Knapsack Unbounded

Introduction

The Knapsack problem is a classic optimization problem in computer science. It involves selecting a subset of items with maximum value, subject to a weight constraint. The Knapsack Unbounded problem is a variation of the Knapsack problem where items can be selected multiple times.

Skills Graph

%%%%{init: {'theme':'neutral'}}%%%% flowchart RL algorithm(("`Algorithm`")) -.-> algorithm/BasicAlgorithmsGroup(["`Basic Algorithms`"]) python(("`Python`")) -.-> python/BasicConceptsGroup(["`Basic Concepts`"]) python(("`Python`")) -.-> python/ControlFlowGroup(["`Control Flow`"]) python(("`Python`")) -.-> python/DataStructuresGroup(["`Data Structures`"]) python(("`Python`")) -.-> python/FunctionsGroup(["`Functions`"]) python(("`Python`")) -.-> python/ObjectOrientedProgrammingGroup(["`Object-Oriented Programming`"]) python(("`Python`")) -.-> python/ErrorandExceptionHandlingGroup(["`Error and Exception Handling`"]) algorithm/BasicAlgorithmsGroup -.-> algorithm/recursion_dynamic("`Recursion Dynamic`") python/BasicConceptsGroup -.-> python/variables_data_types("`Variables and Data Types`") python/BasicConceptsGroup -.-> python/strings("`Strings`") python/BasicConceptsGroup -.-> python/type_conversion("`Type Conversion`") python/ControlFlowGroup -.-> python/conditional_statements("`Conditional Statements`") python/ControlFlowGroup -.-> python/for_loops("`For Loops`") python/DataStructuresGroup -.-> python/lists("`Lists`") python/DataStructuresGroup -.-> python/tuples("`Tuples`") python/FunctionsGroup -.-> python/function_definition("`Function Definition`") python/ObjectOrientedProgrammingGroup -.-> python/classes_objects("`Classes and Objects`") python/ObjectOrientedProgrammingGroup -.-> python/constructor("`Constructor`") python/ObjectOrientedProgrammingGroup -.-> python/polymorphism("`Polymorphism`") python/ObjectOrientedProgrammingGroup -.-> python/encapsulation("`Encapsulation`") python/ErrorandExceptionHandlingGroup -.-> python/raising_exceptions("`Raising Exceptions`") python/FunctionsGroup -.-> python/build_in_functions("`Build-in Functions`") subgraph Lab Skills algorithm/recursion_dynamic -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/variables_data_types -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/strings -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/type_conversion -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/conditional_statements -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/for_loops -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/lists -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/tuples -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/function_definition -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/classes_objects -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/constructor -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/polymorphism -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/encapsulation -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/raising_exceptions -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} python/build_in_functions -.-> lab-268861{{"`Unbounded Knapsack Optimization Problem`"}} end

Problem

Given a knapsack with a total weight capacity and a list of items with weight w(i) and value v(i), determine the maximum total value you can carry. The items can be selected multiple times.

Requirements

To solve the Knapsack Unbounded problem, the following requirements must be met:

The items can be replaced once they are placed in the knapsack.
An item cannot be split.
The input items cannot have a weight or value of 0.
Only the total value needs to be returned, not the items that make up the max total value.
The inputs may not be valid, so validation is required.
The inputs are sorted by val/weight.
Memory constraints are not an issue.

Example Usage

The Knapsack Unbounded problem can be used in various scenarios, such as resource allocation and financial portfolio optimization. Here are some examples of how it can be used:

If the total weight or items are None, an exception should be raised.
If the total weight or items are 0, the result should be 0.
For a general case, suppose the total weight is 8 and the items are:

v w

0 0

1 1

3 2

7 4

The maximum value that can be carried is 14.

v	w
0	0
1	1
3	2
7	4

Summary

The Knapsack Unbounded problem is a variation of the Knapsack problem where items can be selected multiple times. To solve this problem, the items can be replaced once they are placed in the knapsack, and an item cannot be split. The input items cannot have a weight or value of 0, and only the total value needs to be returned. The inputs may not be valid, so validation is required, and the inputs are sorted by val/weight. Memory constraints are not an issue. The Knapsack Unbounded problem can be used in various scenarios, such as resource allocation and financial portfolio optimization.

Unbounded Knapsack Optimization Problem

Introduction

Skills Graph