2.1 ...letters can be repeated and the order of the letters matters? For each of the following problems, you should write your answer as an expression. Do notgive the final numeric value. For example, if your answer is the number of6-permutations of a set with 10 elements, you should write P(10,6) or 10!/4! or 10 x 9×8×7 × 6 × 5, but not 151200.The English alphabet contains 26 letters. How many ways are there tochoose 14 letters of the alphabet if...

Step 1: Analyze the problem and list down the givenEnglish Alphabet contains 26 lettersnumber of…

Answered: 2.1 ...letters can be repeated and the…

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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Write programs with these input and output Given positive integers m and n, find the number of ontofunctions from a set with m elements to a set with n elements.
Transcribed Image Text Let N be the set of all ounting numbers: 1, 2, 3,.... Consider these set definitions: A = {z € N| (4 < =) A (z < 5)} and B- {{4, 5}} Is the equality A = B true? O Yes, it is true. O No, it is not true. o We need more information in order to decide. Not counting N, are we dealing with two sets or one set in this problem? o One set. O Two sets.
The key observation is as follows. If n/2 < A[n/2], then if such anindex exists, it must be in A[1 . . . n/2−1]. This is because A[n/2+1] > A[n/2]+1 >n/2 + 1, A[n/2 + 2] > A[n/2 + 1] + 1 > n/2 + 2 and so on Could you explain why these are true by using actual number and example of array ?A[n/2+1] > A[n/2]+1 > n/2 + 1, A[n/2 + 2] > A[n/2 + 1] + 1 > n/2 + 2 and so on
Consider the given alorithm where A(1:n) is an array of n integers... A) What does the program do? What are the interpretations of B and C? B) What is the EXACT number comparisons in the best case in terms of n? C) What is the EXACT number comparisons in the worst case in terms of n?
Modulo arithmeticFor two integers ‘a’ and ‘b’ and a positive integer ‘n’, let + represent the operation a + b = (a+b)mod(n), that is, the result of a + b is the remainder of the usual sum a + b after dividing by n (using a natural representation). Similarly, let * represent the operation a * b = (a*b)mod(n), that is, the result of a * b is the remainder of the product a*b after dividing by n. For example using the set S = {2, 5, 8} and n = 9, 5 + 8 = 4, since 4 is the remainder after dividing 13 (5 + 8) by 9; and 2 * 8 = 7, since 7 is the remainder after dividing 16 (2*8) by 9.a. For each set S and number n specified below, create two “operation” tables (these are called Cayley tables), one showing the results for the operation +, and one showing the results of the operation * for each pair of elements from S (see the example tables in the notes).i. S1 = {0, 1} and n = 2ii. S2 = {1, 2} and n = 3iii. S3 = {0, 2, 4, 6} and n = 8iv. S4 = {1, 3, 5, 7} and n = 8v. S5 = {1, 2, 3, 4} and n =…
You want to design an algorithm, called minMax(A,p,r), that takes an array of integers and indexes of the first and last elements, and returns the minimum and maximum values in that range. Now write the pseudo code of a divide and conquer (and therefore, recursive) algorithm with the same time complexity (Θ(n)). You can assume that p ≤ r. Also, in your code, you can return two numbers by returning a pair, e.g. “return (a, b)”, and can save the output in a similar way, e.g. “(a, b) = minMax(parameters)”. (Short answer please)
Please help. How to solve this on Java language by using only Dynamic Programming? Thank you. We are given a set A of integers. Check whether we can partition A into three subsets with equal sums. It is important to note that all elements should be included in the equally divided subsets; no element should be left out, and none of the elements should be repeated in the subsets.For example: A={4,7,6,2,10,7,10,2} has such a partition: {4,2,10}, {7,7,2},{6,10}Input: A set, A, of integersOutput: if we can partition A into three subsets with equal sums, print subsets otherwise present a suitable message.
It is straightforward and efficient to compute the union of two sets using Boolean values. We may create a new union set by Oring the matching items of the two BitArrays since the union of two sets is a combination of the members of both sets. At other words, if the value in the corresponding place of either BitArray is True, a member is added to the new set.Computing the intersection of two sets is analogous to computing the union, except that the And operator is used instead of the Or operator Using the same technique we used to detect the difference, we can determine if one set is a subset of another. For example, if:setA(index) && !(setB(index))evaluates to False then setA is not a subset of setB.The BitArray Set ImplementationWrite The code for a CSet class based on a BitArray.
Given an array of strings, return all groups of strings that are anagrams. The groups must be created in order of their appearance in the original array. Look at the sample case for clarification. Note: The final output will be in lexicographic order. Example 1: Input:N = 5words[] = {act,god,cat,dog,tac}Output:act cat tac god dogExplanation:There are 2 groups ofanagrams "god", "dog" make group 1."act", "cat", "tac" make group 2.
Binary Search? When Jojo was a little kid, his teacher asked him a question. What was the answer of 1^2+2^2+3^2+...+N^2? Of course that problem was hard enough for a primary student. Buts ince he is a university student, and he knows that the answer is 1/6∗N∗(N +1)∗(2N +1), such problem is to easy for him. Now Jojo came up with a new problem. If he has an integerM, what is the smallest integer N such that 1^2 + 2^2 + 3^2+ ...+N^2 is greater than or equal to M. After thinking for some time, he came up with a solution, but his solution takes a lot of time. Since you are his nemesis, he challenges you to solve the problem quicker than him. Of course you accept his challenge! Format InputThe first line is an integer T representing the number of test cases.For each test case there will be 1 line consisting of an integerM. Format OutputFor each test case output “Case #X: N”. X is the test case number andN is the smallest integer such that 1^2 + 2^2 + 3^2+ ...+N^2is greater than or equal to…
If you cube each integer in turn from 10 to one million, you will see that 11 of them produce a result that is a palindrome (the same forwards as backwards). For example, 11×11×11=133111×11×11=1331. Write a single line of code to produce those 11 numbers and their cubes in a list of tuples.
Say that you are given as input a collection of n integers and some values may be repeated. Give a randomized algorithm that counts the number of A[i], A[j] so that A[i] = A[j], with best expected running time. For example, if all the numbers are the same, the value is (n/2) = n(n − 1)/2 use either a skiplist or hash function, please provide only pesudo code, or an explanation of an algorithm that better explains the problem.

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