Algorithms Complexity and Data Structures Efficiency (1)

8/2/2019 Algorithms Complexity and Data Structures Efficiency (1)

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Algorithms Complexity and

Data Structures Efficiency

1. Fundamental Data Structures Comparison

Arrays vs. Lists vs. Trees vs. Hash-Tables

2. Choosing Proper Data Structure for a program

will increase the efficiency of a program.

3. Data structures and algorithms are the

foundation of computer programming


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Algorithms Complexity

Algorithmic thinking, problem solving and data

structures are vital for software engineers.

Time Complexity space complexity.

Mean, Average and Worst Case.

Worst-caseAn upper bound on the running time for any input

of given size

Average-case

Assume all inputs of a given size are equally likely Best-case

The lower bound on the running time


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Why we should analyze algorithms?

Predict the resources that the algorithmrequires Computational time (CPU consumption) Memory space (RAM consumption) Communication bandwidth consumption

The running time of an algorithm is: The total number of primitive operations

executed (machine independent steps)

Also known as algorithm complexity


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Big O notation

Time complexity in so-called "Big O"notation.

This, approximately, describe the time

taken for an algorithm to solve thegiven task.

Prefer Time complexity", rather than"space complexity" mostly because now

a days space doesnt matter. The big 0notation will calculate time

complexity in worst case scenario.


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Lists or Tables

Table BST AVL BB+Hashing

For table the


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The time complexity for an table is O(n).

To search an element in an table it may take

maximum of n iteration for n elements. So to over come above problems we

introduced BST(binary search tree).

The time complexity of an BST is O(log2 n).


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Its has no difference between tables and BST if

it is not a balanced tress.


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AVL tress

An AVL tree is a binary search tree which has

the following properties.

The sub-trees of every node differ in height by

at most one.

Every sub-tree is an AVL tree.

An balanced BST is an is an AVL tree.


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B tress

In BST and AVL we have only oneroot element and time complexity isO(log n)

If we have m elements in root thetime complexity is O(log m n).

Where m is number of elements inroot.


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If we have even number of keys the it arises

two cases

left biased

right biased

B+ tree is an advanced version of b tree.

When a leaf node would split off, its reference

is kept in successor node.

If an internal node would split up its same asin B tree.


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Hashing

Hash tables support one of the most efficient types ofsearching hashing. Fundamentally, a hash table consistsof an array in which data is accessed via a special indexcalled a key.

The primary idea behind a hash table is to establish amapping

between the set of all possible keys and positions inthe array using a hash function. A hash function

accepts a key and returns its hash coding, or hashvalue.

Keys vary in type, but hash coding are always integers.


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The complexity of good hash function is O(1).

The complexity of bad hash function is O(n).


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Algorithms Complexity and Data Structures Efficiency (1)