knapsack-problem

I know that Knapsack is NP-complete while it can be solved by DP. They say that the DP solution is pseudo-polynomial , since it is exponential in the "length of input" (i.e. the numbers of bits required to encode the input). Unfortunately I did not get it. Can anybody explain that pseudo-polynomial thing to me slowly ? marcog The running time is O(NW) for an unbounded knapsack problem with N items and knapsack of size W. W is not polynomial in the length of the input though, which is what makes it pseudo -polynomial. Consider W = 1,000,000,000,000. It only takes 40 bits to represent this

I am trying to solve an optimization problem, that it's very similar to the knapsack problem but it can not be solved using the dynamic programming. The problem I want to solve is very similar to this problem: Alex Fleischer indeed you may solve this with CPLEX. Let me show you that in OPL. The model (.mod) {string} categories=...; {string} groups[categories]=...; {string} allGroups=union (c in categories) groups[c]; {string} products[allGroups]=...; {string} allProducts=union (g in allGroups) products[g]; float prices[allProducts]=...; int Uc[categories]=...; float Ug[allGroups]=...; float

There is a list of numbers. The list is to be divided into 2 equal sized lists, with a minimal difference in sum. The sums have to be printed. #Example: >>>que = [2,3,10,5,8,9,7,3,5,2] >>>make_teams(que) 27 27 Is there an error in the following code algorithm for some case? How do I optimize and/or pythonize this? def make_teams(que): que.sort() if len(que)%2: que.insert(0,0) t1,t2 = [],[] while que: val = (que.pop(), que.pop()) if sum(t1)>sum(t2): t2.append(val[0]) t1.append(val[1]) else: t1.append(val[0]) t2.append(val[1]) print min(sum(t1),sum(t2)), max(sum(t1),sum(t2)), "\n" Question is

Given the usual n sets of items (each unlimited, say), with weights and values: w1, v1 w2, v2 ... wn, vn and a target weight W , I need to choose items such that the total weight is at least W and the total value is minimized . This looks to me like a variation (or in some sense converse) of the integer/unbounded knapsack problem. Any help in formulating the DP algorithm would be much appreciated! let TOT = w1 + w2 + ... + wn . In this answer I will describe a second bag. I'll denote the original as 'bag' and to the additional as 'knapsack' Fill the bag with all elements, and start excluding