Suppose we created super-efficient constant time algorithms for sorting an array and graph traversal (sorting = O(1) and graph-traversal = O(1)). How will this impact the running time of the following algorithms? Write the new running time for the following algorithms. Dikstra's algorithm Interval scheduling algorithm Running-time O((m + n)log n) O(n log n) New Running-time

Suppose we created super-efficient constant time algorithms for sorting an array and graph traversal (sorting = O(1) and graph-traversal = O(1)). How will this impact the running time of the following algorithms? Write the new running time for the following algorithms. Dikstra's algorithm Interval scheduling algorithm Running-time O((m + n)log n) O(n log n) New Running-time

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Match each algorithm below with the tightest asymptotic upper bound for its worst-case running time by inserting one of the letters A, B, C, D, and E into the corresponding box. For sorting algorithms, n is the number of input elements. For matrix algorithms, the input matrix has size n X n. For graph algorithms, the number of vertices is n, and the number of edges is 0(n). Insertion Sort Heapsort Depth-first search (for the adjacency list representation) Floyd-Warshall Strassen's O(n^log7) O(n) O(n logn) O(n^2) O(n^3) O(1) O(n^4) ㅇ(logn)
ALGORITHM WYSIWYG(a: sorted array of n integers) i:= 1 p:= 1 while (i < n) if (a[i+1] = a[i+1-p]) %3D p:= p + 1 i:= i+1 return p Someone claims that this algorithm finds the longest sequence of identical values but is unable to prove its correctness. As such, you are required to state its loop invariant and use it to prove its correctness.
A sequential search of a sorted list can halt when the target is less than a givenelement in the list. Define a modified version of this algorithm and state thecomputational complexity, using big-O notation, of its best-, worst-, and average-case performances. Using this template in python: def sequential_search(input_list, target):target_index = -1#TODO: Your work here# Return target_index. If not found, -1return target_indexif __name__ == "__main__":my_list = [1, 2, 3, 4, 5]print(sequential_search(my_list, 3)) # Correct Output: 2print(sequential_search(my_list, 0)) # Correct Output: -1
Computer Science Write the PSEUDOCODE for an algorithm that takes as input a list of numbers that are sorted in nondecreasing order, and finds the location(s) of the most frequently occurring element(s) in the list. If there are more than one element that is the most frequently occurring, then return the locations of all of them. Analyze the worst-case time complexity of this algorithm and give the O() estimate. (A list is in nondecreasing order if each number in the list is greater than or equal to the number preceding it.)
A sequential search of a sorted list can halt when the target is less than a given element in the list. Define a modified version of this algorithm and state the computational complexity, using big-O notation, of its best-, worst-, and average- case performances.
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
For relatively small values of n, algorithms with larger orders can be more efficient than algorithms with smaller orders. Use a graphing calculator or computer to answer this question. For what values of n is an algorithm that requires n operations more efficient than an algorithm that requires [50 log2(n)] operations? (Assume n is an integer such that n > 1.) n?
An array of n elements is almost sorted if and only if every element is at most k spots away from its actual location. Assuming that you can only perform pairwise comparisons, formally prove that any algorithm which can sort almost sorted arrays must have running time S2(n log k), You may assume that n is a multiple of k.
Merge 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…
Implement the following sorting algorithms to find the total number of element comparisons for the given input (n). For each case, randomly generate the input items in the range [0-100]. Compare the practical results with the theoretical average time complexity. How much Quicksort is faster than Selection, Bubble, Insertion, and Mergesort? Note that all algorithms should use the same input random values. Plot the results in a graph where the input size (i.e. n) is in the x-axis and the total number of element comparisons is in the y-axis. n Selection Bubble Insertion Mergesort Quicksort 100 500 1000 1500 2000 3000 4000 5000
Suppose that we sort an array by first inserting each element into a Binary Search Tree. Then, with all the values are in the tree, we perform an In Order traversal to get the array in sorted order. What is the total run time of this sorting algorithm? O O(n) to insert of all elements + O(log n) for the traversal O(n2) to insert all the elements + O(log n) for the traversal O O(n) to insert of all elements + O(n log n) for the traversal O O(n log n) to insert all the elements + O(n) for the traversal
Question 2: Implement sequential search and binary search algorithms on your computer. Note down run time for each algorithm on arrays of size (1, 250, 500, 750, 1000, 1250, 1500, 5000). For both algorithms, store the values 0 throughn 1 in order in the array, and use a variety of random search values in the range 0 to n 1 on each size n. Graph the resulting times. When is sequential search faster than binary search for a sorted array? Solution: Execution Time for Input Size(N) Search Element Execution Time for Sequential Search(n) Binary Search(logn)