing sound when struck. Non-metals: Do not produce sound. Chemical Properties 1. Reaction with Oxygen Metals react with oxygen to form metal oxides. These metal oxides are usually basic. Non-metals react with oxygen to form non-metallic oxides. These oxides are usually acidic. 2. Reaction with Water Metals: Some react vigorously (e.g., sodium). Some react slowly (e.g., iron). Some do not react at all (e.g., gold, silver). Non-metals: Generally do not react with water. 3. Reaction with Acids Metals react with acids to produce salt and hydrogen gas. Non-metals: Do not react with acids. 4. Reaction with Bases Some non-metals react with bases to form salts, but this is rare. Metals generally do not react with bases directly (except amphoteric metals like aluminum and zinc). Displacement Reaction More reactive metals can displace less reactive metals from their salt solutions. Uses of Metals Iron: Making machines, tools, and buildings. Aluminum: Used in aircraft, utensils. Copper: Electrical wires. Gold and Silver: Jewelry. Zinc: Coating iron to prevent rusting (galvanization). Uses of Non-Metals Oxygen: Breathing. Nitrogen: Fertilizers. Chlorine: Water purification. Carbon: Fuel (coal), steel-making (coke). Iodine: Medicines. Alloys An alloy is a mixture of metals or a metal with a non-metal. Alloys have improved properties like strength, resistance to rusting.

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Searching in Arrays

1. Searching in Arrays 1 Instructor Dhiviya Rose J , AP-Sr. Scale | SoCSE

2. INFO 106 – Computer Programming Searching Arrays: Linear Search and Binary Search • Search an array for a key value • Linear search ▫ Simple ▫ Compare each element of array with key value ▫ Useful for small and unsorted arrays 2

3. INFO 106 – Computer Programming Linear Search • Step through array of records, one at a time. • Look for record with matching key. • Search stops when ▫ record with matching key is found ▫ or when search has examined all records without success.

4. INFO 106 – Computer Programming How Linear Search works 4

5. 5 Case 1: Target found

6. 6 Case 1: Target NOT found

7. INFO 106 – Computer Programming 7 Program #include<stdio.h> void main() { int a[10],i,target; printf("Enter array value n"); for(i=0;i<n;i++) scanf("%d",&a[i]); printf("Which value to be search ->"); scanf("%d",&target); /* Linear Search logic */ for(i=0;i<n;i++) if(target==a[i]) { printf(“Value found at %d”,i); } }

8. INFO 106 – Computer Programming Advantages of Linear Search • Don't have to sort the data we search. • Works well if only search operation is minimum • Not optimal in case of large amount of data 8

9. INFO 106 – Computer Programming Binary Search • Assume that we are give an array of records that is sorted. For instance: ▫ an array of records with integer keys sorted from smallest to largest (e.g., ID numbers), or ▫ an array of records with string keys sorted in alphabetical order (e.g., names).

10. Binary Search [ 0 ] [ 1 ] Example: sorted array of integer keys. Target=7. 3 6 7 11 32 33 53 [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ]

11. 11

12. INFO 106 – Computer Programming Binary Search Pseudocode … if(size == 0) found = false; else { middle = index of approximate midpoint of array segment; if(target == a[middle]) target has been found! else if(target < a[middle]) search for target in area before midpoint; else search for target in area after midpoint; } …

13. INFO 106 – Computer Programming Program int result=-1; int low=0; int high=length-1; int mid; while( result==-1 && low<=high ) { mid= low + ((high - low) / 2); if( list[mid] == target ) result = mid; else if( list[mid] < target) low = mid + 1; else high = mid - 1; } 13

14. INFO 106 – Computer Programming Other Searching Algorithms • Interpolation Search • Indexed Searching • Binary Search Trees • Hash Table Searching • Grover's Algorithm • Best-first • A* 14

Searching in Arrays

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