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 14.1, Problem 1E
Program Plan Intro
To show the operation of the procedure OS-SELECT( T.root , 10) on the red black tree T of the figure 14.1.
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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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- Again recall the definition of the set of full binary trees. Suppose that a full binary tree T' is created using the recursive rule applied to full binary trees T1 and T2. Let v(T) denote the number of vertices in tree T. Which expression correctly describes v(T')? Explain your response (no need for a formal proof). a. v(T') = 2 · v(T1) + 2 · v(T2) + 1 . b. v(T') = 2.v(T1) + 2 • v(T2) · c. v(T') = v(T1) + v(T2) + 1 d. v(T') = v(T1) + v(T2)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_forwardGiven the following LLRB tree What is the problem of this tree? How to fix this problem?arrow_forward
- You are given a weighted tree T.(As a reminder, a tree T is a graph that is connected and contains no cycle.) Each node of the tree T has a weight, denoted by w(v). You want to select a subset of tree nodes, such that weight of the selected nodes is maximized, and if a node is selected, then none of its neighbors are selected.arrow_forwardProve the correctness of the RB-INSERT (T, z) algorithm (formal description is given in Chapter 13.3 of the textbook), i.e., the procedure to insert an element into a red-black tree while maintaining the binary search tree properties.arrow_forwardTwo very huge binary trees, T1 and T2, with T1 being far larger than 12. Build a formula to determine whether T2 is a subtree of TI. If a node n in tree TI has a subtree that is identical to tree T2, then tree 12 is a subtree of tree T That is, the two trees would be identical if the tree was cut off at node n.arrow_forward
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