Unbounded Knapsack Problem in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Unbounded Knapsack Problem?

It is a problem where you can take unlimited quantities of each item to maximize the total value without exceeding the knapsack's capacity.

beginner

How does the Unbounded Knapsack Problem differ from the 0/1 Knapsack Problem?

In Unbounded Knapsack, you can use each item multiple times, while in 0/1 Knapsack, each item can be used at most once.

intermediate

What is the main idea behind the dynamic programming solution for Unbounded Knapsack?

Build a table where each entry represents the maximum value for a given capacity, considering all items and allowing repeated use of items.

intermediate

What is the time complexity of the Unbounded Knapsack dynamic programming solution?

It is O(n * W), where n is the number of items and W is the knapsack capacity.

intermediate

In the Unbounded Knapsack problem, why can we consider the same item multiple times in the DP table?

Because the problem allows unlimited copies of each item, so after including an item, we can still include it again if capacity allows.

In the Unbounded Knapsack problem, what does 'unbounded' mean?

A You cannot use any item

B You can use unlimited copies of each item

C You can use each item only once

D You must use all items

Unbounded means unlimited copies of each item can be used.

What is the main difference in the DP approach between 0/1 Knapsack and Unbounded Knapsack?

A Unbounded allows reusing items in the same capacity calculation

B 0/1 Knapsack allows unlimited items

C Unbounded does not use DP

D 0/1 Knapsack uses recursion only

Unbounded Knapsack allows reusing items multiple times in the DP table.

What does the DP array represent in the Unbounded Knapsack solution?

A Total number of items

B Number of items used

C Minimum weight possible

D Maximum value achievable for each capacity

The DP array stores the maximum value achievable for each capacity.

If the knapsack capacity is 5 and item weights are 1 and 3 with values 10 and 40, what is the maximum value in Unbounded Knapsack?

A 60

B 40

C 30

D 10

One item of weight 3 (value 40) and two items of weight 1 (value 10 each, total 20) give a total value of 60.

What is the base case value for DP array at capacity 0 in Unbounded Knapsack?

A 1

B Infinity

C 0

D -1

At capacity 0, maximum value is 0 because no items can be taken.

Explain how dynamic programming solves the Unbounded Knapsack problem step-by-step.

Think about building solutions from smaller capacities to larger.

Describe the difference between 0/1 Knapsack and Unbounded Knapsack and how it affects the solution approach.

Focus on how item repetition changes the DP logic.