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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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.
Find 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:
Given a real number x and given a sequence of real numbers
a0, a1, a2, …, an-1. Give an algorithm to find the value of the
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Analyze the complexity of your solution. Give a O(n) algorithm.
Chapter 15 Solutions
Introduction to Algorithms
Ch. 15.1 - Prob. 1ECh. 15.1 - Prob. 2ECh. 15.1 - Prob. 3ECh. 15.1 - Prob. 4ECh. 15.1 - Prob. 5ECh. 15.2 - Prob. 1ECh. 15.2 - Prob. 2ECh. 15.2 - Prob. 3ECh. 15.2 - Prob. 4ECh. 15.2 - Prob. 5E
Ch. 15.2 - Prob. 6ECh. 15.3 - Prob. 1ECh. 15.3 - Prob. 2ECh. 15.3 - Prob. 3ECh. 15.3 - Prob. 4ECh. 15.3 - Prob. 5ECh. 15.3 - Prob. 6ECh. 15.4 - Prob. 1ECh. 15.4 - Prob. 2ECh. 15.4 - Prob. 3ECh. 15.4 - Prob. 4ECh. 15.4 - Prob. 5ECh. 15.4 - Prob. 6ECh. 15.5 - Prob. 1ECh. 15.5 - Prob. 2ECh. 15.5 - Prob. 3ECh. 15.5 - Prob. 4ECh. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10PCh. 15 - Prob. 11PCh. 15 - Prob. 12P
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- Call a sequence X[1 · · n] of numbers oscillating if X[i] < X[i + 1] for all even i, and X[i] > X[i + 1] for all odd i. Describe an efficient algorithm to compute the length of the longest oscillating subsequence of an arbitrary array A of integers.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_forwardFind an exact closed-form formula for M(n), the worst-case number of *'s performed by the algorithm below on input narrow_forward
- Given a list of n elements in an arbitrary order, describe an O(n) time algorithm to • find the k largest elements. • find the k smallest elementsarrow_forwardLet the sequence (n) be recursively defined by x1 = √2 and Xn+1 = √√2+xn, n≥ 1. Show that (n) converges and evaluate its limit.arrow_forwardFind 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_forward
- Given two sorted arrays a[] and b[], of lengths n1 and n2 and an integer 0≤k<n1+n2, design an algorithm to find a key of rank k. The order of growth of the worst case running time of your algorithm should be log n, where n =n1+n2 using java.arrow_forwardPlease solve sections, Find the asymptotic (large-Θ) limits for the running times of the algorithms whose running time is given iteratively. 1. T (n) = 4T (n/4) + 5n2. T (n) = 4T (n/5) + 5n3. T (n) = 5T (n/4) + 4n4. T (n) = T (n/2) + 2T (n/5) + T (n/10) + 4narrow_forwardlet us use x as an integer, construct an algorithm that determines how many with repetitions the integer × be written as the sum of 1,2,4 and prove its time complexity phsudocodearrow_forward
- Prove that the running time of an algorithm is ‚theta(g(n)) if and only if its worst-case running time is O(g(n)) and its best-case running time is Omega(g(n)).arrow_forwardWrite an iterative algorithm to find base r representation of a decimal number n. Analyse its timecomplexity using O, Ω, Θ.arrow_forwardFind an exact closed-form formula for M(n), the worst-case of *'s performed by the algorithm below on input nn, where n is a power of 3: *and no the other solution avaible is wrongarrow_forward
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