knapsack-problem

I need some clarification from wikipedia: Knapsack , on the part This solution will therefore run in O(nW) time and O(nW) space. Additionally, if we use only a 1-dimensional array m[W] to store the current optimal values and pass over this array i+1 times, rewriting from m[W] to m[1] every time, we get the same result for only O(W) space. I am having trouble understanding how to turn a 2D matrix into a 1D matrix to save space. In addition, to what does rewriting from m[W] to m[1] every time mean (or how does it work). Please provide some example. Say if I have the set {V,W} --> {(5,4),(6,5),(3

I am trying to write an application that generates drawing for compartmentalized Panel. I have N cubicles (2D rectangles) (N <= 40). For each cubicle there is a minimum height (minHeight[i]) and minimum width (minWidth[i]) associated. The panel itself also has a MAXIMUM_HEIGHT constraint. These N cubicles have to be arranged in a column-wise grid such that the above constraints are met for each cubicle. Also, the width of each column is decided by the maximum of minWidths of each cubicle in that column. Also, the height of each column should be the same. This decides the height of the panel We

How would you use dynamic programming to find the list of positive integers in an array whose sum is closest to but not equal to some positive integer K? I'm a little stuck thinking about this. The usual phrasing for this is that you're looking for the value closest to, but not exceeding K. If you mean "less than K", it just means that your value of K is one greater than the usual. If you truly mean just "not equal to K", then you'd basically run through the algorithm twice, once finding the largest sum less than K, then again finding the smallest sum greater than K, then picking the one of

I am trying to solve this problem and I wanted to know if there are known existing algorithms / solutions to solve this. Problem: I have n bags and n items (which are either equal or different weights) to fill into these bag. Each of these bags have a certain weight limit and the n items needs to be put into these bags in such a way that I can use the maximum space in each of these bags. The bags are of equal size. Will also like to know how to solve with bags of unequal size too. Most of the solutions I read was trying to solve a 0/1 knapsack with a weight and value. Should I consider the

I am writing a multi-threaded application in Java in order to improve performance over the sequential version. It is a parallel version of the dynamic programming solution to the 0/1 knapsack problem. I have an Intel Core 2 Duo with both Ubuntu and Windows 7 Professional on different partitions. I am running in Ubuntu. My problem is that the parallel version actually takes longer than the sequential version. I am thinking this may be because the threads are all being mapped to the same kernel thread or that they are being allocated to the same core. Is there a way I could ensure that each Java

If there is more than one constraint (for example, both a volume limit and a weight limit, where the volume and weight of each item are not related), we get the multiply-constrained knapsack problem, multi-dimensional knapsack problem, or m-dimensional knapsack problem. How do I code this in the most optimized fashion? Well, one can develop a brute force recursive solution. May be branch and bound.. but essentially its exponential most of the time until you do some sort of memoization or use dynamic programming which again takes a huge amount of memory if not done well. The problem I am facing