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 8.4, Problem 2E
Program Plan Intro
To explain the reason of worst case running time of bucket sort is
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create assignments for algorithms with given running time:
O(n^2)
Given a sorted array of n comparable items A, and a search value key, return the position (array index) of key in A if it is present, or -1 if it is not present. If key is present in A, your algorithm must run in order O(log k) time, where k is the location of key in A. Otherwise, if key is not present, your algorithm must run in O(log n) time.
Consider a divide-and-conquer algorithm that calculates the sum of all elements in a set of n numbers by dividing the set into two sets of n/2 numbers each, finding the sum of each of the two subsets recursively, and then adding the result. What is the recurrence relation for the number of operations required for this algorithm?
Answer is f(n) = 2 f(n/2) + 1. Please show why this is the case.
Chapter 8 Solutions
Introduction to Algorithms
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- Second order Spada numbers are well established in the insurance industry. Formally they are defined by the recurrence: Si={Si−1 %( Si−2+1) :i≥ 2 , 1:i=0 ,7 :i=1} Give an O(n) time algorithm to compute the n-th Second order Spada numberarrow_forwardGiven two sorted arrays A and B, design a linear (O(IA|+|B|)) time algorithm for computing the set C containing elements that are in A or B, but not in both. That is, C = (AU B) \ (AN B). You can assume that elements in A have different values and elements in B also have different values. Please state the steps of your algorithm clearly, prove that it is correct, and analyze its running time. Pls give the code in C++, or very clear steps of the algorithmarrow_forwardLet C(n) = 1^3 + 2^3 + 3^3+…+n^3 be the sum of the first n cubes.a. Write a recursive algorithm to compute C(n).b. What is the recurrence relation for your algorithm?c. What is the time complexity of the algorithm you developed? Do not copy from online or Use AIarrow_forward
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