Proper Answer 1. Given a directed graph below, find its shortest paths from vertex VO to every othervertex in the graph. Show each step clearly.45VO50VI10V4V215V33V52. Given an array A shown in the following table, which is used to represent acomplete binary treei123 456A[i]2214962Answer the following three questions:a. Draw the corresponding binary tree T.b. Is it a max heap or min heap? Why?c. Sequentially do two heap operations: INSERT(17), INSERT(29) on T.Show the result after each operation.201015203562

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1. Given a directed graph below, find its shortest paths from vertex VO to every other vertex in the graph. Show each step clearly. 45 VO 50 10 V4 10 15 20 V2 15 V3 V5 2. Given an array A shown in the following table, which is used to represent complete binary tree 12 3 4 5 6 Ai 22 14 9 6 11 2 Answer the following three questions: a. Draw the corresponding binary tree T. b. Is it a max heap or min heap? Why? c. Sequentially do two heap operations: INSERT(17), INSERT(29) on T. Show the result after each operation. 20 35 62

1. Given a directed graph below, find its shortest paths from vertex VO to every other vertex in the graph. Show each step clearly. 45 VO 50 10 V4 10 15 20 V2 15 V3 V5 2. Given an array A shown in the following table, which is used to represent complete binary tree 12 3 4 5 6 Ai 22 14 9 6 11 2 Answer the following three questions: a. Draw the corresponding binary tree T. b. Is it a max heap or min heap? Why? c. Sequentially do two heap operations: INSERT(17), INSERT(29) on T. Show the result after each operation. 20 35 62

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Topic: Binary Tree Graph
b) Apply an algorithm to find the minimum spanning tree. To solve this problem, you need to transfer the unweighted graph into weighted graph and you can do it by using your mobile number (11 digits). Just assign the digits sequentially (left to right) to the edges of binary tree segment (means black color edges). And for rest of the edges, you may write 1 as their weights.
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A complete binary tree is a graph defined through the following recursive definition. Basis step: A single vertex is a complete binary tree. Inductive step: If T1 and T2 are disjoint complete binary trees with roots r1, r2, respectively, the the graph formed by starting with a root r, and adding an edge from r to each of the vertices r1, r2 is also a complete binary tree. The set of leaves of a complete binary tree can also be defined recursively. Basis step: The root r is a leaf of the complete binary tree with exactly one vertex r. Inductive step: The set of leaves of the tree T built from trees T1, T2 is the union of the sets of leaves of T1 and the set of leaves of T2. The height h(T) of a binary tree is defined in the class. Use structural induction to show that `(T), the number of leaves of a complete binary tree T, satisfies the following inequality `(T) ≤ 2 h(T) .
Recursively, a complete binary tree is a graph. Basis step: One vertex forms a binary tree. Inductive step: If T1 and T2 are disjoint complete binary trees with roots r1, r2, respectively, the graph produced by starting with a root r and adding an edge from r to each of the vertices r1, r2 is also complete. Recursively define a complete binary tree's leaves. Base step: The full binary tree has one root, r. Inductive step: T's leaves are the union of T1's and T2's. Class defines binary tree height h(T). Use structural induction to prove that `(T), the number of leaves of a complete binary tree T, is less than 2 h(T).
Please help me with this algorithm. The algorithm should be in psuedocode format. Thank you. Consider a situation in which you are provided some minimum spanning tree Twhich was formed from the vertices and edges contained in the graph G = (V, E).Now, suppose that I provided you with some edge (u, v) such that u, v ∈ G.V andδ(u, v) = w(u, v) (they are directly connected). We can say that a new graph G'can be formed such that G' = (V, E ∪ (u, v)). Design an algorithm that constructs T'from G' in O(V + E) time in the worst case(it may be bounded below this, but it cannot be bounded higher).
you need to write the solutions in python and provide a brief explanation of your codes and the efficiency analysis with comments. 3. Consider a loop tree which is an undirected wighted graph formed by taking a binary tree and adding an edge from exactly one of the leaves to another node in the tree as follows: Letnbe the number of vertices in a loop tree. How long does it take Prim's or Kruskal's algorithms to find the minimum spanning tree in terms ofn? Devise a more efficient algorithm that takes an nxn adjacency weighted matrix as input, and finds the minimum spanning tree of a loop tree. 三 input1 - Not Defteri Dosya Düzenle 1078000000 700650060 800006400 060000000 050000021 006000000 004000000 060020000 000010000 output1 - Not Defteri Dosya Düzenle Görünü p 14873265 三 input2 - Not Defteri Dosya Düzenle Görünüm0210000200344010000000300000040005604005000000
Correct answer will be upvoted else Multiple Downvoted. Computer science. You are given n chains of lengths l1,l2,… ,ln. You intend to fabricate a tree utilizing some of them. Every vertex of the tree is either white or dark. The tree at first just has a white root vertex. All chains at first comprise just of white vertices. You can take one of the chains and interface any of its vertices to any white vertex of the tree with an edge. The chain turns out to be important for the tree. The two endpoints of this edge become dark. Each chain can be utilized close to once. A few chains can be left unused. The distance between two vertices of the tree is the number of edges on the most brief way between them. Assuming there is essentially k white vertices in the subsequent tree, the worth of the tree is the distance between the root and the k-th nearest white vertex. What's the base worth of the tree you can get? In case it is absolutely impossible to construct…
Draw a DFS tree from the following graph starting from vertex E. A D в E
Apply Prim's algorithm or Kruskal's algorithm or Borvuka's algorithm to find the minimum spanning tree for the following graph. Illustrate the algorithm stepwise while applying it on the graph. |1
Let n be 22 . Let T be a binary rooted tree with n vertices. (a) What is the least number of levels that T can have? Explain your answer. (b) What is the greatest number of levels that T can have? Explain your answer. Please answer both a and b. I will provide you positive response. Thanks