Fractional Knapsack Quiz

What is the main difference between 0/1 knapsack and fractional knapsack?

• Fractional allows only full items
• 0/1 allows fractional parts
• Fractional allows partial items
• Both allow only one item

What is the greedy choice based on in the fractional knapsack problem?

• Highest value
• Lowest weight
• Lowest cost
• Highest value-to-weight ratio

If an item has value $200 and weight 20kg, what is its value-to-weight ratio?

• 5
• 10
• 15
• 20

Can a greedy algorithm guarantee optimal solution for fractional knapsack?

• Yes
• No
• Only if sorted
• Depends on the values

Find Optimal Solution, Capacity =50 kg. Items with weights 10kg, 20kg, 30kg and values $6 0, $100, $120 respectively.

• $280
• $240
• $260
• $300

The greedy method works for fractional knapsack because:

• It checks all combinations
• It ignores weight
• It uses value/weight ratio and allows partial items
• It uses dynamic programming

What happens if two items have the same value/weight ratio?

• Skip one
• Take the heavier one
• Any order works
• None are taken

Why do we stop when the knapsack is full?

• To avoid adding too much value
• It's required in the algorithm
• Capacity limit is reached
• To take only one item

What property guarantees the greedy algorithm works for fractional knapsack?

• Dynamic Optimality
• Greedy Choice Property
• Local Minimum Principle
• Heuristic Analysis