2. For each of the following computations, write the worst case complexity (using big O notation) and indicate when the worst case happens (under what conditions). Worst-Case When does the worst case happen (under what conditions)? Computation Complexity (in O notation) Sorting an array of length Nusing the Merge Sort algorithm. Inserting a node in an unordered doubly linked list of N nodes. Partitioning an array of size N into two parts: a left part containing all the array elements less or equal than a pivot value and a right part containing all the array elements bigger than the pivot value. Inserting a node in a binary search tree of N nodes. Searching for an item in a hash table that uses linear probing for resolving collisions, assuming the hash table is of length M and the total number of items currently in the table is N.

2. For each of the following computations, write the worst case complexity (using big O notation) and indicate when the worst case happens (under what conditions). Worst-Case When does the worst case happen (under what conditions)? Computation Complexity (in O notation) Sorting an array of length Nusing the Merge Sort algorithm. Inserting a node in an unordered doubly linked list of N nodes. Partitioning an array of size N into two parts: a left part containing all the array elements less or equal than a pivot value and a right part containing all the array elements bigger than the pivot value. Inserting a node in a binary search tree of N nodes. Searching for an item in a hash table that uses linear probing for resolving collisions, assuming the hash table is of length M and the total number of items currently in the table is N.

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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For each of the following situations, name the best sorting algorithm we studied. (For one or two questions, there may be more than one answer deserving full credit, butyou only need to give one answer for each.)(a) The array is mostly sorted already (a few elements are in the wrong place).(b) You need an O(n log n) sort even in the worst case and you cannot use any extraspace except for a few local variables.(d) You have many data sets to sort separately, and each one has only around 10elements.(e) You have a large data set, but all the data has only one of about 10 values forsorting purposes (e.g., the data is records of elementary-school students and thesort is by age in years).(f) Instead of sorting the entire data set, you only need the k smallest elements wherek is an input to the algorithm but is likely to be much smaller than the size of theentire data set.
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…
develop an implementation TwoSumFaster that uses a linear algorithm to count the pairs that sum to zero after the array is sorted (instead of the binary-search-based linearithmic algorithm). Then apply a similar idea to develop a quadratic algorithm for the 3-sum problem.
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Consider the problem of sorting elements in an array of n numbers. Design two algorithms to implement the quicksort as follows: Recursive algorithm, and Non-recursive algorithm Analyze the efficiency of your algorithms as follows: For the recursive algorithm, figure out the recurrence relation and use the Master Theorem to find out the time efficiency in Big-O notation. For the non-recursive algorithm, use counting method to count the number of comparisons in Big-O notation.
Consider a Binary Search Algorithm that performs a search for the number 48 within the following unsorted list. Using paper and pencil, show the detailed steps for that search algorithm until 48 is found. You must use bubble sort if need it.1019134353415604870
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.)
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