Create Graph and Trie

data-structures/Graph and Trie

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+Graph
+
+Graph is a data structure that consists of following two components:
+A finite set of vertices also called as nodes.
+A finite set of ordered pair of the form (u, v) called as edge. The pair is ordered because (u, v) is not same as (v, u) in case of directed graph(di-graph). The pair of form (u, v) indicates that there is an edge from vertex u to vertex v. The edges may contain weight/value/cost.
+V -> Number of Vertices.
+E -> Number of Edges.
+
+
+
+
+Graph can be classified on the basis of many things, below are the two most common classifications :
+
+Direction :
+Undirected Graph : The graph in which all the edges are bidirectional.Directed Graph : The graph in which all the edges are unidirectional.
+Weight :
+Weighted Graph : The Graph in which weight is associated with the edges.Unweighted Graph : The Graph in which their is no weight associated to the edges.
+Graph can be represented in many ways, below are the two most common representations :
+
+Let us take below example graph two see two representations of graph.
+
+
+
+Adjacency Matrix Representation of the above graph
+
+Adjacency List Representation of Graph
+Adjacency List Representation of the above Graph
+
+Time Complexities in case of Adjacency Matrix :
+Traversal :(By BFS or DFS) O(V^2)
+Space : O(V^2)
+
+Time Complexities in case of Adjacency List :
+Traversal :(By BFS or DFS) O(V + E)
+Space : O(V+E)
+Examples : The most common example of the graph is to find shortest path in any network. Used in google maps or bing. Another common use application of graph are social networking websites where the friend suggestion depends on number of intermediate suggestions and other things.
+
+Trie
+
+Trie is an efficient data structure for searching words in dictionaries, search complexity with Trie is linear in terms of word (or key) length to be searched. If we store keys in binary search tree, a well balanced BST will need time proportional to M * log N, where M is maximum string length and N is number of keys in tree. Using trie, we can search the key in O(M) time. So it is much faster than BST.
+
+Hashing also provides word search in O(n) time on average. But the advantages of Trie are there are no collisions (like hashing) so worst case time complexity is O(n). Also, the most important thing is Prefix Search. With Trie, we can find all words beginning with a prefix (This is not possible with Hashing). The only problem with Tries is they require a lot of extra space. Tries are also known as radix tree or prefix tree.
+
+The Trie structure can be defined as follows :
+struct trie_node
+{
+    int value; /* Used to mark leaf nodes */
+    trie_node_t *children[ALPHABET_SIZE];
+};
+
+
+                       root
+                    /   \    \
+                    t   a     b
+                    |   |     |
+                    h   n     y
+                    |   |  \  |
+                    e   s  y  e
+                 /  |   |
+                 i  r   w
+                 |  |   |
+                 r  e   e
+                        |
+                        r
+
+The leaf nodes are in blue.
+
+Insert time : O(M) where M is the length of the string.
+Search time : O(M) where M is the length of the string.
+Space : O(ALPHABET_SIZE * M * N) where N is number of 
+        keys in trie, ALPHABET_SIZE is 26 if we are 
+        only considering upper case Latin characters.
+Deletion time : O(M)