Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 14.2, Problem 1E
Program Plan Intro
To describe the dynamic set queries MINIMUM, MAXIMUM, SUCCESSOR and PREDECESSOR by adding the pointers to the nodes in
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Given a world map in the form of a Generic M-ary Tree consisting of N nodes and an array of queries[], the task is to implement the functions Lock, Unlock and Upgrade for the given tree. For each query in queries[], the functions return true when the operation is performed successfully, otherwise, it returns false.
The functions are defined as: X: Name of the node in the tree and will be uniqueuid: User Id for the person who accesses node X
1. Lock(X, uid): Lock takes exclusive access to the subtree rooted.- Once Lock(X, uid) succeeds, then lock(A, any user) should fail, where A is a descendant of X.- Lock(B. any user) should fail where X is a descendant of B.- Lock operation cannot be performed on a node that is already locked.
2. Unlock(X, uid): To unlock the locked node.- The unlock reverts what was done by the Lock operation.- It can only be called on same and unlocked by same uid.
3. UpgradeLock(X, uid): The user uid can upgrade their lock to an ancestor node.- It is only possible…
Given a world map in the form of a Generic M-ary Tree consisting of N nodes and an array of queries[], the task is to implement the functions Lock, Unlock and Upgrade for the given tree. For each query in queries[], the functions return true when the operation is performed successfully, otherwise, it returns false.
The functions are defined as: X: Name of the node in the tree and will be uniqueuid: User Id for the person who accesses node X
1. Lock(X, uid): Lock takes exclusive access to the subtree rooted.- Once Lock(X, uid) succeeds, then lock(A, any user) should fail, where A is a descendant of X.- Lock(B. any user) should fail where X is a descendant of B.- Lock operation cannot be performed on a node that is already locked.
2. Unlock(X, uid): To unlock the locked node.- The unlock reverts what was done by the Lock operation.- It can only be called on same and unlocked by same uid.
3. UpgradeLock(X, uid): The user uid can upgrade their lock to an ancestor node.- It is only possible…
Given a world map in the form of a Generic M-ary Tree consisting of N nodes and an array of queries[], the task is to implement the functions Lock, Unlock and Upgrade for the given tree. For each query in queries[], the functions return true when the operation is performed successfully, otherwise, it returns false.
The functions are defined as: X: Name of the node in the tree and will be uniqueuid: User Id for the person who accesses node X
1. Lock(X, uid): Lock takes exclusive access to the subtree rooted.- Once Lock(X, uid) succeeds, then lock(A, any user) should fail, where A is a descendant of X.- Lock(B. any user) should fail where X is a descendant of B.- Lock operation cannot be performed on a node that is already locked.
2. Unlock(X, uid): To unlock the locked node.- The unlock reverts what was done by the Lock operation.- It can only be called on same and unlocked by same uid.
3. UpgradeLock(X, uid): The user uid can upgrade their lock to an ancestor node.- It is only possible…
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- Give a recursive procedure to efficiently compute the spatial join of two relations with R-tree indices. (Hint: Use bounding boxes to check if leaf entries under a pair of internal nodes may intersect.)arrow_forwardIn this problem, we will consider how to use/modify range trees to answer a number of queries. In each case, the input is an n-element point set P in IRd . In each case, explain what points are stored in the range tree, what the various levels of the range tree are, and how queries are answered. Finally, justify your algorithm’s correctness and derive its storage and running time as a function of n. Note that you don’t have to re-copy entire pieces of pseudocode or proof - if it is the sameas the one covered in class or the lecture notes or book, just say so! If it’s very close, youare welcome to discuss (in detail) only the differences with the version covered in class or thebook. (a) A skewed rectangle is defined by two points q− = (x−, y−) and q+ = (x+, y+). The therange shape is a parallelogram that has two vertical sides and two sides with a slope of+1. The lower left corner is q− and the upper right corner is q+. The answer to thequery is the number of points of P that lie within…arrow_forwardGive an explanation of the two most important advantages of using a binary search tree (referenced based approach).arrow_forward
- 4. Given an AVL tree T storing n keys, what are the asymptotic running times, using O notation, for each dictionary operation (i.e., search, insertion, and deletion) on T in the worst-case?arrow_forwardA binary search tree may be balanced or unbalanced based on the arrangement of the nodes of the tree. With your knowledge in Binary search tree: i. Explain the best and worst case scenarios of the time and space complexity of both type of binary trees above.arrow_forwardGiven 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;arrow_forward
- Question 4. Show the result of inserting 2, 1, 4, 5, 9, 3, 6, 7 into an initially empty AVL tree.arrow_forwardGiven the following general tree(s), show how the tree(s) will look when it is represented using the following implementations. Your representation must arrange the nodes by depth (as alphabetically). 1. Linked Implementations Using a Linked-List of Child Pointers 2. Linked Implementations of Left-Child / Right-Sibling В E N G. H K Rarrow_forwardApply the exhaustive parsing algorithm to determine whether or not bbaaaba ∈ L(G5), where G5 is this CFG: S ⟶ bSR | a (1) (2) R ⟶ aRb | a (3) (4) To illustrate the workings of the algorithm, show the breadth-first tree that it, in effect, traversed during its execution. (Each node of that tree is labeled by a sentential form.)arrow_forward
- M is the matrix representation of a relation R on A. A has n elements. M is a n x n matrix. M contains how many 1s and 0s if R is a rooted (directed) tree?arrow_forwardWrite the CFG for L-{a^bm | m>-n; n=1,2,3.......... Draw and upload the parse tree or derivation tree for w-ab5 and w=a³b4 on the same file.arrow_forwardDesign a data structure for a set in which insertions, deletions, and membership queries can be processed in O(1) tim e in the worst case. You m ay assume that the set elements are integers drawn from a finite set {1, 2,...,n}.arrow_forward
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