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 21.3, Problem 3E
Program Plan Intro
To give a sequence of m MAKE-SET, UNION and FIND-SET operations, n of which are MAKE-SET operations that take
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- Let B = {a + bi|a, b ∈ N}. Prove that B is countable.arrow_forwardCreate an algorithm for parallel regularity testing.Input: a set S of permutation group G generators on;The output indicates whether G is regular or not.arrow_forwardFor the algorthim write a recurrence for its runtime, use the recurrence tree method to solve the recurrence, and and find the tightest asymptotic upper bound on the runtime of the algorthim. Algorrthim Problem: Algorithm V divides an instance of size n into 6 subproblems of size n/6 each, recursively solves each one, and then takes O(n) time to combine the solutions and output the answer.arrow_forward
- Question 10. Let A, B and C be sets. Show that (A − C) n (C − B) = Øarrow_forwardUse the divide and conquer strategy to understand the binary search for a sorted list of n elements. Let T(n) denote the time complexity function for the binary search. Derive a recurrence relation for T(n) and solve for T(n) to get a close form expression.arrow_forwardFor the algorthim write a recurrence for its runtime, use the recurrence tree method to solve the recurrence, and and find the tightest asymptotic upper bound on the runtime of the algorthim. Algorthim Problem: Algorithm H divides an instance of size n into 4 subproblems of size n/3 each, recursively solves each one, and then takes O(n^2) time to combine the solutions and output the answer.arrow_forward
- Please help me with this recurrence relation: B(0) = 1, B(n) = B(n −1) + n + 3 for n > 0 Use the method of unraveling to find a closed form for B(n).arrow_forwardWe are given a recurrence of T(n) = T(n-1) + (n). For this recurrence it must be proven that T(n) is Ⓒ (n^2).arrow_forwardAbout a set X of numbers we say that it is almost sum-free if the sum of two different elements of X never belongs to X. For instance, the set {1, 2, 4} is almost sum-free. Almost-Schur number A(k) is the largest integer n for which the interval {1, . . . , n} can be partitioned into k almost sum-free sets. Use clingo to find the exact values of A(1), A(2), A(3) and try to find the largest lower bound for A(4), i.e., the largest number l such that A(4) ≥ l. Hint: you do not need to find all partitions to find the values of A(k). PLEASE USE CLINGO.arrow_forward
- Make K-map as followsarrow_forwardQuestion: What is the worst-case running time of Find-Index-2(A[1 : n])? What about its worst-caseexpected running time? Remember to prove your answer formally.arrow_forwardUse two ways to count the number of r-combinations of[n]={1,2,…,n}that contains 1 or 2 or 3. First, separate cases with Case 1 counting all r-combinations of [n] that contains 1 , Case 2 counting all r-combination of [n] that contains 2 but not 1 , and Case 3 counting allrcombination of [n] that contains 3 but not 1 or 2 . Second, count all r-combinations of [n] not containing any of1,2,3and use the subtraction rule.arrow_forward
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