Given the following input instance for the 0/1 Knapsack problem. Show how the algorithm given in the class works on this input instance. Complete the whole (M+1)x(n+1) table, and give the answer for the optimal solution, where M is the capacity of the knapsack and n is the number of objects. Object 1 Object 2 Object 3 Object 5 |Object 6 Profit pi 3 3 5 1 4 Weight w; | 2 4 5 3 М-10

Given the following input instance for the 0/1 Knapsack problem. Show how the algorithm given in the class works on this input instance. Complete the whole (M+1)x(n+1) table, and give the answer for the optimal solution, where M is the capacity of the knapsack and n is the number of objects. Object 1 Object 2 Object 3 Object 5 |Object 6 Profit pi 3 3 5 1 4 Weight w; | 2 4 5 3 М-10

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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An agent is trying to eat all the food in a maze that contains obstacles, but he now has the help of his friends! An agent cannot occupy a squarethat has an obstacle. There are initially k pieces of food (represented by dots), at positions (f1,...,fk). Thereare also n agents at positions (p1,...,pn). Initially, all agents start at random locations in the maze. Consider a search problem in which all agents move simultaneously;that is, in each step each agent moves into some adjacent position (N, S, E, or W, or STOP). Note that any number of agents may occupy the same position. Figure 1: A maze with 3 agents Give a search formulation to the problem of looking for both gold and diamondin a maze (wirte step with detail)? Knowing that you have M squares in the maze that do not have an What is the maximum size of the state space.
Consider a maze represented by a matrix of m rows and n columns with obstacles (see the figure below). A cell with a value = -1 is an obstacle that cannot be overcome. The goal is to start from cell [0, 0] and reach the last cell [m-1, n-1]. This may be possible by taking several paths. Count the number of these paths. The movement is allowed from cells (i+ 1, j) and (i, j+ 1) only. -1 -1 Provide two solutions, one iterative and one recursive to the above problem.
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) {//…
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You are given a set W of n widgets and a set Gof 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 E Σ |W(w) – W (g)|. - (w,g)EM 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
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