data structures using universe of keys (uk actual keys (kfigure null null null null null keys being hashed to chained hash table operations on chained hash table searching for value in chained hash table is as simple as scanning linked list for an entry with the given key insertion operation appends the key to the end of the linked list pointed by the hashed location deleting key requires searching the list and removing the element chained hash tables with linked lists are widely used due to the simplicity of the algorithms to insertdeleteand search key the code for these algorithms is exactly the same as that for insertingdeletingand searching value in single linked list that we have already studied in while the cost of inserting key in chained hash table is ( )the cost of deleting and searching value is given as (mwhere is the number of elements in the list of that location searching and deleting takes more time because these operations scan the entries of the selected location for the desired key in the worst casesearching value may take running time of ( )where is the number of key values stored in the chained hash table this case arises when all the key values are inserted into the linked list of the same location (of the hash tablein this casethe hash table is ineffective table gives the code to initialize hash table as well as the codes to insertdelete and search value in chained hash table table codes to initializeinsertdeleteand search value in chained hash table struture of the node code to insert value typedef struct node_ht int valuestruct node *next}node/the element is inserted at the beginning of the linked list whose pointer to its head is stored in the location given by (kthe running time of the insert operation is ( )as the new key value is always added as the first element of the list irrespective of the size of the linked list as well as that of the chained hash table *node *insert_valuenode *hash_table[]int valnode *new_nodenew_node (node *)malloc(sizeof(node))new_node value valnew_node next hash_ table[ ( )]hash_table[ ( )new_nodecode to initialize chained hash table /initializes location in the chained hash table the operation takes running time of ( *void initializehashtable (node *hash_table[]int mint ifor( = <= ; ++hash_table[ ]=nullcont