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 12.2, Problem 7E
Program Plan Intro
To prove that the
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Chapter 12 Solutions
Introduction to Algorithms
Ch. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5E
Ch. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - Prob. 3PCh. 12 - Prob. 4P
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- Prove that the depth of a random binary search tree (depth of the deepest node) is O(logN), on average.arrow_forwardConsider a weight balanced tree such that, the number of nodes in the left sub tree is at least half and at most twice the number of nodes in the right sub tree. The maximum possible height (number of nodes on the path from the root to the farthest leaf) of such a tree on k nodes can be described asa) log2 nb) log4/3 nc) log3 nd) log3/2 narrow_forwardProve that efficient computation of the height of a BinaryTree musttake time proportional to the number of nodes in the tree.arrow_forward
- Prove Proposition : In a 2-3 tree with N keys, search and insert operations are guaranteed to visit at least lg N nodes.arrow_forwardA binary tree is \emph{full} if every non-leaf node has exactly two children. For context, recall that we saw in lecture that a binary tree of height $h$ can have at most $2^{h+1}-1$ nodes and at most $2^h$ leaves, and that it achieves these maxima when it is \emph{complete}, meaning that it is full and all leaves are at the same distance from the root. Find $\nu(h)$, the \emph{minimum} number of leaves that a full binary tree of height $h$ can have, and prove your answer using ordinary induction on $h$. Note that tree of height of 0 is a single (leaf) node. \textit{Hint 1: try a few simple cases ($h = 0, 1, 2, 3, \dots$) and see if you can guess what $\nu(h)$ is.}arrow_forwardConsider an empty B-Tree with minimum degree of two(maximum 3 keys for each node). We insert 10 items to this B-Tree consecutively. How many node splitting operations are required in the worst-case? Explain your answer for each insertion.arrow_forward
- Implement straight forward recursive algorithm to check if a given binary tree is BST?arrow_forwardsuppose we have a general double-parent binary tree T with root nodes given in the array r. write algorithm that finds the depth of each node.arrow_forwardProve that the number of leaves in a binary tree T is (n+1)/2. where n is the number of vertices.arrow_forward
- When comparing tree-search algorithms, we measure the number ofnodes expanded. How many nodes are expanded (in the worst case)by each of the following search techniques when searching a tree withbranching factor b to find a goal at a depth of d?(a) Breadth-first search(b) Depth-first search(c) Depth-limited search (limit = d)(d) Iterative deepening depth-first searcharrow_forwardUse the procedure TREE-SUCCESSOR and TREE-MINIMUM to write a function of x, x is a node in a binary search tree, to produce the output that INORDERTREE-WALK function would produce. Determine the upper bound running time complexity of F(x) and prove its correctness.arrow_forward21. A B-tree of order m has maximum of _____________ children. a. m b. m+1 c. m-1 d. m/2arrow_forward
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