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 2.3, Problem 7E
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Describe an algorithm that takes as input a list of n integers in non-decreasing orderand produces the list of all values that occur more than once
Give an O(n^2)-time algorithm to nd the longest monotonically increasing subsequence of a sequence of n numbers.Illustrate your algorithm on the sequence:8, 3, 7, 5, 9, 3, 4, 1, 9, 2, 6.
Create an algorithm that can conduct a sequence of m union and find operations on a Universal set of n items in time O(m + n), consisting of a sequence of unions followed by a sequence of finds.
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- Give an O(n2)-time algorithm to find the longest monotonically increasing subsequence of a sequence of n numbers.arrow_forwardWhen the order of growth of the running time of an algorithm is N log N, the doubling test will lead to the hypothesis that the running time is ~ a N for a constant a. Isn’tthat a problem?arrow_forwardGive an example of an algorithm that is O(1), an algorithm that is O(n) and an algorithm that is O(n2). Discuss the difference between them.arrow_forward
- Describe an algorithm that given two regular expressions R1 and R2 outputs YES if andonly if every string generated by R1 is also generated by R2. (I.e., output YES exactlywhen the set of strings generated by R1 is a subset of the set of strings generated by R2.)arrow_forwardImplement an algorithm to print all valid (i.e., properly opened and closed) combinationsof n pairs of parentheses.EXAMPLEInput: 3Output: (( () ) ) , ( () () ) , ( () ) () , () ( () ) , () () ()arrow_forwardGive a Θ(lg n) algorithm that computes the remainder when xn is divided byp. For simplicity, you may assume that n is a power of 2. That is, n = 2k forsome positive integer k.arrow_forward
- Find the correct asymptotic complexity of an algorithm with runtime T(n) where T(x) = O(n) + T(3 * x /4) + T(x / 4) Can't really understand the available solution hence, i am asking againarrow_forwardFind the correct asymptotic complexity of an algorithm with runtime T(n) where T(x) = O(n) + T((2*x)/8)arrow_forwardFind an exact closed-form formula for M(n), the worst-case of *'s performed by the algorithm below on input n, where n is a power of 3:arrow_forward
- create assignments for algorithms with given running time: O(n)arrow_forwardAn array A[1 . . n] of integers is a mountain if it consists of an increasing sequence followed by a decreasing sequence, or more precisely,If there is an index m ∈ {1, 2, . . . , n} such that• A[i] < A[i + 1] for all 1 ≤ i < m, and• A[i] > A[i + 1] for all m ≤ i < n.In particular, A[m] is the maximum element, and it is the unique “locally maximum” element surrounded by smaller elements (A[m − 1] and A[m + 1]).Give an algorithm to compute the maximum element of a mountain input array A[1 . . n] in O(log(n)) time.arrow_forwardDesign an algorithmthat can performa sequence m union and find operations on a Universal set of n elements, consisting of a sequence of unions followed by a sequence of finds, in time O(m + n).arrow_forward
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