b. Suppose you are gifted a collection of 3" pokéballs; all of the the pokéballs have the same size and weight except for one which is slightly heavier, and otherwise look and feel exactly the same as the others. You are tasked with identifying the heavy pokéball and have at your disposal a set of balancing scales which can be used to compare the weights of two collections of pokéballs. The scales can show whether the two collections have the same weight, or can show which collection is heavier if the weights are different. Prove using strong induction that you can identify the heavy pokéball out of 3" pokéballs using n weighing operations.

b. Suppose you are gifted a collection of 3" pokéballs; all of the the pokéballs have the same size and weight except for one which is slightly heavier, and otherwise look and feel exactly the same as the others. You are tasked with identifying the heavy pokéball and have at your disposal a set of balancing scales which can be used to compare the weights of two collections of pokéballs. The scales can show whether the two collections have the same weight, or can show which collection is heavier if the weights are different. Prove using strong induction that you can identify the heavy pokéball out of 3" pokéballs using n weighing operations.

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

See similar textbooks

Similar questions

You will be given a square chess board with one queen and a number of obstacles placed on it. Determine how many squares the queen can attack. A queen is standing on an chessboard. The chess board's rows are numbered from to , going from bottom to top. Its columns are numbered from to , going from left to right. Each square is referenced by a tuple, , describing the row, , and column, , where the square is located. The queen is standing at position . In a single move, she can attack any square in any of the eight directions (left, right, up, down, and the four diagonals). In the diagram below, the green circles denote all the cells the queen can attack from : There are obstacles on the chessboard, each preventing the queen from attacking any square beyond it on that path. For example, an obstacle at location in the diagram above prevents the queen from attacking cells , , and : Given the queen's position and the locations of all the obstacles, find and print the number of…
Q. There is an island that has two kinds of inhabitants, knights, who always tellthe truth, and their opposites, knaves, who always lie. It is assumed that every inhabitant of theisland is either a knight or a knave. Below there are 3 inhabitants, who are denoted by A, B andC.A. What are A, B and C if A says “If B is a knave then C is a knave”, and B says “If Cis a knight then A is a knave”? Briefly explain your reasoning.B. What are A,B and C if A says “B is a knight and C is a knight”, and B says “A is aknight if and only if C is a knave”? Briefly explain your reasoning.
You are the chief commander of US Army; you have been deployed in an ongoing war training of defusing the mine. Mines are placed on the ground which can be considered as a gird of size N*M. Each block (i, j) has a mine in it if and only if the summation of the block coordinates is divisible by 2. Your task is to move from the first row to the last row. The mines will not blow if the given rules are followed: • If you are on even row you can move to any cell that is in the neighborhood • If you are on odd row, you can only go the odd row that has mine on that and same with the unmined row. You have to develop a python program to calculate the number of ways to reach row number N starting from row number 1. Test Cases: 4 8 Output: 10
A deck of cards contains 52 cards with four suits: club, diamond, heart and spade ranging in values from 2, ... to 10, Jack, Queen, King and Ace. Ace has the highest value in the same suit. Cards can be compared using their face values. A card with higher face value is bigger than a card with lower face value. If two cards have the same face value, then the suit determines the order. Club is smaller than diamond which is smaller than heart which is smaller than spade. For example: club 2 < diamond 2 < heart 2 < spade 2 if compared.Write an interactive Java program that allows you play cards with a computer. For this project, we are going to focus on one suit of the deck of cards. There are only 13 cards (value: 2, ... to 10, Jack, Queen, King and Ace) in a suit. To play:(a). You first pick a suit at random from the four suits (club, diamond, heart and spade), and display the suit. (b) Then you randomly draw a card from the suit, and let computer draw a card from the same…
A deck of cards contains 52 cards with four suits: club, diamond, heart and spade ranging in values from 2, ... to 10, Jack, Queen, King and Ace. Ace has the highest value in the same suit. Cards can be compared using the face value. A card with higher face value is bigger than a card with lower face value. If two cards have the same face value, then the suit determines the order. Club is smaller than diamond which is smaller than heart which is smaller than spade. For example: club 2 < diamond 2 < heart 2 < spade 2 if compared. Write an interactive Java program that allows a user to randomly pick a card from the deck of 52 cards (using a random number between 1 and 4 to represent the four suits: club, diamond, heart and spade and then another random number to represent the face value) to play. Show the suit and face value of the user card. Then the program acts as a card dealer which randomly draws another card and displays the card (again showing the suit and face value of…
Player A and player B invented a game in which a person who sorts playing cards is a winner. The cards with red color should come before those with black color, and cards with small numbers should come before those with big numbers. The cards with images should be in this order: Jack, Queen and King. The game allows player to start by small number of cards, then increase step by step, e.g, 2,3,4, ....n. Design an efficient algorithm that helps a player A to win the game by sorting n number of cards faster than player B. Note that n number of cards which is very large can be obtained by repeating cards with the same number and same color, e.g, card 3 with color red can be repeated m times while m
A hungry mouse wants to eat all four fruits in a maze such as the one below, in as few moves as possible.. At each turn the mouse can move any number of squares in one of the directions up, down, left or right, but it is not allowed to enter (or jump over) any walls (i.e., the black squares). Thus, the mouse moves just like a rook in chess. To eat a fruit, the mouse has to stop at that square. Assume that the maze has 4 fruits, and the size of b xh squares. 1. Give a suitable representatión of the states in this searching problem. 2. How many possible actions can the mouse perform at each move? (1.e., what is the branching factor?)
We have n glasses which can hold a varying amount of liquid. We will say that glass1 is size q1 quarts and glass2 is size q2 quarts, etc. We now give you a size, say x quarts. You must give me a glass of exactly x quarts. You are allowed to fill any glass to exactly its size and to pour any liquid from one glass into another. When you pour, you either have to empty the glass you are pouring from or fill the glass you are pouring into. Can you do it?More concrete example: G1 has size 10 quarts. G2 has size 4 quarts. G3 has size 1 quart. You can get a 5 quart drink by filling G1, pouring 4 quarts from it into G2 and 1 quart of it into G1. After that, G1 has exactly 5 quarts. In the same problem, we could get 8 quarts by filling G2 twice and emptying it into G1 twice. Given This: Write an algorithm to do this and determine its complexity.
On a chess board of r rows and c columns there is a lone white rook surrounded by a group of opponent's black knights. Each knight attacks 8 squares as in a typical chess game, which are shown in the figure - the knight on the red square attacks the 8 squares with a red dot. The rook can move horizontally and vertically by any number of squares. The rook can safely pass through an empty square that is attacked by a knight, but it must move to a square that is not attacked by any knight. The rook cannot jump over a knight while moving. If the rook moves to a square that contains a knight, it may capture it and remove it from the board. The black knights. never move. Can the rook eventually safely move to the designated target square? The figure illustrates how the white rook can move to the blue target square at the top-right corner in the first sample case. The rook captures one black knight at the bottom-right of the board on its way. Rok nd kight lcoes by Chunen Input The first line…
Bowling involves 10 frames. Each frame starts with 10 pins. The bowler has two throws to knock all 10 pins down. The total score is the sum of pins knocked down, with some special rules. For the first 9 frames: If all 10 pins are knocked down on a frame's first throw (a "strike"), that frame's score is the previous frame plus 10 plus the next two throws. (No second throw is taken). If all 10 pins are knocked down after a frame's second throw (a "spare"), that frame's score is the previous frame plus 10 plus the next throw. In the 10th frame, if the bowler's first throw is a strike, or the first two throws yields a spare, the bowler gets a third throw. The 10th frame's score is the previous frame's score plus the pins knocked down in the 10th frame's two or three throws. Given integers represents all throws for a game, output on one line each frame's score followed by a space (and end with a newline). Note that the number of throws may be as few as 11 (strikes in first 9 frames,…
Bowling involves 10 frames. Each frame starts with 10 pins. The bowler has two throws to knock all 10 pins down. The total score is the sum of pins knocked down, with some special rules. For the first 9 frames: If all 10 pins are knocked down on a frame's first throw (a "strike"), that frame's score is the previous frame plus 10 plus the next two throws. (No second throw is taken). If all 10 pins are knocked down after a frame's second throw (a "spare"), that frame's score is the previous frame plus 10 plus the next throw. In the 10th frame, if the bowler's first throw is a strike, or the first two throws yields a spare, the bowler gets a third throw. The 10th frame's score is the previous frame's score plus the pins knocked down in the 10th frame's two or three throws. Given integers represents all throws for a game, output on one line each frame's score followed by a space (and end with a newline). Note that the number of throws may be as few as 11 (strikes in first 9 frames,…
Bowling involves 10 frames. Each frame starts with 10 pins. The bowler has two throws to knock all 10 pins down. The total score is the sum of pins knocked down, with some special rules. For the first 9 frames: If all 10 pins are knocked down on a frame's first throw (a "strike"), that frame's score is the previous frame plus 10 plus the next two throws. (No second throw is taken). If all 10 pins are knocked down after a frame's second throw (a "spare"), that frame's score is the previous frame plus 10 plus the next throw. In the 10th frame, if the bowler's first throw is a strike, or the first two throws yields a spare, the bowler gets a third throw. The 10th frame's score is the previous frame's score plus the pins knocked down in the 10th frame's two or three throws. Given integers represents all throws for a game, output on one line each frame's score followed by a space (and end with a newline). Note that the number of throws may be as few as 11 (strikes in first 9 frames,…