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
I need the answer as soon as possible
Suppose you have a hash table of size N = 64, and you are using pseudo-random probing. The
keys in your hash are 4-digit integers (0000 through 9999) and your hash function is h(k) = (the
sum of the digits in k).
Assume that the first 4 slots of your pseudo-random probing array contain: 5, 10, 60, 30
What are the first 4 values in the probe sequence (starting with the home position) for a record
with key k=1948?
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)
Knowledge Booster
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?arrow_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_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
- 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_forwardWrite 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_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_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_forwardThe dotted-decimal notation for the IP address 10010000 10101010 01011011 00101000 The dotted-decimal notation for the IP address 10000001 10100101 01010011 00110011 2 15 19 30 41 59 77 81 85 100 Search for element 45 in the list above using a binary search algorithm. Clearly, show the first, middle, and last indexes as well as the target in every iteration. Show all the steps taken. Use the table below as a guideline with the provided format. Instructions: Start your index at 0 Show all steps Mark the first row as header(The text will be in bold). Use the index number to show the first, last, and mid Use the floor function to find the middle element If struggling to insert a table, you may work this from a Word document and upload your work using the plus sign on the editing options. First last mid 0 1 2 3 4 5 6 7 8 9 target = 45arrow_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
- We 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_forwardWhat 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_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