Greedy Knapsack Problem - by Y Achchuthan
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The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the count of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most useful items. http://java90.blogspot.com/2012/02/knapsack-problem-in-java.html
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Knapsack Problem
The document discusses the knapsack problem, which involves selecting a subset of items that fit within a knapsack of limited capacity to maximize the total value. There are two versions - the 0-1 knapsack problem where items can only be selected entirely or not at all, and the fractional knapsack problem where items can be partially selected. Solutions include brute force, greedy algorithms, and dynamic programming. Dynamic programming builds up the optimal solution by considering all sub-problems.
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Knapsack problem
Knapsack problem ==>>
Given some items, pack the knapsack to get
the maximum total value. Each item has some
weight and some value. Total weight that we can
carry is no more than some fixed number W.
So we must consider weights of items as well as
their values.
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The document discusses the knapsack problem and provides examples to illustrate the recursive solution approach. It describes the knapsack problem as selecting items to place in a knapsack with a weight capacity to maximize the total benefit without exceeding the weight limit. It shows that the optimal solution can be found using a recursive function f(w) that returns the maximum benefit for a knapsack of weight w. The examples demonstrate computing f(w) values to find the optimal solutions for sample knapsack problems.
01 knapsack using backtracking
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The document discusses the 0/1 knapsack problem and the greedy algorithm approach. It describes the knapsack problem as selecting a subset of items with weights and values that fit within a knapsack capacity while maximizing the total value. The greedy algorithm works by selecting the highest value item at each step that fits within remaining capacity. The document provides an example problem of selecting boxes to fill a knapsack of 15kg capacity to maximize profit. It outlines the recurrence relation and time/space complexity of the greedy knapsack algorithm.
Knapsack problem
Knapsack problem ==>>
Given some items, pack the knapsack to get
the maximum total value. Each item has some
weight and some value. Total weight that we can
carry is no more than some fixed number W.
So we must consider weights of items as well as
their values.
Knapsack Algorithm www.geekssay.com
The document discusses the knapsack problem and provides examples to illustrate the recursive solution approach. It describes the knapsack problem as selecting items to place in a knapsack with a weight capacity to maximize the total benefit without exceeding the weight limit. It shows that the optimal solution can be found using a recursive function f(w) that returns the maximum benefit for a knapsack of weight w. The examples demonstrate computing f(w) values to find the optimal solutions for sample knapsack problems.
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