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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Question
Chapter 7, Problem 4P
(a)
Program Plan Intro
To argue the TAIL-RECURSIVE-QUICKSORT
(b)
Program Plan Intro
To describe a scenario in which TAIL-RECURSIVE-QUICKSORT’s stack depth is
(c)
Program Plan Intro
To modify the code for TAIL-RECURSIVE-QUICKSORT so that the worse-case stack depth is
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Use queues to implement MSD text sorting as follows: Maintain a list for every bin. Place each object to be sorted into the proper queue on the first pass, taking into account the leading character value. Then, combine all of the lines into a sorted whole by sorting the sublists. Keep in mind that this technique avoids using the count[] arrays inside the recursive method.
a)Implement a recursive algorithm that takes a decimal number n and converts n to its corresponding (you may return as a string) binary number.
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20
10
Note: you’ll need a Singly Node class for this code.
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Add a recursive function to BST called avgCompares() that computes the average number of comparisons required by a random search hit in a particular BST (the internal path length of the tree divided by its size plus one). Create two implementations: a recursive approach (which requires linear time and space proportionate to the height) and a way similar to size() that adds a field to each node in the tree (which requires linear space and constant time each query).
Chapter 7 Solutions
Introduction to Algorithms
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- Write a recursive function treeToList(Node root) that takesan ordered binary tree and rearranges the internal pointers to make a circular doubly linked list outof the tree nodes. The "previous" pointers should be stored in the "small" field and the "next"pointers should be stored in the "large" field. The list should be arranged so that the nodes are inincreasing order. Return the head pointer to the new list. The operation can be done in O(n) time -- essentially operating on each node once. Try the problem directly, or see the hints below.Hint #1 The recursion is key. Trust that the recursive call on each sub-tree works and concentrate onassembling the outputs of the recursive calls to build the result. It's too complex to delve into howeach recursive call is going to work -- trust that it did work and assemble the answer from there.Hint #2The recursion will go down the tree, recursively changing the small and large sub-trees into lists,and then append those lists together with the…arrow_forwardDraw the recursion tree for the merge sort procedure on an array of 16 elements. Explain why memoization fails to speed up a good divide-and-conquer algorithm such as merge sort.arrow_forwardRewrite the procedure DFS (depth first search), using a stack to eliminate recursion.arrow_forward
- Given the following non-recursive implementation of depth-first search: A. Complete the implementation of depth-first search by filling in the TODO sections with the appropriate C++ code. Remember to: Print out each node you visit. Visit each node exactly once. B. What is the purpose of stack<string> q? C. What is the purpose of set<string> v?arrow_forwardFor Exercises 1–7, show the threaded BST that results from right-threading the binary search tree. Exercises 6 and 7 ask you to write functions for right-threaded BSTs. You should also test your functions with driver programs as instructed in Programming Problems 28 and 29 at the end of this chapter. Write a function to implement the inorder traversal algorithm for a right-threaded BST given in the text.arrow_forwardA sml binarySearch function that recursively implements the binary search algorithm to search a sorted integer list for a specified integer and returns true if it is found, false otherwise. For example, binarySearch ([100,200,300,400,500], 200) returns true, whereas binarySearch([100,200,300,400,500], 299) returns false. Hint: Write a helper function mid that returns a tuple (index, value) representing the middle value in a list. For example, mid [10, 2, 40, 8, 22] returns (2,40) because the value 40 at index 2 is the middle value in the list. Similarly, mid [10, 20] would return (1, 20). Use mid in conjunction with slice to implement binarySearch.arrow_forward
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