Dynamic Programming: Knapsack Problems (01 Knapsack, Unbounded Knapsack, Two - Dimensional Cost Knapsack)
1. Knapsack Problem Overview
The knapsack problem is a combinatorial optimization problem in the NP - complete class. It can be described as: Given a set of items, each with a weight and a value, under a limited total weight, how to select items to maximize the total value.
Based on the number of each item, it is classified as follows:
01 Knap ...
Posted on Fri, 16 Oct 2026 16:02:33 +0000 by lilleman
Dynamic Programming Approaches to Knapsack Problems for Coding Competitions
01 Knapsack Problem
Problem Statement
Given item_count items and a knapsack with capacity capacity, each item has a weight w and value val. Calculate the maximum total value achievable without exceeding the knapsack capacity.
Input Example:
5 20
1 6
2 5
3 8
5 15
3 3
Output Example:
37
Solution Idea
The 01 knapsack problem restricts each item ...
Posted on Tue, 21 Jul 2026 17:11:09 +0000 by chrisdarby