Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST. According to the definition of LCA: “The lowest common ancestor is defined between two nodes p and q as the lowest node in t that has both p and q as descendants (where we allow a node to be a descendant of itself)." For example, in the figure from question 1, the LCA between nodes 5 and 46 is 21. You may use the following typedef structure. The function returns the reference of the node that is considered the LCA. typedef struct node_s{ int data; struct node_s * leftchild; struct node_s * rightchild; }node_t;

Problem Description Using the binary search tree (BST) data structure, we can sort a sequence of n elements by first calling an insertion procedure for n times to maintain a BST, and then performing an INORDER-TREE-WALK on the BST to output the elements in sorted order. To insert a node, we've discussed the TREE-INSERT procedure in class (also from page 294 of the text- book). This TREE-INSERT procedure can actually be improved to reduce the number of key comparisons so that each node's key is compared with the new node's key for at most once during each insertion. For example, given the following BST, The improved insertion procedure will make • 2 comparisons to insert a node with key = 1 • 3 comparisons to insert a node with key = 3 • 2 comparisons to insert a node with key = 8 5. Program Requirements In this programming assignment, you will implement in Java this sorting algorithm using BST, by using the improved insertion procedure. Note that each node of a BST is an object…

In a circular linked list, how can you determine if a given node is the last node in the list? Describe the approach you would take to solve this problem.

Assume that the nodes of the singly linked lists are arranged in decreasing order of the exponents of the variable x in order to add the two polynomials.The objective is to create a fresh list of nodes that represents the addition of P1 and P2. This is done by adding the COEFF fields of nodes in lists P1 and P2 that have identical powers of variable x, and then making a new node in the resulting list P1 + P2. The key part of the technique is shown below.The start pointers of the singly linked lists that correspond to the polynomials P1 and P2 are P1 and P2, respectively. Two temporary pointers, PTR1 and PTR2, are created with starting values of P1 and P2, respectively. Make procedural code.