Sorting Technique – Quick Sort, Shell Sort, Merge Sort

Contains Different Type Of Sorting IN Data Structure such as –

Quick Sort
Heap Sort
Merge Sort
Shell Sort
ETC.

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Sorting Technique – Bubble Sort, Selection Sort, Insertion Sort

This Post is all about Different types of Sorting Techniques used in Data Structures.
It Contains algorithms of

• Bubble Sort
• Selection Sort
• Insertion Sort

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Heapsort – C++

Heap sort is simple to implement, performs an O(n·lg(n)) in-place sort, but is not stable.

The first loop, the Θ(n) “heapify” phase, puts the array into heap order. The second loop, the O(n·lg(n)) “sortdown” phase, repeatedly extracts the maximum and restores heap order.
Example –

• Not stable
• O(1) extra space (see discussion)
• O(n·lg(n)) time
• Not really adaptive

Algorithm –

(1) for x on list L do
(2) INSERT(x, S);
(3) while not EMPTY(S) do begin
(4) y := MIN(S);
(5) writeln(y);
(6) DELETE(y, S)
end

Click Down For Program –

Floyd-Warshall’s Algorithm – C++

Floyd-Warshall algorithm known as Modified Warshall’s Algorithm used to solve the All-Pairs Shortest Path problem in Graphs. The Algorithm’s time complexity is O(n³) for a graph with n nodes.

Algorithm–

For each vertex v
	dist[v][v] ← 0
For each edge (u,v)
	dist[u][v] ← w(u,v) 
For k from 1 to |V|       
	for i from 1 to |V|
		for j from 1 to |V|
			if dist[i][k] + dist[k][j] < dist[i][j] then   
				dist[i][j] ← dist[i][k] + dist[k][j]  

Click below for Program –

Dijkstra Algorithm : PPT

DIJKSTRA (G, w, s)

1. INITIALIZE SINGLE-SOURCE (G, s)
2. S ← { }     // S will ultimately contains vertices of final shortest-path weights from s
3. Initialize priority queue Q i.e., Q  ←  V[G]
4. while priority queue Q  is not empty do
5. u  ←  EXTRACT_MIN(Q)    // Pull out new vertex
6.     S  ←  S È {u}
       // Perform relaxation for each vertex v adjacent to u
7.     for each vertex v in Adj[u] do
8.         Relax (u, v, w)

Above is the algorithm for dijkstra’s minimum path. Click below for more…

Minimum Spanning Tree : PPT

A subgraph that spans (reaches out to ) all vertices of a graph is called a spanning subgraph.

A subgraph that is a tree and that spans (reaches out to ) all vertices of the original graph is called a spanning tree.

Among all the spanning trees of a weighted and connected graph, the one (possibly more) with the least total weight is called a minimum spanning tree (MST).

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BELLMAN FORD ALGO : PPT

The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph.

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HUFFMAN CODING :PPT

Huffman coding is a coding technique for lossless compression of data base based upon the frequency of occurance of a symbol in that file.

In huffman coding every Data is based upon 0’s and 1’s which reduces the size of file.

Using binary representation, the number of bits required to represent each character depends upon the number of characters that have to be represented. Using one bit we can represent two characters, i.e., 0 represents the first character and 1 represents the second character.

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BINARY SEARCH TREE : TRAVERSAL, INSERTION, SEARCHING

Binary Search Tree : Binary Search Tree is an ordered or sorted binary tree,in which traversing and searching a bit little complexion; Node having small value arranged in left side of root node, whether high value is arranged in in right side of root node.

Priority Queue

Priority Queue is the queue based on the priority input; Lesser priority will be entertain first then another node of higher priority is set in increasing order. Program is given here related to Priority Queue.