Draw the portion of the state space tree generated by LCBB for the following instances. n = 4, m = 15, (P₁, ..., P) = (10, 10, 12, 18) (w₁,..... W 4) = (2, 4, 6, 9).
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Draw the portion of the state space tree generated by LCBB for the following instances. n = 4, m = 15, (P₁, ..., P) = (10, 10, 12, 18) (w₁,..... W 4) = (2, 4, 6, 9).
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- If n1, n, ., nk is a sequence of nodes in the tree such that n; is the parent of n41 for 1Let T be an arbitrary splay tree storing n elements A1, A2, . An, where A1 ≤ A2 ≤ . . . ≤ An. We perform n search operations in T, and the ith search operation looks for element Ai. That is, we search for items A1, A2, . . . , An one by one. What will T look like after all these n operations are performed? For example, what will the shape of the tree be like? Which node stores A1, which node stores A2, etc.? Prove the answer you gave for formally. Your proof should work no matter what the shape of T was like before these operations.4. Consider the graph G, shown below, which is simply a copy of K5. 02 V3 5 V1 24 V5 How many distinct spanning trees does G have? (Hint: Break up your search by the isomorphism type of the tree, as discovered on the previous page. So for example, start by counting the paths of length 5 in G. Then proceed to the next type of tree with 5 vertices. The total number of trees is 125, but please use this answer only to check that your solution is complete!)Consider the implementation of disjoint sets using forests. Assume the union is done by weight, i.e., the root of the tree with lesser nodes points to the root of the tree with more nodes: The following operations are applied on an initial set of elements {x, x2, X3, X4, X5} : union (x, x2); union (x1, x3); union (x4, xg); union (x4, x1). Show the forest after each operation.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;Sereja likes to hang around trees. A tree is an undirected graph on N vertices with N-1 edges and no cycles. Sereja has his own peculiar way of comparing two trees. To describe it, let's start with the way Sereja stores a tree. For every tree, Sereja has a value V– the root of the tree, and for every vertex i, he has an ordered list Q[i] with L[i] elements – Q[i][1], Q[i][2], ..., Q[iLI] which are children of the vertex i. Sereja assumes two trees to be equal if their roots are the same and for every i, the ordered list Q[i] is the same in both the trees that Sereja compares. So if Sereja has tree#1 given as [V=1, Q[1]=[2, 3], Q[2]=[], Q[3]=0] and tree#2 given as [V=1, Q[1]=[3, 2], Q[2]=[], Q[3]=[]], they will be considered different because Q[1] in the first tree is not equal to Q[1] in the second tree. For any vertex İ, Sereja calls number of vertices adjacent to it as E[i). Given an array C of N elements, Let f(C) be the number of different trees (in Sereja's representation) such…Give the internal vertices of the ff. rooted tree: a d i k 1 т п O e, f,I, m, n O e, g, i, k, I, m, n, o, p, r, s, u O a, b, c, d, f, h, j, q, t O b, c, d, f, h, j, q, tPlease Answer this in Python language: You're given a simple undirected graph G with N vertices and M edges. You have to assign, to each vertex i, a number C; such that 1 ≤ C; ≤ N and Vi‡j, C; ‡ Cj. For any such assignment, we define D; to be the number of neighbours j of i such that C; < C₁. You want to minimise maai[1..N) Di - mini[1..N) Di. Output the minimum possible value of this expression for a valid assignment as described above, and also print the corresponding assignment. Note: The given graph need not be connected. • If there are multiple possible assignments, output anyone. • Since the input is large, prefer using fast input-output methods. Input 1 57 12 13 14 23 24 25 35 Output 2 43251 QA binary tree can be used to sort n elements of an array data. First, create acomplete binary tree, a tree with all leaves at one level, whose height h = (lg n) + 1, and store all elements of the array in the first n leaves. In each empty leaf, store an element E greater than any element in the array.Figure (a) shows an example for data = 8, 20, 41, 7, 2, h = (lg(5)) + 1 = 4,and E = 42. Then, starting from the bottom of the tree, assign to each node the minimum of its two children values, as in Figure (b), so that the smallest element emin in the tree is assigned to the root.If a leaf node is to be removed, this node is replaced by a new node with the same value of its parent node. If a node is added into the tree, it will be a leaf node. Normally a node with value E is replaced with new value. It’s necessary to verify recursively all values of its parent and make any possible modification if necessary so that the tree rules are respected. Implement this tree structure in C/C++ with…Your second function is called “isTree". Its input is a graph G, which is a dictionary whose keys are the vertices, and whose values are lists of vertices that are adjacent to the given vertex. Its output is True if G is a tree and False if G is not a tree. Hint: You may want to make use of your "connected" function from the last coding assignment.Write a program that will undertake a range search of all elements lying within limits a, b along a dimension i of the multidimensional data set, representedas a k-d tree. For example, given the data set {(7, 5), (4, 2), (6, 8), (1, 4), (3, 5), (2, 4), (3, 7),(9, 1), (6, 6), (5, 1)} represented as a k-d tree (k = 2), a range search of data elements lying within (a = 3, b = 7) along dimension i = 2 yields {(7, 5), (1, 4), (3, 5), (3, 7), (6, 6)}.Suppose an array is given A = [A, C, E, F, K, L, M, N, Y, Z] a. Draw a complete TERNARY tree from array A.b. Write preorder and postorder traversal for the created complete ternary.c. Draw the adjacency matrix and adjacency list for the complete ternary tree/graph. [You must consider the tree direction from top to bottom when drawing adjacencymatrix and list]SEE MORE QUESTIONS