• Given a list of n distinct integers, devise an algorithm to print the index of all pairs having the sum equals to a given input value k. This method takes a list, and an integer k as input arguments. So for example, if the pair az = 2 and ag = 3 and k = 5, then the algorithm should print(3, 6), and all other pairs with the same property. What is the running time of this algorithm? Assume for the previous problem the input list is sorted, modify the previous algorithm to run faster. What is the running time now? (No Credit will be given for O(n2) algorithms)

• Given a list of n distinct integers, devise an algorithm to print the index of all pairs having the sum equals to a given input value k. This method takes a list, and an integer k as input arguments. So for example, if the pair az = 2 and ag = 3 and k = 5, then the algorithm should print(3, 6), and all other pairs with the same property. What is the running time of this algorithm? Assume for the previous problem the input list is sorted, modify the previous algorithm to run faster. What is the running time now? (No Credit will be given for O(n2) algorithms)

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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2. Let n be a positive integer, and let A be a list of positive integers. We say that the integer n can be factorized by A if there exists a sequence of integers 11, 12,..., ik (with 0 ≤i; < len (A), for j = 1,..., k) such that n is the product of the integers A[i], A[i2],..., A[ik]. Write an efficient algorithm factorizable (n, A) that returns True if n can be factorized by A, and False otherwise. Prove that your algorithm is correct, and bound its running time. Larger scores will be awarded to faster solutions. Example 1: if n = 6 and A [4,2,3], then factorizable (n, A) should return True, L[1] * L[2]. since n == Example 2: if n = 8 and A = L[0] * L[0] * L[0]. [2,5], then factorizable (n, A) should return True, since ,2,3,5,7], then factorizable (n, A) should return Example 3: if n = 13 and A = False since n cannot be factorized by A.
a. Write a version of the sequential search algorithm that can be used to search a sorted list. (1, 2) b. Consider the following list: 2, 20, 38, 41, 49, 56, 62, 70, 88, 95, 100, 135, 145 Using a sequential search on ordered lists, that you designed in (a), how many comparisons are required to determine whether the following items are in the list? (Recall that comparisons mean item comparisons, not index comparisons.) (1, 2) 2 57 88 70 135 Write a program to test the function you designed. Note: Have the function,seqOrdSearch, return -1 if the item is not found in the list. (return the index of the item if found).
We are given a collection of n key-value pairs (k,m) in which k is a positive integer number in arange [0,N-1] for small enough N. Assume that we may have multiple values for the same keys.a) if m is a positive number in a range [0,M-1] for some small enough integer M, design alookup table for storing these items such that the time complexity of search, insert and deleteare constant. b) if m is an arbitrary integer number, design a lookup table for storing these itemssuch that the time complexity of search is log n.
You are given an array of integers nums and an integer target. Return the indices of two numbers in the array such that they add up to target. You may assume that each input would have exactly one solution, and you may not use the same element twice. Implement a function in Java to solve this problem using a hash map, and explain the time and space complexity of your solution.
The median m of a sequence of n elements is the element that would fall in the middle if the sequence was sorted. That is, e ≤ m for half the elements, and m ≤ e for the others. Clearly, one can obtain the median by sorting the sequence, but one can do quite a bit better with the following algorithm that finds the kth element of a sequence between a (inclusive) and b (exclusive). (For the median, use k = n/2, a = 0, and b = n.) select(k, a, b)Pick a pivot p in the subsequence between a and b.Partition the subsequence elements into three subsequences: the elements <p, =p, >p Let n1, n2, n3 be the sizes of each of these subsequences.if k < n1 return select(k, 0, n1).else if (k > n1 + n2) return select(k, n1 + n2, n).else return p. c++
Create an algorithm that demonstrates the Fibonacci search process. The number of data elements in this instance, n, is such that: I Fk+1 > (n+1); and (ii) Fk + m = (n +1) for some m 0, where Fk+1 and Fk are two consecutive Fibonacci numbers.
Given a non-empty list items of positive integers in strictly ascending order, find and return thelongest arithmetic progression whose all values exist somewhere in that sequence. Return the answer as a tuple (start, stride, n) of the values that define the progression. To ensure unique results to facilitate automated testing, if there exist several progressions of the same length, this function should return the one with the lowest start. If several progressions of equal length emanate from the lowest start, return the progression with the smallest stride. INTRUCTIONS: Input a comment or a solution on how you solve the problem, write a psuodocode and flow chart about th problem
(a) Implement a program that tries successive values of r, i.e., r = 0, 1, 2, 3, . . ., computes H(s||r), compares it with t and halts whenever H(s||r) < t, with the output r. You need to provide the program and the output r. (b) Modify the program from part (a) by adding i to s, where i = 0 to 999 inclusive, and for each i computing the hash until the value falls before the target. What is the average number of attempts (over 1,000) before you found the target? You need to provide your program. (c) If you drew random values between 0 and 2255 inclusive, how many attempts on average it would take before you find a value below the target? What does it tell you about SHA-256?
Develop a brute-force algorithm that finds the longest common sequential elements of two given lists with the Java programming language. For example, the following two lists are given: S1 = [B,C,D,A,A,C,D] S2 = [A,C,D,B,A,C] Common lists are: [B,C], [C,D,A,C], [D,A,C], [A,A,C], [A,C], [C,D], … Note that although both lists have a common [C,D,A,C] (sub)list, both list items are skipped and the left-to-right order is intact. Apply the brute force algorithm. Explain Time Complexity?
An array A[1 . . n] of integers is a mountain if it consists of an increasing sequence followed by a decreasing sequence, or more precisely,If there is an index m ∈ {1, 2, . . . , n} such that• A[i] < A[i + 1] for all 1 ≤ i < m, and• A[i] > A[i + 1] for all m ≤ i < n.In particular, A[m] is the maximum element, and it is the unique “locally maximum” element surrounded by smaller elements (A[m − 1] and A[m + 1]).Give an algorithm to compute the maximum element of a mountain input array A[1 . . n] in O(log(n)) time.
You are given a list of randomly arranged numbers, for example (11,7,18,5,17,13). The triple (11,7, 5) is called the "inversion triple" because (5<7<11) in terms of value, while the index of 5 in the list is greater than the index of 7, and the index of 7 is greater than 11. Therefore, we can find 2 inversions in such list as follows: (11,7,5), and (18,17,13). Your main task is to find the total number of inversions in any given list. a) Design a brute-force algorithm to return the number of possible inversions, and analyse the complexity of your solution b) Develop a python code to implement your brute-force algorithm. [The marks depend on the correctness of the code, indentation, comments, test-case] c) Design a more efficient algorithm to do the same task with less complexity, and analyse the complexity of your solution. [Important instruction to be followed: Create an arbitrary unsorted list of 8 characters and use it to provide full explanation of how your proposed…
In class HashTable implement a hash table and consider the following:(i) Keys are integers (therefore also negative!) and should be stored in the tableint[] data.(ii) As a hash function take h(x) = (x · 701) mod 2000. The size of the table istherefore 2000. Be careful when computing the index of a negative key. Forexample, the index of the key x = −10 ish(−10) = (−7010) mod 2000 = (2000(−4) + 990) mod 2000 = 990.Hence, indices should be non-negative integers between 0 and 1999!(iii) Implement insert, which takes an integer and inserts it into a table. Themethod returns true, if the insertion is successful. If an element is already inthe table, the function insert should return false.(iv) Implement search, which takes an integer and finds it in the table. The methodreturns true, if the search is successful and false otherwise.(v) Implement delete, which takes an integer and deletes it form the table. Themethod returns true, if the deletion is successful and false otherwise.(vi)…