Describe a data structure to represent sets of elements (each element with a unique key) that would support the following operations: insert(x, A) - insert an element x into A (assume the key of x is not in .4 yet) count (A, k) - return the number of elements in A with key at least k. Solution we can use Hashset for this.a simple code in hashset is given below public class MyNode { ... } public class MyDataStructure { private HashSet nodes = new HashSet(); /// /// Inserts an element to this data structure. /// If the element already exists, returns false. /// Complexity is averaged O(1). /// public bool Add(MyNode node) { return node != null && this.nodes.Add(node); } /// /// Removes a random element from the data structure. /// Returns the element if an element was found. /// Returns null if the data structure is empty. /// Complexity is averaged O(1). /// public MyNode Pop() { // This loop can execute 1 or 0 times. foreach (MyNode node in nodes) { this.nodes.Remove(node); return node; } return null; } } the unique key can also be achieved using dictioneries hence code for this is given below: public class FixedIntDictionary { // Our internal node structure. // We use structs instead of objects to not add pressure to the garbage collector. // We mantains our own way to manage garbage through the use of a free list. private struct Entry { // The key of the node internal int Key; // Next index in pEntries array. // This field is both used in the free list, if node was removed // or in the table, if node was inserted. // -1 means null. internal int Next; // The value of the node. internal T Value; } // The actual hash table. Contains indices to pEntries array. // The hash table can be seen as an array of singlt linked list. // We store indices to pEntries array instead of objects for performance // and to avoid pressure to the garbage collector. // An index -1 means null. private int[] pBuckets; // This array contains the memory for the nodes of the dictionary. private Entry[] pEntries; // This is the first node of a singly linked list of free nodes. // This data structure is called the FreeList and we use it to // reuse removed nodes instead of allocating new ones. private int pFirstFreeEntry; // Contains simply the number of items in this dictionary. private int pCount; // Contains the number of used entries (both in the dictionary or in the free list) in pEntries array. // This field is going only to grow with insertions. private int pEntriesCount; /// /// Creates a new FixedIntDictionary. /// tableBucketsCount should be a prime number /// greater than the number of items that this /// dictionary should store. /// The performance of this hash table will be very bad /// if you don\'t follow this rule! /// public FixedIntDictionary(int tableBucketsCount) { // Our free list is initially empty. this.pFirstFreeEntry = -1; // Initializes the entries array with a minimal amount of items. this.pEntries = new Entry[8]; // Allocate buckets and initial.