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Lecture 1(Graphs Learning)

Types of data structures

• Linear : array , linked list , stack , queue
• Non Linear : Tree , Graphs

Graphs

• Node (data ) connected via edges
• Edges : Directed and un directed
• nodes (order is not important)
• Graphs may or may not have cycle
• If graph has atleast one cycle is called undirected/directed cyclic graph
• Path : list of nodes [ start to end] connected via edges
• Degree of node : number of edges connected to a node
• Total degree of graph = 2 X (number of edges)
• Edge weight : edges might have weight also known as cost of an edge (by default it is 1)

Graph representation

1 3
1 2
3 4
3 5
2 4
4 5

Approach 1 Adjacency Matrix

• number of nodes : 5 (1,2,3,4,5)
• number of edges : 6
• array [n+1 ][n+1] : 0 based indexing

graph = [
            [0,0,0,0,0,0],
            [0,0,1,1,0,0],
            [0,1,0,1,0,0],
            [0,1,0,0,1,1],
            [0,0,1,1,0,1],
            [0,0,0,1,1,0]
            
        ]

Space Needed

• O(N^2)

Approach 2 Adjaceny List

• number of nodes : 5 (1,2,3,4,5)
• number of edges : 6
• array [n+1 ] : 0 based indexing

graph = [[1,2],[1,3],[2,4],[3,4],[3,5],[4,5]]