Graphs:
=======
it is a pictorial representation of a set of objects where some pair of objects are connected by the links.
==> The interconnection between the objects are represented as "vertices".
==> links that connects to the vertices are called as "edges".

# graph

graph = {
    "a" : ["b","c"],
    "b" : ["a","d"],
    "c" : ["a","d"],
    "d" : ["b","e"],
    "e" : ["d"]
}

print(graph)

====================
Displaying of graph Vertices:
=============================

class graph:
    def __init__(self,gdict = None):
        if gdict is None:
            gdict = []
        self.gdict = gdict

    def getVertices(self):
        return list(self.gdict.keys())

graph_structure = {
    "a" : ["b","c"],
    "b" : ["a","d"],
    "c" : ["a","d"],
    "d" : ["b","e"],
    "e" : ["d"]
}
gobj = graph(graph_structure)
print("The Vertices of the given graph are:",gobj.getVertices())

==========================================================
Displaying graph edges:
=======================

class graph:
    def __init__(self,gdict = None):
        if gdict is None:
            gdict = []
        self.gdict = gdict

    def edges(self):
        return self.findedges()

    def findedges(self):
        edgename = []
        for i in self.gdict:    # keys vertices
            for j in self.gdict[i]: # values edges
                if(j,i) not in edgename:
                    edgename.append({i,j})

        return edgename



graph_structure = {
    "a" : ["b","c"],
    "b" : ["a","d"],
    "c" : ["a","d"],
    "d" : ["b","e"],
    "e" : ["d"]
}
gobj = graph(graph_structure)
print("The Edges = ",gobj.edges())

==================================================
Adding Vertex:
==============

class graph:
    def __init__(self,gdict = None):
        if gdict is None:
            gdict = []
        self.gdict = gdict

    def getVertices(self):
        return list(self.gdict.keys())

    def addVertex(self,vertex):
        if vertex not in self.gdict:
            self.gdict[vertex] = []

graph_data = {
    "a" : ["b","c"],
    "b" : ["a","d"],
    "c" : ["d","a"],
    "d" : ["b","e"],
    "e" : ["d"]
}

gobj = graph(graph_data)
gobj.addVertex("f")
print(gobj.getVertices())

===============================================
Adding of an edge to the graph:
===============================

class graph:
    def __init__(self,gdict = None):
        if gdict is None:
            gdict = []
        self.gdict = gdict

    def edges(self):
        return self.findEdges()

    def findEdges(self):
        edgename = []
        for i in self.gdict:  # keys vertices
            for j in self.gdict[i]:  # values edges
                if (j, i) not in edgename:
                    edgename.append({i, j})

        return edgename

    def addEdge(self,edge):
        edge = set(edge)
        (vertex1,vertex2) = tuple(edge)
        if vertex1 in self.gdict:
            self.gdict[vertex1].append(vertex2)
        else:
            self.gdict[vertex1] = [vertex2]

graph_data = {
    "a" : ["b","c"],
    "b" : ["a","d"],
    "c" : ["a","d"],
    "d" : ["b","e"],
    "e" : ["d"]
}

gobj = graph(graph_data)
gobj.addEdge({'a','e'})
gobj.addEdge({'a','c'})

print(gobj.edges())

=================================================

Searching Algorithms:
=====================

Ecoomerce: Flipkart
	clothes:Kart(02-10-10pm)
	phones: Kart(02-10-8pm)
	beauty products:Kart(03-10-6am)


1) Linear search:
=================

# Linear search

def linearSearch(array,n,x):
    for i in range(0,n):
        if array[i] == x:
            return i

    return -1

array = [2,4,0,1,9,7,11,5]
x = 100
n = len(array)

resultant_position = linearSearch(array,n,x)

if resultant_position == -1:
    print("The Given Searching object is not found in an array.")
else:
    print("The Given Searching object is identifies in an array at:{}".format(resultant_position))

====================================================

Binary Search:
==============

# Binary Search

def binarySearch(array, x, low, high):
    while low <= high:
        mid = low + (high-low)//2

        if x == array[mid]:
            return mid

        elif x > array[mid]:
            low = mid + 1

        else:
            high = mid - 1

    return -1

array = [3,4,5,6,7,8,9]
x = 8

position = binarySearch(array,x,0,len(array)-1)

if position == -1:
    print("Results not found.")
else:
    print("The Searching object is at:",position)