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Intermediate Topic 26 of 51 Algorithms

Knapsack Problem

Choosing items under a capacity to maximize value.

How it works

Given items with weights and values and a capacity W, choose items to maximize value. The 0/1 version has DP: dp[i][w] = max(dp[i-1][w], dp[i-1][w-wt]+val) in O(nW).

Where it is used

Budget allocation, cargo loading.

Common pitfall

O(nW) is pseudo-polynomial; the problem is NP-hard in terms of input bits.

Where it fits in the course

Knapsack Problem is topic 26 of 51 in Algorithms, rated Intermediate. It follows Dynamic Programming. The next topic is Longest Common Subsequence.

Practice and explore

How to study this topic

  1. Read the explanation above and restate the definition in your own words.
  2. Open the interactive lesson and answer its mini quiz.
  3. Read the common pitfall, then write a short example that avoids it.
  4. Check your understanding in the Algorithms quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is Knapsack Problem?
Choosing items under a capacity to maximize value. It belongs to Algorithms and is an intermediate-level topic.
Where do people use Knapsack Problem?
Budget allocation, cargo loading.
What is the most common mistake with Knapsack Problem?
O(nW) is pseudo-polynomial; the problem is NP-hard in terms of input bits.
What should I learn before this topic?
Start with Dynamic Programming, the topic just before it in Algorithms.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Algorithms quiz. You can also explore DP Table (LCS) in the Visual Lab.
Is Knapsack Problem hard to learn?
It is an Intermediate topic. Be comfortable with the Beginner topics in this area first, then read the common pitfall carefully, since it is where most mistakes happen.
How long does it take to learn Knapsack Problem?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Knapsack Problem?
Dynamic Programming, Longest Common Subsequence, Greedy Algorithms are closely connected. The full list is in the related topics section of this page.
What should I study after Knapsack Problem?
Continue with Longest Common Subsequence, the next topic in Algorithms.

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