Fractional Knapsack Problem in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

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

DSA C#

double ratio = items[i].value [1] items[i].weight;

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 which does not give a ratio.

The value-to-weight ratio is calculated by dividing the value by the weight.

2fill in blank

medium

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

DSA C#

Array.Sort(items, (a, b) => b.[1].CompareTo(a.[1]));

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

Aratio

Bvalue

Cweight

Dindex

Attempts:

3 left

💡 Hint

Common Mistakes

Sorting by value or weight alone.

Sorting in ascending order instead of descending.

We sort items by their ratio to pick the best value per weight first.

3fill in blank

hard

Fix the error in the loop condition to stop when knapsack is full or all items are processed.

DSA C#

for (int i = 0; i [1] items.Length && capacity > 0; i++)

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

A<

B>

C>=

D<=

Attempts:

3 left

💡 Hint

Common Mistakes

Using greater than or equal which causes no iterations or errors.

Using greater than which skips the loop.

The loop should continue while i is less than the number of items.

4fill in blank

hard

Fill both blanks to add the full item value or fractional value to totalValue and reduce capacity.

DSA C#

if (items[i].weight <= capacity) {
    totalValue += items[i].value;
    capacity [1]= items[i].weight;
} else {
    double fraction = (double)capacity [2] items[i].weight;
    totalValue += items[i].value * fraction;
    capacity = 0;
}

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

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Adding weight to capacity instead of subtracting.

Multiplying instead of dividing to get fraction.

We subtract the item's weight from capacity and calculate fraction by dividing capacity by item's weight.

5fill in blank

hard

Fill all three blanks to create a dictionary of item indices and their fractional amounts taken.

DSA C#

Dictionary<int, double> fractions = new Dictionary<int, double>();
for (int i = 0; i < items.Length; i++) {
    double fraction = (capacity > 0) ? Math.Min(1, (double)capacity [1] items[i].weight) : 0;
    fractions[items[i].[2]] = fraction;
    capacity [3]= (int)(items[i].weight * fraction);
}

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

A/

Bindex

C-

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong property for dictionary key.

Multiplying instead of dividing for fraction.

Adding instead of subtracting capacity.

Fraction is capacity divided by weight, key is item index, capacity reduces by weight times fraction.

Practice

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

easy

A. Maximize number of items regardless of weight

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

C. Minimize total weight by selecting whole items only

D. Select items randomly without considering value or weight

Solution

1. Step 1: Understand the problem goal

   The fractional knapsack problem allows taking parts of items to maximize total value within a weight limit.

2. Step 2: Compare options

   Only Maximize total value by taking fractions of items within weight limit correctly states maximizing total value by taking fractions within weight limit.

3. Final Answer:

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

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 C# syntax correctly declares a class named Item with public fields weight and value?

easy

A. class Item { public int weight; public int value; }

B. class Item { int weight; int value; }

C. public Item { int weight; int value; }

D. class Item { public weight; public value; }

Solution

1. Step 1: Check class declaration syntax

   In C#, class fields must have type and access modifier for public fields.

2. Step 2: Validate each option

   class Item { public int weight; public int value; } correctly declares public int fields. class Item { int weight; int value; } lacks access modifier. public Item { int weight; int value; } misses class keyword. class Item { public weight; public value; } misses types.

3. Final Answer:

   class Item { public int weight; public int value; } -> Option A

4. Quick Check:

   Correct class syntax = class Item { public int weight; public int value; } [OK]

Hint: Public fields need type and access modifier [OK]

Common Mistakes:

• Omitting access modifiers
• Missing data types
• Incorrect class keyword usage

3. What is the output of this C# code snippet for fractional knapsack?

var items = new[] {
  new Item { weight = 10, value = 60 },
  new Item { weight = 20, value = 100 },
  new Item { weight = 30, value = 120 }
};
int capacity = 50;
double maxValue = 0;
Array.Sort(items, (a, b) => (b.value / (double)b.weight).CompareTo(a.value / (double)a.weight));
int remaining = capacity;
foreach (var item in items) {
  if (item.weight <= remaining) {
    maxValue += item.value;
    remaining -= item.weight;
  } else {
    maxValue += item.value * (remaining / (double)item.weight);
    break;
  }
}
Console.WriteLine(Math.Round(maxValue, 2));

medium

A. 200.00

B. 220.00

C. 180.00

D. 240.00

Solution

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

   Ratios: Item1=6, Item2=5, Item3=4. Sorted order: Item1, Item2, Item3.

2. Step 2: Add items until capacity 50

   Take Item1 fully (weight 10, value 60), remaining=40. Take Item2 fully (weight 20, value 100), remaining=20. Take 20/30 fraction of Item3: value = 120 * (20/30) = 80.

3. Step 3: Calculate total value

   Total = 60 + 100 + 80 = 240. Rounded to 240.00.

4. Final Answer:

   240.00 -> Option D

5. Quick Check:

   Sum values with fractions = 240.00 [OK]

Hint: Sort by value/weight, take full then fraction [OK]

Common Mistakes:

• Not sorting by value/weight ratio
• Taking items without fraction
• Incorrect fraction calculation

4. Identify the bug in this fractional knapsack code snippet:

int capacity = 50;
var items = new List<Item> {
  new Item { weight = 10, value = 60 },
  new Item { weight = 20, value = 100 },
  new Item { weight = 30, value = 120 }
};
items.Sort((a, b) => (a.value / a.weight).CompareTo(b.value / b.weight));
double maxValue = 0;
int remaining = capacity;
foreach (var item in items) {
  if (item.weight <= remaining) {
    maxValue += item.value;
    remaining -= item.weight;
  } else {
    maxValue += item.value * (remaining / item.weight);
    break;
  }
}
Console.WriteLine(maxValue);

medium

A. Sorting order is ascending instead of descending

B. Missing check for zero weight items

C. Integer division causes incorrect ratio calculation

D. Using List instead of array causes error

Solution

1. Step 1: Analyze sorting comparator

   The comparator uses integer division (a.value / a.weight) which truncates decimals, causing wrong ratios.

2. Step 2: Impact on sorting and calculation

   Integer division leads to incorrect sorting order and wrong maxValue calculation.

3. Final Answer:

   Integer division causes incorrect ratio calculation -> Option C

4. Quick Check:

   Use double division for correct ratios [OK]

Hint: Use double division for ratios, not integer division [OK]

Common Mistakes:

• Sorting ascending instead of descending
• Ignoring integer division truncation
• Assuming List causes error

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

hard

A. 85

B. 75

C. 80

D. 70

Solution

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

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

2. Step 2: Fill knapsack capacity 20

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

3. Step 3: Calculate total value

   Total value = 30 + 40 + 15 = 85.

4. Final Answer:

   85 -> Option A

5. Quick Check:

   Sum with fractions = 85 [OK]

Hint: Sort by ratio, take full items first, then fraction [OK]

Common Mistakes:

• Not sorting by value/weight ratio
• Taking items without fraction
• Incorrect fraction calculation