Fractional Knapsack Problem in DSA Rust - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the value per weight ratio for each item.

DSA Rust

let value_per_weight = items[i].value as f64 [1] items[i].weight as f64;

Drag options to blanks, or click blank then click option'

A+

B*

C/

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication instead of division

Using addition or subtraction instead of division

The value per weight ratio is calculated by dividing the value by the weight.

2fill in blank

medium

Complete the code to sort items by their value per weight ratio in descending order.

DSA Rust

items.sort_by_key(|a| [1]a.value_per_weight);

Drag options to blanks, or click blank then click option'

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Not negating the key (sorts ascending)

Using binary operators (+, *, /) instead of unary '-'

Using unary '-' on value_per_weight with sort_by_key sorts in descending order by value per weight ratio, as sort_by_key sorts ascending by key.

3fill in blank

hard

Fix the error in the code to add the fractional value correctly when the knapsack cannot hold the full item weight.

DSA Rust

total_value += (items[i].value as f64) [1] (capacity as f64 [2] items[i].weight as f64);

Drag options to blanks, or click blank then click option'

A*

B+

C-

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition or subtraction instead of multiplication

Using multiplication instead of division for fraction

Multiply the item's value by the fraction of capacity left over the item's weight.

4fill in blank

hard

Fill both blanks to update the capacity after adding an item fully or partially.

DSA Rust

capacity = capacity [1] items[i].weight; total_value = total_value [2] items[i].value;

Drag options to blanks, or click blank then click option'

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Adding weight to capacity

Subtracting value from total value

Subtract the item's weight from capacity and add the item's value to total value.

5fill in blank

hard

Fill all three blanks to complete the loop that processes each item until the knapsack is full.

DSA Rust

for i in 0..items.len() {
    if capacity == 0 {
        break;
    }
    if items[i].weight <= capacity {
        total_value [1]= items[i].value;
        capacity [2]= items[i].weight;
    } else {
        total_value [3]= (items[i].value as f64) * (capacity as f64 / items[i].weight as f64);
        capacity = 0;
    }
}

Drag options to blanks, or click blank then click option'

A+

B-

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong operators for updating values

Not breaking loop when capacity is zero

Add full item value to total_value, subtract weight from capacity, and add fractional value when partial item is taken.

Practice

1. What is the main goal of the Fractional Knapsack Problem?

easy

A. Maximize total value by taking fractions of items within weight limit

B. Minimize total weight by selecting whole items only

C. Maximize number of items regardless of weight

D. Select items randomly without considering value or weight

Solution

1. Step 1: Understand problem objective

   The fractional knapsack problem aims to maximize the total value of items placed in a knapsack without exceeding its weight capacity.

2. Step 2: Recognize fractional selection

   Unlike the 0/1 knapsack, it allows taking fractions of items to fill the knapsack optimally.

3. Final Answer:

   Maximize total value by taking fractions of items within weight limit -> Option A

4. Quick Check:

   Goal = maximize value with fractions [OK]

Hint: Remember: fractional means partial items allowed [OK]

Common Mistakes:

• Thinking only whole items can be taken
• Confusing with minimizing weight
• Ignoring value-to-weight ratio

2. Which Rust code snippet correctly defines a struct to represent an item with weight and value for the fractional knapsack?

easy

A. struct Item { weight: usize, value: bool }

B. struct Item { weight: f64, value: f64 }

C. struct Item { weight: String, value: String }

D. struct Item(weight: i32, value: i32);

Solution

1. Step 1: Identify correct struct syntax

   Rust structs use curly braces with field names and types, e.g., struct Item { weight: f64, value: f64 }.

2. Step 2: Check field types for fractional knapsack

   Weights and values can be fractional, so f64 (floating-point) is appropriate.

3. Final Answer:

   struct Item { weight: f64, value: f64 } -> Option B

4. Quick Check:

   Correct struct syntax with f64 fields [OK]

Hint: Use f64 for fractional weights and values [OK]

Common Mistakes:

• Using tuple struct syntax incorrectly
• Using integer or wrong types for fractional values
• Using incompatible types like String or bool

3. What is the output of this Rust code snippet that calculates maximum value for fractional knapsack?

struct Item { weight: f64, value: f64 }

fn fractional_knapsack(items: &mut Vec<Item>, capacity: f64) -> f64 {
    items.sort_by(|a, b| (b.value / b.weight).partial_cmp(&(a.value / a.weight)).unwrap());
    let mut total_value = 0.0;
    let mut remaining = capacity;
    for item in items.iter() {
        if item.weight <= remaining {
            total_value += item.value;
            remaining -= item.weight;
        } else {
            total_value += item.value * (remaining / item.weight);
            break;
        }
    }
    total_value
}

fn main() {
    let mut items = vec![
        Item { weight: 10.0, value: 60.0 },
        Item { weight: 20.0, value: 100.0 },
        Item { weight: 30.0, value: 120.0 },
    ];
    let capacity = 50.0;
    let max_value = fractional_knapsack(&mut items, capacity);
    println!("{:.2}", max_value);
}

medium

A. 180.00

B. 220.00

C. 200.00

D. 240.00

Solution

1. Step 1: Sort items by value/weight ratio descending

   Ratios: 60/10=6, 100/20=5, 120/30=4. Sorted order: Item1, Item2, Item3.

2. Step 2: Add items until capacity 50

   Add Item1 fully (weight 10, value 60), remaining 40.
   Add Item2 fully (weight 20, value 100), remaining 20.
   Add fraction of Item3: fraction = 20/30 = 2/3, value = 120 * 2/3 = 80.
   Total value = 60 + 100 + 80 = 240.

3. Final Answer:

   240.00 -> Option D

4. Quick Check:

   Sum values with fractions = 240.00 [OK]

Hint: Sort by value/weight ratio, fill capacity greedily [OK]

Common Mistakes:

• Not sorting items by ratio
• Taking whole items only
• Incorrect fraction calculation

4. Identify the bug in this Rust function for fractional knapsack:

fn fractional_knapsack(items: &mut Vec<Item>, capacity: f64) -> f64 {
    items.sort_by(|a, b| (a.value / a.weight).partial_cmp(&(b.value / b.weight)).unwrap());
    let mut total_value = 0.0;
    let mut remaining = capacity;
    for item in items.iter() {
        if item.weight <= remaining {
            total_value += item.value;
            remaining -= item.weight;
        } else {
            total_value += item.value * (remaining / item.weight);
            break;
        }
    }
    total_value
}

medium

A. Sorting order is ascending, should be descending by value/weight

B. Using iter() instead of into_iter() causes ownership error

C. Incorrect calculation of fractional value inside else block

D. Missing return statement at the end of function

Solution

1. Step 1: Check sorting comparator

   The code sorts by (a.value / a.weight).partial_cmp(&(b.value / b.weight)), which sorts ascending by ratio.

2. Step 2: Correct sorting order for greedy approach

   Fractional knapsack requires descending order by value/weight ratio to pick highest value items first.

3. Final Answer:

   Sorting order is ascending, should be descending by value/weight -> Option A

4. Quick Check:

   Sort descending by ratio for max value [OK]

Hint: Sort descending by value/weight ratio, not ascending [OK]

Common Mistakes:

• Sorting ascending instead of descending
• Confusing iter() and into_iter() ownership
• Miscomputing fractional value

5. Given items with weights and values:
[(5, 30), (10, 40), (15, 45)] and knapsack capacity 20, what is the maximum value using fractional knapsack?

hard

A. 70

B. 80

C. 85

D. 75

Solution

1. Step 1: Calculate value/weight ratios and sort descending

   Ratios: 30/5=6, 40/10=4, 45/15=3.
   Sorted order: (5,30), (10,40), (15,45).

2. Step 2: Fill knapsack capacity 20 greedily

   Take full (5,30), remaining 15, total value 30.
   Take full (10,40), remaining 5, total value 70.
   Take fraction of (15,45): fraction = 5/15 = 1/3, value = 45 * 1/3 = 15.
   Total value = 70 + 15 = 85.

3. Step 3: Verify options

   85 is 85, matching calculation.

4. Final Answer:

   85 -> Option C

5. Quick Check:

   Greedy fill with fractions = 85 [OK]

Hint: Sort by ratio, fill capacity fully, then fractionally [OK]

Common Mistakes:

• Not sorting by ratio
• Taking items in wrong order
• Incorrect fraction calculation