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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Chapter 8 Solutions
Introduction to Algorithms
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- Given this implementation of insertion sort as seen in the photo below, What is the worst-case time complexity of this implementation? and why? kindly explain and/or provide examples.arrow_forwardGiven 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.arrow_forwardConsider 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.arrow_forward
- Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a problem into 10 sub-instances of size n=3, and the dividing and combining steps take a time in O(n2). Write a recurrence equation for the running time T (n), and solve the equation for T (n).arrow_forwardPerform an asymptotic analysis of the insertion-sort algorithm. What are the worst-case and best-case running times?arrow_forwardWe argued in class that if the input is not uniformally distributed, the worst-case running time of Bucket Sort (using Insertion Sort in each bucket) in O(n^2). The reason: all those numbers could fall in the same bucket, and then the time of Insertion sorting then dominates. How many out of the total n numbers could fall in one bucket and the algorithm still run in linear time if the rest are evenly distributed? (Choose one option, no points if you choose more than one.) A. O(1)B. O(√n)C. O(On)D. O(log n)E. None of the abovearrow_forward
- create assignments for algorithms with given running time: O(n)arrow_forwardIn what ways (in terms of auxiliary space and average time complexity) is randomized quick sort difficult to implement?arrow_forwardFor the 8-queens problem, define a heuristic function, design a Best First Search algorithm in which the search process is guided by f(n) = g(n) + h(n), where g(n) is the depth of node n and h(n) is the heuristic function you define, and give the pseudo code description.arrow_forward
- Suppose we are to sort a set of 'n' integers using an algorithm with time complexity O (n) that takes 1 ms (milliseconds) in the worst case when n = 50,000. How large an element can the algorithm then handle at least 0.2 ms?arrow_forwardLet C(n) denote the number of comparisons performed by quicksort in sorting an array of size n in the worst case. Write the recurrence relation for C(n) and solve.arrow_forwardThe worst-case scenario for the fast sort algorithm occurs when each partition consists of a single empty subarray, all partitions are of equal size, and the selection of the pivot element is indeterminate. Are the elements in the initial array completely randomized?arrow_forward
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