We all studied Divide and Conquer approaches for solving problems. We used this method for sorting and counting inversions. Let's talk about another problem called - 'Finding the closest pair of points. In this problem, we are given n points and we need to find out the closest two points among them. Straight forward! Isn't it? Yes, we could just take all the possible pairs and calculate their distances. But, when the number of points is too high, this is going to be a very costly approach. Here comes Divide and Conquer (DnC) - for our help. Let's not talk too much about it. Your responsibility is to write on: (a) how DnC works, (b) how it shortens the time complexity, (c) how DnC solves the above-mentioned problem, and (d) time-complexity of your solution.

We all studied Divide and Conquer approaches for solving problems. We used this method for sorting and counting inversions. Let's talk about another problem called - 'Finding the closest pair of points. In this problem, we are given n points and we need to find out the closest two points among them. Straight forward! Isn't it? Yes, we could just take all the possible pairs and calculate their distances. But, when the number of points is too high, this is going to be a very costly approach. Here comes Divide and Conquer (DnC) - for our help. Let's not talk too much about it. Your responsibility is to write on: (a) how DnC works, (b) how it shortens the time complexity, (c) how DnC solves the above-mentioned problem, and (d) time-complexity of your solution.

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

What is Benford’s Law? Benford’s Law involves looking at the first digit of a series of numbers. For example, suppose that you were to use a random number generator to generate integers in the range of 100 to 999 and you looked at how often the number begins with 1, how often it begins with 2, and so on. Any decent random number generator would spread the answers out evenly among the 9 regions, so we’d expect to see each digit about one-ninth of the time (11.1%). But with a lot of real-world data, we see a very different distribution. The expected distribution under Benford’s Law is shown below:1: 30.1%, 2: 17.6%, 3: 12.5%, 4: 9.7%, 5: 7.9%, 6: 6.7%, 7: 5.8%, 8: 5.1%, 9: 4.6% You should use this distribution in your program. You are being provided with a text file giving population data for 247 countries and territories. Your program should read in the data in this file and extract the information needed to keep count of how often each first digit is found. It may be useful to know…
This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 931 tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total number of matches to be played altogether, in all the rounds of the tournament? Your answer: Hint: This is much simpler than you think. When you see the answer you will say "of course".
An n × n square consists of black and white cells arranged in a certain way. The problem is to determine the number of white areas and the number of white cells in each area. For example, a regular 8 × 8 chessboard has 32 one-cell white areas; the square in Figure 5.22a consists of 10 areas, 2 of them of 10 cells, and 8 of 2 cells; the square in Figure 5.22b has 5 white areas of 1, 3, 21, 10, and 2 cells. Write a program that, for a given n × n square, outputs the number of white areas and their sizes. Use an (n + 2) × (n + 2) array with properly marked cells. Two ad- ditional rows and columns constitute a frame of black cells surrounding the entered square to simplify your implementation. For instance, the square in Figure 5.22b is stored as the square in Figure 5.22c. (a–b) Two n 3 n squares of black and white cells and (c) an (n + 2) 3 (n + 2) array implementing square (b). bbbbbbbbbb bwbbwwbwwb bbbbbwbwwb bwwwbbwwwb bwbwbwwbbb bwbwwwbwbb bwbbbbwwwb bwbwbbwwwb bwbwbbwwwb…
IN PYTHON A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal and the ones immediately above and below it.Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don't need to be modified or added. As an example, consider a linear system Ax = b with 100,000 unknowns and the same number of equations. The coefficient matrix A is tridiagonal, with all elements on the main diagonal equal to 3 and all elements on the diagonals above and below it equal to 1. The vector of constant terms b contains all ones, except that the first and last elements are zero. You can use td to find that x1= −0.10557. The following code format should help: def td(l, m, u, b): '''Solve a linear system Ax = b where A is tridiagonal Inputs: l, lower diagonal of A, n-1 vector m, main diagonal of A, n vector u,…
Imagine there are N teams competing in a tournament, and that each team plays each of the other teams once. If a tournament were to take place, it should be demonstrated (using an example) that every team would lose to at least one other team in the tournament.
The digital root of a positive integer is found by summing the digits of the integer. If the resulting value is a single digit then that digit is the digital root. If the resulting value contains two or more digits, those digits are summed and the process is repeated. This is continued as long as necessary to obtain a single digit. For example, consider the positive integer 24. Adding the 2 and the 4 yields a value of 6. Since 6 is a single digit, 6 is the digital root of 24. Now consider the positive integer 39. Adding the 3 and the 9 yields 12. Since 12 is not a single digit, the process must be repeated. Adding the 1 and the 2 yields 3, a single digit and also the digital root of 39. Input File: The input file will contain a list of positive integers, one per line. The end of the input will be indicated by an integer value of zero. Output File: For each integer in the input, output its digital root on a separate line of the output. Example Input: 24 39…
Write a function find_equivalent_matchings that takes a matching and returns all matchings with the same pattern (including the original one). Using this function, draw all matchings equivalent to {(0, 7), (1, 4), (2, 3), (5, 6)}. You might find it helpful to generate all permutations of a list using itertools.permutation (imported above) as in the following code template. perms=permutations (list_of_items) for p in perms:
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.
The density of an object is 2 g/cm3. To convert this to kg/m3, we need to divide it by 1000 to change grams to kilograms. Then, we need to multiply it by 10 to the power of what number to change cm3 to m3.
The coordinates of a polygon can be represented as a list of tuples: [(x1, y1), (x2, y2), .., (xn, yn)], where (x1, y1), ., (xn, yn) are points of the polygon in a counterclockwise order. Find the area of such a polygon using using shoelace formula. It is no longer required to take absolute value. п-1 п—1 A = > xi+1Yi ) – x1Yn i=1 i=1 1 x142 + x2Y3 + + xn-1Yn + xnY1 - x2y1 – X3Y2 – ··- xn Yn-1 – x1Yn| >>> area ([(0,0), (1,0), (0,1)]) 0.5 >>> area ([(0,0), (1,0),(1,1),(0,1)]) 1.0 >> area([(0,0),(2,0), (2,2),(1,2), (0,1)]) 3.5 Write the function area(C) to find the area of a triangle with vertices at c = [(x1, y1), (x2, y2),..., (xn, yn)].
You are a computer research scientist at Tesla, and your task is to create a computer vision application for self-driving cars to detect object and avoid collision. You know that Graham's scan is a method of computing the convex hull of a finite set of points in the plane. You decide to apply this algorithm to achieve the goal of your task. a) Suppose Graham's scan executes n points, where n >= 3. Prove that, at the end of the program, the stack S consists of, from bottom to top, exactly the vertices of convex hull in counter-clockwise order.
Write a program that generates a 6-by-6 two-dimensionalmatrix filled with 0s and 1s, displays the matrix, and checks if every row andevery column have an even number of 1s.