A square number is an integer number whose square root is also an integer. For example 1, 4, 81 are some square numbers. Given two numbers a and b you will have to find out how many square numbers are there between a and b (inclusive). Input Each line contains two integers a and b (0 < a

A square number is an integer number whose square root is also an integer. For example 1, 4, 81 are some square numbers. Given two numbers a and b you will have to find out how many square numbers are there between a and b (inclusive). Input Each line contains two integers a and b (0 < a

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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Euclid’s algorithm (or the Euclidean algorithm) is an algorithm that computes thegreatest common divisor, denoted by gcd, of two integers. Below are the original versions ofEuclid’s algorithm that uses repeated subtraction and another one that uses the remainder.int gcd_sub(int a, int b){ if (!a) return b; while (b) if (a > b) a = a – b; else b = b – a; return a;}int gcd_rem(int a, int b){ int t; while (b) { t = b; b = a % b; a = t; } return a;}1. Trace each of the above algorithm using specific values for a and b.2. Compare both algorithms.
1. depends on pseudo code described algorithm below find primes up to N in java rogramming language. For all numbers a : from 2 to sqrt(N) IF a is unmarked THEN a is prime For all multiples of a (a < n) mark them as composite All unmarked numbers are prime Input N: 200 Primes up to 200: 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 Hint: Put 1 to n in a array. Mark composites with 0.
In computer science and mathematics, the Josephus Problem (or Josephus permutation) is a theoretical problem. Following is the problem statement: There are n people standing in a circle waiting to be executed. The counting out begins at some point (rear) in the circle and proceeds around the circle in a fixed direction. In each step, a certain number (k) of people are skipped and the next person is executed. The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last person remains, who is given freedom. Given the total number of persons n and a number k which indicates that k-1 persons are skipped and kth person is killed in circle. The task is to choose the place in the initial circle so that you are the last one remaining and so survive. For example, if n = 5 and k = 2, then the safe position is 3. Firstly, the person at position 2 is killed, then person at position 4 is killed, then person at position 1…
The intersection of two sets contains the list of elements that are common to both, without repetition. As such, you are required to write an algorithm that finds and returns the intersection of two sets A and B. The sets A and B and the resulting intersection set are all lists. Assume the size of A is n and that of B is m. (a) Write an iterative algorithm that finds the intersection. (b) Prove the correctness of your algorithm; i.e. state its loop invariant and prove it by induc- tion. (c) Analyze the time complexity of your algorithm. (d) Think of a way to enhance the complexity of your algorithm by sorting both lists A and B before calculating their intersection. Write the enhanced version and prove that it has a better time complexity.
Suppose a string Z is formed by interspersing the characters from other two strings X and Y. The new string Z is called a shuffle of X and Y if characters in Z com- ing from the same string still keep the order as in the original string. For example, the strings PRODGYRNAMAMMIINCG and DYPRONGARMAMMICING are both shuffles of DYNAMIC and PROGRAMMING: PRODGYRNAMAMMIINCG DYPRONGARMAMMICING Given three strings A[1..m], B[1..n], and C[1..m+n], design a dynamic programming algorithm to determine if C is a shuffle of A and B.
In python, The Longest Subsequence Problem is a well-studied problem in Computer Science, where given a sequence of distinct positive integers, the goal is to output the longest subsequence whose elements appear from smallest to largest, or from largest to smallest. For example, consider the sequence S= [9,7,4,10,6,8,2,1,3,5]. The longest increasing subsequence of S has length three ([4,6,8] or [2,3,5]), and the longest decreasing subsequence of S has length five([9,7,4,2,1] or [9,7,6,2,1]). And if we have the sequence S = [531,339,298,247,246,195,104,73,52,31], then the length of the longest increasing subsequence is 1 and the length of the longest decreasing subsequence is 10. Question: Find a sequence with nine distinct integers for which the length of the longest increasing subsequence is 3, and the length of the longest decreasing subsequence is 3. Briefly explain how youconstructed your sequence.
Write code for complete application that includes all the code for computing the shortest paths using Dijkstra’s algorithm, along with a program to test the implementation:
The algorithm of Euclid computes the greatest common divisor (GCD) of two integer numbers a and b. The following pseudo-code is the original version of this algorithm. Algorithm 1 Euclid1(a,b)Require: a, b > 0Ensure: a = GCD(a, b) while a ̸= b do if a > b then a ← a − b else b ← b − a end if end whilereturn a We want to prove the correctness of this algorithm using the loop invariant technique. a. In a first attempt to prove the correctness of this algorithm, we propose the following loop invariant property: “GCD(a, b) is a factor of a and b”. Explain why this property willnot help you as is. b. Use your previous observation to propose another loop invariant property that willhelp you to prove the correctness of the version of Euclid’s algorithm presented above. c. Show that your loop invariant property is true before executing the While loop forthe first time (i.e., initialization property)
The algorithm of Euclid computes the greatest common divisor (GCD) of two integer numbers a and b. The following pseudo-code is the original version of this algorithm. Algorithm 1 Euclid1(a,b)Require: a, b > 0Ensure: a = GCD(a, b) while a ̸= b do if a > b then a ← a − b else b ← b − a end if end whilereturn a We want to prove the correctness of this algorithm using the loop invariant technique. Answer the following questions: a. Show the property is maintained during the execuation of the While loop (i.e., maintenance property). b. Prove the termination property and conclude. c. What would happen if a > 0 and b = 0 and thus the pre-condition is not satisfied?
1. Analyze the word finder with wild card characters scenario to form the algorithm and compute the time complexity. You are given a list of characters with size n, m. You need to read character data provided as input into this list. There is also a list of p words that you need to find in the given problem. You can only search in left, right, up and down direction from a position. There are two wild characters *' and '+' ,if there is any instance of wild card characters for example '+' appears you can match whatever character in your word that you are searching at this position (only one character). Similarly, if you got wildcard *' you can skip any number of characters ( A sequence of characters not necessary same in between the characters) but the last character should be matched in the given data. This means you are not allowed to match a first and last character with *' wildeard. Input: The first line of the input will give you two integers n and m. From the next line you will get…
CAN THE SOLUTION BE SUBMITTED WITH TEXT AND NOT A PDF IMAGE PLEASE! This assignment requires you to write a non-verbose input-driven java program for maintaining a binary search tree (BST) of integer elements (negative, zero or positive). The speciality of your BST will be that itwill record the frequency of occurrence for each integer element in it. Actions provisioned on the BST. When your program is running, a user should be able to select one of the following actions to be performed on the BST. 1. Insert an element into the BST2. Search for an element in the BST3. Find the maximum element from the BST4. Find the minimum element from the BST5. Print the elements in the BST in preorder6. Print the elements in the BST in postorder7. Print the elements in the BST in inorder8. Delete an element Anything else to exit the program. The user will provide their choice of action on the BST, by entering one of the numbers between 1 to 8 thatcorrespond to their choice. For example, if the…
solve in java Integer arrays originalArr and filterArr are read from input, each containing two elements. If an element in originalArr is not a multiple of the corresponding element in filterArr, replace the element in originalArr with the corresponding element in filterArr times 2. Ex: If the input is: 16 9 8 4 then the output is: 16 8 Note: Given integers A and B, A is a multiple of B only if A % B == 0. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 import java.util.Scanner; public class ReplaceNumbers { publicstaticvoidmain(String[] args) { Scannerscnr=newScanner(System.in); finalintNUM_VALS=2; int[] originalArr=newint[NUM_VALS]; int[] filterArr=newint[NUM_VALS]; inti; for (i=0; i<NUM_VALS; ++i) { originalArr[i] =scnr.nextInt(); } for (i=0; i<NUM_VALS; ++i) { filterArr[i] =scnr.nextInt(); } /* Your code goes here */ for (i = 0; i < originalArr.length; ++i) { System.out.print(originalArr[i] + " "); } System.out.println();…