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 9.3, Problem 1E
Program Plan Intro
To decide whether the
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The average time complexity for an algorithm can be found by adding the best time and worst time
and dividing that answer by 2.
O True
False
Given 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 algorithm
The first time you run algorithm A on a dataset of n elements; it is faster than
algorithm B. The second time you run algorithm A on a dataset of n elements; it is slower than
algorithm B. Explain how this is possible. Give an example for algorithm A and algorithm B.
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- Solving the organization of the matches of a tournament resembles the (parallel) selection algorithms. For example, the structure of the hill-climbing tournament is similar to searching for a maximum of n values sequentially describes how to search for a maximum value in parallelarrow_forward| The Longest Common Subsequence algorithm takes as input, two stings, X and Y. If we consider comparison of characters the characteristic operation for this algorithm. What is the time complexity as a function of the lengths ofX and Y? Explain your answer. 6.arrow_forwardGiven an n-element sequence of integers, an algorithm executes an O(n)-time computation for each even number in the sequence, and an O(logn)-time computation for each odd number in the sequence. What are the best-case and worst-case running times of this algorithm? Why? Show with proper notations.arrow_forward
- The search algorithm developed will be used for users to search the catalog for all items matching the search keyword(s), and there are a total of 15000 items in the catalog. During development, three different algorithms were created. • Algorithm A runs in constant time, with a maximum runtime of 1.10 seconds and returns all matching results. ● Algorithm B runs in logarithmic time, with a maximum runtime of 0.3 seconds, and returns only the first result. ● Algorithm C runs in linear time, with a maximum runtime of 1.50 seconds and returns all matching results. Which algorithm would be the least suitable for the requirements stated? In your answer, justify your choice by explaining why you picked that algorithm, and why you did not pick the other two algorithms.OND OND OND DADarrow_forwardPlease help with question: Determine the running time of the following algorithms. Write summations to represent loops and simplify. Show all work. If bounding is used, the upper and lower bounds must only differ by a constant. Note: This is not the line-by-line analysis method. Loops are inclusive.arrow_forwardRecall that in the deterministic approach for choosing the pivot in the SELECT algorithm, first we split the elements of the array into groups of size 5. We want to see how the running time of SELECT changes by varying the size of groups. Consider the following cases: (a) Split the array into groups of size 3 (b) Split the array into groups of size 7 For each case, write the corresponding recursion for the running time of the SELECT algorithm, draw the corresponding recursion tree for the worst case, and use it to solve the recursion for the worst case. For full credit, your answers must use O(.) notation (You do NOT need to use strong induction to prove your result).arrow_forward
- Describe a divide and conquer algorithm approach that will compute the number of times a specific number appears in a sequence of numbers. Example {3,4,5,4,3,5,4,4,3} want to know the number of 5s - returns 2. Show all the steps on how your algorithm would work on the example numbers.arrow_forwardMerge sort is an efficient sorting algorithm with a time complexity of O(n log n). This means that as the number of elements (chocolates or students) increases significantly, the efficiency of merge sort remains relatively stable compared to other sorting algorithms. Merge sort achieves this efficiency by recursively dividing the input array into smaller sub-arrays, sorting them individually, and then merging them back together. The efficiency of merge sort is primarily determined by its time complexity, which is , where n is the number of elements in the array. This time complexity indicates that the time taken by merge sort grows logarithmically with the size of the input array. Therefore, even as the number of chocolates or students increases significantly, merge sort maintains its relatively efficient performance. Regarding the distribution of a given set of x to y using iterative and recursive functions, the complexity analysis depends on the specific implementation of each…arrow_forwardA magic square of order n is an arrangement of the integers from 1 to n2 in an n × n matrix, with each number occurring exactly once, so that each row, each column, and each main diagonal has the same sum Design and implement an exhaustive-search algorithm for generating all magic squares of order n.arrow_forward
- Suppose that I searched for a number x in a sorted list of n items by comparing against the 5th item, then the 10th, then the 15th, etc. until I found an item bigger than x, and then I searched backwards from that point. Which expression best describes the approximate running time of this algorithm:arrow_forwardComputer Science for python The SELECT algorithm uses median of sub-medians as the pivot (let us call it s). Show that if n ≥ 140, then at least ⌈n/4⌉ elements are greater than p and at least ⌈n/4⌉ elements are less than parrow_forwardDesign a transform-and-conquer algorithm for finding the minimum and the maximum element of n numbers using no more than 3n/2 comparisons. Justify the number of comparisons of your algorithm.arrow_forward
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