Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 14.3, Problem 6E
Program Plan Intro
To maintain a dynamic set Q of numbers that supports the operation MIN-GAP that gives the magnitude of difference of the two closest numbers in Q.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Suppose we use a hash function h to hash n distinct keys into an array T oflength m. Assuming simple uniform hashing, what is the expected number ofcollisions? More precisely, what is the expected cardinality of ffk; lg W k ¤ l andh.k/ D h.l/g?
What is the time complexity of functions foo() and bar() respectively in below given code
snippets, given that n is the total size of the input and L and R are Vectors
def foo(L, R):
S = Vector()
for x in L:
if x in R:
S.add_back(x)
return S
def bar(L, R):
R_hash= HashTable()
for r in R:
R_hash.insert(r, False)
S = Vector()
for x in L:
if R_hash.contains(x):
S.add_back(x)
return S
O(N^2), O(N)
O(N), O(N)
O(N^2), O(N^2)
O(1), O(N)
Consider a list L = {387, 690, 234, 435, 567, 123, 441}. Here, the number ofelements n = 7, the number of digits l = 3 and radix r = 10. This means that radixsort would require 10 bins and would complete the sorting in 3 passes.
illustrates the passes of radix sort over the list. It is assumed that each key is thrown into the bin face down. At the end of each pass, when the keys are collected from each bin in order, the list of keys in each bin is turned upside down to be appended to the output list
Knowledge Booster
Similar questions
- وقت الامتمان ساعة واطدة فقط Ahi 100 Q1: Let A = {a, b}, B= {e} and C = {d.c}, find (A × B) x (B x C)? Q2: Let A = {a, b, c, d}, find (THREE) partitions of A? Q3: Given an example of two non-empty sets 4 and B such that A- B= 6 and B-A= A? إضاقة ملف 3 2 Google MtansryanUriversry.cearrow_forwardImplement the insertionSort function and modify the quicksortHelper() function so that it calls insertion sort to sort any sublist whose size is less than 50 items. Compare the performance of this version with that of the original one, using data sets of 50, 500, and 5000 items. Afterwards, adjust the threshold for using the insertion sort to determine an optimal setting based on your findings from the step above. To test your program run the main() method in the testquicksort.py file.arrow_forwardA hash table is an efficient data structure to store and access data via keys. In this problem, you need to find the longest subarray of distinct elements. For example, given an array A = <milk, water, 6724, water, soda, beer, apple, grape, wine>, the longest subarray is <milk, water, 6724, soda, beer, apple, grape, wine> Hint: you need to keep track and update the positions of the elements. a) Explain how many unique subarrays are there from a given array b) Describe your ideas on how to solve the problem, especially how hash tables can be used to keep track of the important information c) Write the most efficient algorithm (pseudo code) to solve this problem with complexity analysis. You can assume that a good hash function is given.arrow_forward
- Write a bottom-up mergesort that makes use of the array's order by carrying out the following steps each time it needs to locate two arrays to merge: locate the first element in an array that is smaller than its predecessor, then locate the next, and finally merge them to form a sorted subarray. Consider the array size and the number of maximal ascending sequences in the array while analysing the running time of this method.arrow_forwardBuild a bottom-up mergesort that makes use of the array's order by carrying out the following steps each time it needs to locate two arrays to merge: Find the first element in an array that is smaller than its predecessor, then locate the next, and finally merge them to form a sorted subarray. Consider the array size and the number of maximal ascending sequences in the array while analysing the running time of this technique.arrow_forward• Given a list of n distinct integers, devise an algorithm to print the index of all pairs having the sum equals to a given input value k. This method takes a list, and an integer k as input arguments. So for example, if the pair az = 2 and a6 = 3 and k = print(3, 6), and all other pairs with the same property. What is the running time of this algorithm? 5, then the algorithm should Assume for the previous problem the input list is sorted, modify the previous algorithm to run faster. What is the running time now? (No Credit will be given for O(n2) algorithms)arrow_forward
- L is a list of data items that is linear. Implement the list as: I an ordered list; (ii) a linear open addressed hash table using a suitable hash function of your choosing.Use binary search or hashing to find a collection of keys on representations I and ii), respectively. Compare how well the two approaches performed over list L.arrow_forwardGiven a hash table of size 9 with hash function x%9. Write the element order of the linear probe hash table when these keys are inserted in the given order. 1,20,11,28,25,9,18 Answer is just a sequence of elements in the same format. Use hypen - to indicate empty space. For example a table like below must be written as in the following: 11 28 9,28,-,11,1,-,- Cevap: Kalan Süre 1:37:31arrow_forwardFor the word count example, for the input of the Map function, keys are document IDs and values are document contents. For the output of the Map function, keys are words and values are counts of words (e.g., (a, 1)). After shuffling via a hashing function on keys of the output, we combine those values with the same key into a list, for example, (a, {1, 5}), which are used as the input of the Reduce function. Within the reduce function, it will count (sum up) the numbers in the value list of a key, and return the key/value pair (e.g., (a, 6)). How to Implement the WordCount example on Hadoop?arrow_forward
- What is the worst-case performance of a lookup operation in a hashmap and why? Group of answer choices A- O(1), hashmap always has a constant time lookup, and that is why we like using this associative data structure. B- O(lg(n)) hashmap has a log(n) lookup because we are able to perform a binary search on the keys because our hashmap always maintains a sorted order of entries added. C- O(n) because we can have a bad hash function that puts all of our items in the same bucket, thus we would have to iterate through all n items.arrow_forwardCreate an insertion sort implementation that, by positioning the smallest item first, gets rid of the j>0 condition in the inner loop.To determine whether doing so is successful, use SortCompare. This method frequently avoids an index-out-of-bounds test; the component that makes this feasible is referred to as a sentinel.arrow_forwardWe have n elements {x1, ..., xn} we want to hash into a table T of size s = 2n. Let us consider the following method of hashing these n elements into T: For each i = 1,..., n, do the following: 1. Pick a permutation of [1,..., s] uniformly at random. Call this permutation T; : [s] → [s], which maps each index to the element which ends up in that index. 2. Set j : : 1. 3. While T[T;(j)] has an element in it, increment j. 4. Place x; in T[T;(j)]. 1.1 Show that while inserting any ;, the probability that there are at least t iterations of the while loop in Step 3 is at most 2-t.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill Education
Starting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSON
Digital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSON
Database Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage Learning
Programmable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education