You are given a set W of n widgets and a set G of n gadgets. Each widget w has a weight W(v) and each gadget g has a weight W(g). You would like to match each widget w in W to a unique gadget g in G so as to minimize the sum of the absolute values of the weight differences of the matched pairs. That is, you would like to find a perfect matching M between W and G that minimizes |W(w) – W (g)|. (w,g)ƐM Design an efficient greedy algorithm to solve the given problem. Prove that your algorithm is correct. Analyze the worst-case running time of your algorithm

You are given a set W of n widgets and a set G of n gadgets. Each widget w has a weight W(v) and each gadget g has a weight W(g). You would like to match each widget w in W to a unique gadget g in G so as to minimize the sum of the absolute values of the weight differences of the matched pairs. That is, you would like to find a perfect matching M between W and G that minimizes |W(w) – W (g)|. (w,g)ƐM Design an efficient greedy algorithm to solve the given problem. Prove that your algorithm is correct. Analyze the worst-case running time of your algorithm

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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Create and explain a generic m-round winner tournament for players P called Round-Winner-Tournament(P,m), where participants are matched at random in rounds 0, 1,..., m 1 and the winners advance to the next round. The winner is chosen at random from the remaining participants after round m 1. It's interesting to note that this tournament structure contains the following special cases: the random selection tournament (m = 0), the random pairing tournament (m = 1), and the single elimination seeding tournament (m = lg |P|).
A salesman would like to visit a set of n cities. The cities are connected pairwise by a direct trains. The cost of a train ticket varies depending on the cities it connects. This salesman would like to fly into one city, then use trains to visit each city exactly one, and then fly out of the last city on his trip. The cost of his trip is the total cost of all the train tickets (the plane tickets are not included). The salesman may chose any city to fly into and any city to fly out of. Let the problem of determining if there is a trip that costs at most k dollars be called T rainSalesman. Show that this problem is NP-complete.
There are m towns in a straight line, with a road joining each pair of consecutive towns. Legends say that an ordinary person in one of these towns will become a hero by completing a sequence of n quests. The first quest will be completed in their home town, but after each quest they may complete their next quest either in the same town or after moving to a neighbouring town.For example, if n = 5 and m = 4, a resident of town 2 may become a hero as follows:• begin in town 2 for quest 1,• then move to town 3 for quest 2,• stay in town 3 for quest 3,• return to town 2 for quest 4, and• move to town 1 for quest 5.Design an algorithm which runs in O(nm) time and finds the total number of waysto complete n quests.
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:
Implement Velocity Verlet • Bouncing test: Simulate two particles starting from some distance approaching each other with some speed. Plot x(t), v(t), V(t), K(t) and H(t). Are they bouncing? Is H conserved? • Find the longest ∆t that conserves H to high precision in the bouncing test . I want simulation in python
You are given a N*N maze with a rat placed at maze[0][0]. Find whether any path exist that rat can follow to reach its destination i.e. maze[N-1][N-1]. Rat can move in any direction ( left, right, up and down).Value of every cell in the maze can either be 0 or 1. Cells with value 0 are blocked means rat cannot enter into those cells and those with value 1 are open.Input FormatLine 1: Integer NNext N Lines: Each line will contain ith row elements (separated by space)Output Format :The output line contains true if any path exists for the rat to reach its destination otherwise print false.Sample Input 1 :31 0 11 0 11 1 1Sample Output 1 :trueSample Input 2 :31 0 11 0 10 1 1Sample Output 2 : false Solution: //// public class Solution { public static boolean ratInAMaze(int maze[][]){ int n = maze.length; int path[][] = new int[n][n]; return solveMaze(maze, 0, 0, path); } public static boolean solveMaze(int[][] maze, int i, int j, int[][] path) {//…
Let's say you're going to invite some people to a party. You're considering n friends, but you know that they will have a good time only if each of them knows at least k others at the party. (Assume that if A knows B, then B automatically knows A.) Solve your problem by designing an algorithm for finding the largest possible subset of your friends where everyone knows at least k of the others, if such a subset exists. Please comment on code and show all work so I can better understand the problem and please use python thank you, To help you get started l've made a graph of "my friends": G={'Rachel':['Ross Monica'], 'Ross':['Rachel', 'Monica'], 'Monica':['Rachel', 'Ross'], 'Jon Snow':['Daenerys' "Sansa' "Arya'), 'Daenerys':['Jon Snow "Sansa "Arya' Khal Drogo'), 'Sansa':['Jon Snow DaenerysArya'), 'Arya':['Jon Snow "Daenerys' Sansa'), 'Khal Drogo':['Daenerys'], 'Cersei':['Jaime'], 'Jaime':['Cersei'], 'Bart':['Milhouse'], 'Milhouse':['Bart','Lisa'], 'Lisa':['Milhouse'],…
Given a deck of 52 playing cards, we place all cards in random order face up next to each other. Then we put a chip on each card that has at least one neighbour with the same face value (e.g., on that has another queen next to it), we put a chip. Finally, we collect all chips that were each queen placed on the cards. For example, for the sequence of cards A♡, 54, A4, 10O, 10♡, 104, 94, 30, 3♡, Q4, 34 we receive 5 chips: One chip gets placed on each of the cards 100, 10♡, 104, 30, 3♡. (a) Let p5 be the probability that we receive a chip for the 5th card (i.e., the face value of the 5th card matches the face value of one of its two neighbours). Determine p5 (rounded to 2 decimal places). (b) Determine the expected number of chips we receive in total (rounded to 2 decimal places). (c) For the purpose of this question, you can assume that the expectation of part (b) is 6 or smaller. Assume that each chip is worth v dollars. Further, assume that as a result of this game we receive at least…
Consider a billboard that consists of n vertical panels of width 1 and varying integer heights, hanged down and held by a horizontal roller from the top. The panel i has a height h For the objective of placing two banners, it is allowed to move each panel up by any integer length using the roller. Once the necessary moves are completed, you may place two banners completely inside of the panels. Based on the above description, what is the maximum total area that you can provide for the two posters? Output Print a single integer- the maximum total area the two posters can cover together. Example 1: 6 Input: Output: 18 Input The first line of input contains one integer n (1
A grid must have a mechanism for numbering the tiles in order to support random-access search.A square grid, for example, contains rows and columns that provide a natural numbering for the tiles. Create designs for triangular and hexagonal grids. Define a rule for finding the neighbourhood (i.e. nearby tiles) of a particular tile in the grid using the numbering scheme. For example, if we have a four-connected square grid with indices I for rows and j for columns, we may define the neighbourhood of tile I j as neighbourhood(i, j) = I 1, j,i, j 1.
There is a legend about a magical park with N × N trees. The trees are positioned in a square grid with Nrows (numbered from 1 to N from north to south) and N columns (numbered from 1 to N from west to east).The height (in metres) of each tree is an integer between 1 and N × N, inclusive. Magically, the height ofall trees is unique.Bunga is standing on the northmost point of the park and wants to count the number of visible trees for eachcolumn. Similarly, Lestari is standing on the westmost point of the park and wants to count the number ofvisible trees for each row. A tree X is visible if all other trees in front of the tree X are shorter than the treeX.For example, let N = 3 and the height (in metres) of the trees are as follows.6 1 87 5 32 9 4• On the first column, Bunga can see two trees, as the tree on the third row is obstructed by the othertrees.• On the second column, Bunga can see all three trees.• On the third column, Bunga can see only the tree on the first row, as the…
Given a set of n types of rectangular 3-D boxes, where the ith box has height hi, width wi and depth di (all real numbers). Create a stack of boxes which is as tall as possible, but you can only stack a box on top of another box if the dimensions of the 2-D base of the lower box are each strictly larger than those of the 2-D base of the higher box. It is possible to rotate a box so that any side functions as its base. It is also allowable to use multiple instances of the same type of box. Precisely define the subproblem.Provide the recurrence equation.Describe the algorithm in pseudocode to compute the optimal value.Describe the algorithm in pseudocode to print out an optimal solution.