Q1.1 Big Omega 1 Point Select the option which best matches the meaning of: f(n) = N(n²) O For sufficiently large values of n, every input of size n causes the algorithm to do at least c. n² multiplications (for some choice of c). For sufficiently large values of n, every input of size n causes the algorithm to do at most cn² multiplications (for some choice of c). For sufficiently large values of n, there exists an input of size n which causes the algorithm to do at most c. n² multiplications (for some choice of c). You cannot analyze a worst-case running time using , so the statement is meaningless. O For sufficiently large values of n, there exists an input of size ŉ which causes the algorithm to do at least c. n² multiplications (for some choice of c).

Q1.1 Big Omega 1 Point Select the option which best matches the meaning of: f(n) = N(n²) O For sufficiently large values of n, every input of size n causes the algorithm to do at least c. n² multiplications (for some choice of c). For sufficiently large values of n, every input of size n causes the algorithm to do at most cn² multiplications (for some choice of c). For sufficiently large values of n, there exists an input of size n which causes the algorithm to do at most c. n² multiplications (for some choice of c). You cannot analyze a worst-case running time using , so the statement is meaningless. O For sufficiently large values of n, there exists an input of size ŉ which causes the algorithm to do at least c. n² multiplications (for some choice of c).

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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Count consecutive summers def count_consecutive_summers(n): Like a majestic wild horse waiting for someone to come and tame it, positive integers can be broken down as sums of consecutive positive integers in various ways. For example, the integer 42 often used as placeholder in this kind of discussions can be broken down into such a sum in four different ways: (a) 3 + 4 + 5 + 6 + 7 + 8 + 9, (b) 9 + 10 + 11 + 12, (c) 13 + 14 + 15 and (d) 42. As the last solution (d) shows, any positive integer can always be trivially expressed as a singleton sum that consists of that integer alone. Given a positive integer n, determine how many different ways it can be expressed as a sum of consecutive positive integers, and return that count. The count of how many different ways a positive integer n can be represented as a sum of consecutive integers is also called its politeness, and can be alternatively computed by counting how many odd divisors that number has. However, note that the linked…
Count consecutive summers def count_consecutive_summers(n): Like a majestic wild horse waiting for the rugged hero to tame it, positive integers can be broken down as sums of consecutive positive integers in various ways. For example, the integer 42 often used as placeholder in this kind of discussions can be broken down into such a sum in four different ways: (a) 3 + 4 + 5 + 6 + 7 + 8 + 9, (b) 9 + 10 + 11 + 12, (c) 13 + 14 + 15 and (d) 42. As the last solution (d) shows, any positive integer can always be trivially expressed as a singleton sum that consists of that integer alone. Given a positive integer n, determine how many different ways it can be expressed as a sum of consecutive positive integers, and return that count. The number of ways that a positive integer n can be represented as a sum of consecutive integers is called its politeness, and can also be computed by tallying up the number of odd divisors of that number. However, note that the linked Wikipedia de0inition…
Q2. ""Euler's totient function, also known as phi-function ϕ(n),counts the number of integers between 1 and n inclusive,which are coprime to n.(Two numbers are coprime if their greatest common divisor (GCD) equals 1)."""def euler_totient(n): """Euler's totient function or Phi function. Time Complexity: O(sqrt(n)).""" result = n for i in range(2, int(n ** 0.5) + 1): if n % i == 0: while n % i == 0: n //= i. .
“Rectangles” A rectangle can be specified in a 2-dimensional plane using the top left (north west) point and the bottom right (south east) point. Given n rectangles (using 2 points each), give an O(n log n) algorithm that tells if any two rectangles from the list overlap. Two rectangles are said to overlap, if there is a common point in both of them. [If a rectangle is entirely contained in another, they are still said to “overlap”, even though their lines don’t cross.]
Artificial Intelligence - Local Search Starting from a randomly generated state of the 15-puzzle game, steepest-ascent hill-climbing (the vanilla version of hill-climbing search) gets stuck 76% of the time, i.e., solving only 24% of problem instances. But it works very quickly, i.e., it takes just 6 steps on average when it succeeds and 5 steps when it gets stuck. In contrast, if sideways moves are allowed, this raises the percentage of problem instances solved by hill-climbing from 24% to 81%, with the success at a cost: the algorithm averages roughly 7 steps for each successful instance and 32 steps for each failure. Now suppose that we are implementing random-restart hill climbing (i.e., if a search fails, it keeps to try, and try, until it gets a success) by the following two versions: one uses vanilla steepest-ascent hill climbing, and the other one uses hill climbing with sideways moves. Can you please tell which version of random-restart hill-climbing listed above runs faster…
Start with any positive number n. If n is even divide it by 2, if n is odd multiply by 3 and add 1. Repeat until n becomes 1. The sequence that is generated is called a bumpy sequence. For example, the bumpy sequence that starts at n = 10 is: 10, 5, 16, 8, 4, 2, 1and the one that starts at 11 is11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1 Write a function named lengthBumpy that returns the length of the bumpy sequence generated by its integer argument. The signature of the function is int lengthBumpy(int n) Examples:lengthBumpy(10) returns 7, and lengthBumpy(11) returns 15. You may assume that the argument n is positive and that the sequence converges to 1 without arithmetic overflow.
Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. Ridbit begins with an integer n. In one action, he can perform one of the accompanying tasks: partition n by one of its appropriate divisors, or take away 1 from n in case n is more prominent than 1. An appropriate divisor is a divisor of a number, barring itself. For instance, 1, 2, 4, 5, and 10 are appropriate divisors of 20, however 20 itself isn't. What is the base number of moves Ridbit is needed to make to decrease n to 1? Input The principal line contains a solitary integer t (1≤t≤1000) — the number of experiments. The main line of each experiment contains a solitary integer n (1≤n≤109). Output For each experiment, output the base number of moves needed to lessen n to 1.
4.2) (L4) Give truth values for the propositional variables that cause the two expressions to have different truth values. For example, given p ∨ q and p ⊕ q, the correct answer would be p = q = T, because when p and q are both true, p ∨ q is true but p ⊕ q is false. Note that there may be more than one correct answer. r ∧ (p ∨ q) (r ∧ p) ∨ q
Artificial Intelligence - Local Search Starting from a randomly generated state of the 15-puzzle game (https://en.wikipedia.org/wiki/15_puzzle), steepest-ascent hill-climbing (the vanilla version of hill-climbing search) gets stuck 76% of the time, i.e., solving only 24% of problem instances. But it works very quickly, i.e., it takes just 6 steps on average when it succeeds and 5 steps when it gets stuck. In contrast, if sideways moves are allowed, this raises the percentage of problem instances solved by hill-climbing from 24% to 81%, with the success at a cost: the algorithm averages roughly 7 steps for each successful instance and 32 steps for each failure. Now suppose that we are implementing random-restart hill climbing (i.e., if a search fails, it keeps to try, and try, until it gets a success) by the following two versions: one uses vanilla steepest-ascent hill climbing, and the other one uses hill climbing with sideways moves. Can you please tell which version of…
A popular word game involves finding words from a grid of randomly generatedletters. Words must be at least three letters long and formed from adjoining letters.Letters may not be reused and it is valid to move across diagonals. As an example,consider the following 4 * 4 grid of letters: A B C DE F G HI J K LM N O P The word “FAB” is valid (letters in the upper left corner) and the word “KNIFE”is valid. The word “BABE” is not valid because the “B” may not be reused. Theword “MINE” is not valid because the “E” is not adjacent to the “N”. Write a program that uses a 4 * 4 two-dimensional array to represent the gameboard. The program should randomly select letters for the board. You may wishto select vowels with a higher probability than consonants. You may also wish toalways place a “U” next to a “Q” or to treat “QU” as a single letter. The programshould read the words from the text file words.txt (included on the website withthis book) and then use a recursive algorithm to…
Given a positive integer, N, the ’3N+1’ sequence starting from N is defined as follows: If N is an even number, then divide N by two to get a new value for N. If N is an odd number, then multiply N by 3 and add 1 to get a new value for N. Continue to generate numbers in this way until N becomes equal to 1. For example, starting from N = 3 the complete ’3N+1’ sequence would be:3, 10, 5, 16, 8, 4, 2, 1 Do the following: Write a code in C++ to ask the user to enter a positive integer (N) in the main() function. Write a function sequence() that receives the integer value N and display the ‘3N+1’ sequence starting from the integer value that wasreceived (entered by the user). The function must also count and return the numbers that the sequence consists of. The returned value must be displayed from the main() function. Example input and output is given in the following image.
Correct answer will be upvoted else downvoted. Computer science. Presently Nezzar has a beatmap of n particular focuses A1,A2,… ,An. Nezzar might want to reorder these n focuses so the subsequent beatmap is great. Officially, you are needed to find a change p1,p2,… ,pn of integers from 1 to n, to such an extent that beatmap Ap1,Ap2,… ,Apn is great. In case it is unthinkable, you ought to decide it. Input The primary line contains a solitary integer n (3≤n≤5000). Then, at that point, n lines follow, I-th of them contains two integers xi, yi (−109≤xi,yi≤109) — directions of point Ai. It is ensured that all focuses are unmistakable. Output In case there is no arrangement, print −1. In any case, print n integers, addressing a legitimate change p. In case there are numerous potential replies, you can print any.