# Algorithms and Data Structures

1. Given a directed graph, described with the set of vertices and the set of edges,  · Draw the picture of the graph· Give an example of a path, a simple path, a cycle· Determine whether the graph is connected or disconnected· Give the matrix representation of the graph· Give the adjacency lists representation of the graphEssay Question:What      in your opinion is the single most important motivation for the      development of hashing schemes while there already are other techniques      that can be used to realize the same functionality provided by hashing      methods?3. Must a hash table be implemented using an array? Will an alternative data structure achieve the same efficiency? If yes, why? If no, what condition must the data structure satisfy to ensure the same efficiency as provided by arrays?No. we could not implement the HashTable with arrray. But can be possible with other algorithm E.g. a Red-Black tree This offers O(logN) access time. But Hash Table is expected to have O(1) access time (at best case – no collisions). This can be achieved only via an array which offers the possibility of random access in constant time.Must have a comparable performance (less than O(N)) with an array. A treemap has O(logN) worst access time for all operations