Question

Questions 1a–d are about developing an efficient implementation of a Set that combines the advantages of a hash table and a balanced binary search tree. In particular, the search function for your data structure should have O (lg n ) worst case complexity and Θ(1) expected case complexity, and it should not be limited to values in a small range (as a bit vector would).

(a) Describe how you would store data values in memory.

(b) Give pseudocode for how you would insert a new value into your data structure.

(c) Give pseudocode for how you would search for a given value. (

d) Briefly justify why your search function has O (lg n ) worst case and Θ(1) expected case complexit

Answer 1

(a) answer>>>If we want implementation of a Set that combines the advantages of a hash table and a balanced binary search tree than We can choose treeset whose internal implementation is binary search tree ...it is efficient if we are more concerned in insertion, removal and retrieval operations.

(b)answer>>>

struct node* insert(struct node* node, int key)

{

    if (node == NULL) return newNode(key);

    if (key < node->key)

        node->left = insert(node->left, key);

    else if (key > node->key)

        node->right = insert(node->right, key);   

    return node;

}

   

// Driver Program to test above functions

int main()

   

    // print inoder traversal of the BST

    inorder(root);

   

    return 0;

}

(c)answer>>>

struct node* search(struct node* root, int key)

{

    if (root == NULL || root->key == key)

       return root;

    if (root->key < key)

       return search(root->right, key);

    return search(root->left, key);

}

(d)answer>>>

 The maximum number of times that the for-loop can run is than  worst case occurs and when  the value being searched for is not present in the array. 

Binary search internally uses log(n) time complexity