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Using AI - Voice to Text Keyword, Phrases or Number Type here > tap SEARCH 2
Time to Search Sorted Database
Big O Notation in Computer Science
| Known operation time to read a sorted index is 10 millisecond | 2 read operations means 2 x 10 = 20 ms |
| Total operation time = O * log (N) where O = 10 milliseconds; N total number of records | Binary search log 2 (1,000,000) = 20 read |
| Total operation time = 10 ms * 20 reads | Binary search total operation time = 200 ms or 0.2 sec |
| Instead of using O * log 2(N), Use O * log 100 (N) | Binary search log100(1,000,000) = 3 read operations |
| Using modified binary search the total execution time is lowered by a factor of 6 | Execution time or Operation time = 10 ms * 3 reads = 30 ms |
| O(1) - Constant notation. Hashing Algorithm is an example of constant time to locate/search a record in a database. It doesn't matter how big the database is. | Explain how it is possible. Hash algorithm uses complex mathematical equation to take user input we will called it a key then the hashing algorithm will process the given input to output a unique value. That unique value is the row number in hash table. Then the row will contain many columns of information. |
| Known memory storage for user name is 2^32 = 4,294,967,296 range is 0 to 4,294,967,295. Computer index counting start with 0. | The Hash algorithm will add the ASCII number of given input key then use the MOD division operation and will use the remainder answer as the unique hash key value. For example the total ASCII number 775 MOD 4,294,967,294 remainder is 775. |
In computer science using the ordinary binary search to find a certain record in a sorted database, how long will it take? Answer: The binary search will do comparison operation in roughly Log 2 N . It means if the table has N = 1,000,000 rows of records, then to find a certain record it will take 20 comparison operations. How many millisecond each comparison? ( assuming it is 10 millisecond to read a record on a disk ) then 20 x 10 millisecond = 200 ms or 0.2 second to find and display the query record. Log 2 1,000,000 = 19.9 or 20 comparison to find the record. 1,000,000 is also equal to 1e6 when written in exponential notation.
In 1972 B-Tree was invented by Rudolf Bayer and Edward M. McCreight while working at Boeing Research Lab. In computer science, B-Tree is a self balancing tree data structure. Compare to self-balancing binary search trees, the B-Tree is optimized for systems that read and write large blocks of data. B-Trees are a good example of a data structure for external memory. B-Tree data structure is commonly used in databases and filesystems. --source : Wikipedia
Log b N is the optimize way of doing binary search using B-Tree.
Where b is the blocking factor, meaning if you divide your sorted 1,000,000 records by 100 blocks, you can optimize your binary search capability . Log 100 1,000,000 = 3 reads . Then 3 reads x 10 milliseconds = 30 milliseconds.--source : Wikipedia
IBM Cloudant NoSQL document database , MapReduce views are indexes into the dataset with key value pairs and stored in a B-Tree for efficient retrieval by key or range of keys.
So for binary search, Logarithm Log 2 (32) = 5 operation
For base 100 (Blocking search of 100) , change base 2 to 100. To write big number use exponential notation. 1,000,000 is 1e6.
Log base =
( )
=
Common logarithm is base 10. The base number is usually not written because it is commonly assumed as base 10. Here it is shown as a reminder.
Log 10 (1000) is commonly written as Log (1000 ) = 3
Log 10
=
In Natural Logarithm the base is " e " and its value e = 2.718
Ln e
=
Reviewer: Manual Calculation
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Source: How People Learn II: Learners, Contexts, and Cultures
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