Fractional Knapsack Problem in DSA Java - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

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

DSA Java

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 instead of division.

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 Java

Arrays.sort(items, (a, b) -> Double.compare(b.[1], a.[1]));

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Aratio

Bweight

Cvalue

Dindex

Attempts:

3 left

💡 Hint

Common Mistakes

Sorting by value or weight instead of ratio.

Sorting in ascending order.

We sort items by their ratio to pick the most valuable per weight first.

3fill in blank

hard

Fix the error in the loop condition to process items until capacity is full or all items are checked.

DSA Java

while (i < n && [1] > 0) {

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

Aweight

Bcapacity

Cvalue

Dratio

Attempts:

3 left

💡 Hint

Common Mistakes

Using weight or value instead of capacity.

Using capacity < 0 which never runs.

The loop continues while there is capacity left to fill.

4fill in blank

hard

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

DSA Java

if (items[i].weight <= [1]) {
    totalValue += items[i].value;
    [2] -= items[i].weight;
}

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

Acapacity

BtotalValue

Cweight

Dvalue

Attempts:

3 left

💡 Hint

Common Mistakes

Updating totalValue instead of capacity.

Using wrong variable names.

We check if the item fits in capacity, add full value, and reduce capacity by item's weight.

5fill in blank

hard

Fill all three blanks to add fractional value when item weight exceeds capacity and set capacity to zero.

DSA Java

else {
    totalValue += items[i].ratio [1] [2];
    [3] = 0;
}

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

A*

Bcapacity

DtotalValue

Attempts:

3 left

💡 Hint

Common Mistakes

Using addition instead of multiplication for fractional value.

Not setting capacity to zero.

When item weight is more than capacity, add fraction of value and set capacity to zero.

Practice

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

easy

A. Select only whole items to maximize value

B. Minimize total weight of items selected

C. Sort items by weight only

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

Solution

1. Step 1: Understand problem objective

   The fractional knapsack problem allows taking parts of items to maximize total value without exceeding weight limit.

2. Step 2: Compare options

   Maximize total value by taking fractions of items within weight limit correctly states maximizing value by taking fractions. Others focus on minimizing weight or whole items only, which is incorrect.

3. Final Answer:

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

4. Quick Check:

   Goal = Maximize value with fractions [OK]

Hint: Remember: fractional means parts allowed, maximize value [OK]

Common Mistakes:

• Thinking only whole items can be taken
• Confusing weight minimization with value maximization
• Ignoring fractional parts possibility

2. Which Java code snippet correctly sorts items by value-to-weight ratio for the fractional knapsack?

easy

A. Arrays.sort(items, (a, b) -> Double.compare((double)b.value / b.weight, (double)a.value / a.weight));

B. Arrays.sort(items, (a, b) -> Double.compare(a.weight, b.weight));

C. Arrays.sort(items, (a, b) -> Integer.compare(a.value, b.value));

D. Arrays.sort(items, (a, b) -> a.value - b.value);

Solution

1. Step 1: Identify sorting criteria

   We must sort by value-to-weight ratio in descending order to pick best value fractions first.

2. Step 2: Check code correctness

   Arrays.sort(items, (a, b) -> Double.compare((double)b.value / b.weight, (double)a.value / a.weight)); sorts by ratio ((double)b.value/b.weight vs (double)a.value/a.weight) descending. Others sort by weight or value only, which is incorrect.

3. Final Answer:

   Arrays.sort(items, (a, b) -> Double.compare((double)b.value / b.weight, (double)a.value / a.weight)); -> Option A

4. Quick Check:

   Sort by ratio descending = Arrays.sort(items, (a, b) -> Double.compare((double)b.value / b.weight, (double)a.value / a.weight)); [OK]

Hint: Sort by value/weight descending for best fractions first [OK]

Common Mistakes:

• Sorting by weight or value alone
• Sorting in ascending order instead of descending
• Using integer division instead of double

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

class Item {
  int value, weight;
  Item(int v, int w) { value = v; weight = w; }
}

Item[] items = {new Item(60, 10), new Item(100, 20), new Item(120, 30)};
int W = 50;
double maxValue = 0;
Arrays.sort(items, (a, b) -> Double.compare((double)b.value / b.weight, (double)a.value / a.weight));
int remaining = W;
for (Item item : items) {
  if (item.weight <= remaining) {
    maxValue += item.value;
    remaining -= item.weight;
  } else {
    maxValue += item.value * ((double)remaining / item.weight);
    break;
  }
}
System.out.println((int)maxValue);

medium

A. 180

B. 220

C. 240

D. 200

Solution

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

   Ratios: 60/10=6, 100/20=5, 120/30=4. Sorted order: (60,10), (100,20), (120,30).

2. Step 2: Calculate max value with weight limit 50

   Take full (60,10): value=60, remaining=40
   Take full (100,20): value=160, remaining=20
   Take fraction of (120,30): fraction=20/30=2/3, value added=120*(2/3)=80
   Total value=60+100+80=240 but code casts to int after adding fractions, so 240.

3. Final Answer:

   240 -> Option C

4. Quick Check:

   Sum values with fractions = 240 [OK]

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

Common Mistakes:

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

4. Find the error in this Java code for fractional knapsack:

int maxValue = 0;
for (Item item : items) {
  if (item.weight <= W) {
    maxValue += item.value;
    W -= item.weight;
  } else {
    maxValue += item.value * (W / item.weight);
    break;
  }
}

medium

A. Loop condition should be item.weight <= W, not < W

B. Using integer division in fraction calculation causes wrong value

C. maxValue should be double, not int

D. No error, code is correct

Solution

1. Step 1: Analyze fraction calculation

   Expression (W / item.weight) uses integer division, truncating fraction to 0 or 1 incorrectly.

2. Step 2: Correct fraction calculation

   It should use floating division: (double)W / item.weight to get correct fraction value.

3. Final Answer:

   Using integer division in fraction calculation causes wrong value -> Option B

4. Quick Check:

   Integer division in fraction = error [OK]

Hint: Cast to double for fraction division to avoid integer truncation [OK]

Common Mistakes:

• Forgetting to cast to double in fraction
• Failing to sort items by value-to-weight ratio before iterating
• Declaring maxValue as int but adding fractions

5. Given items with values and weights: [(40, 2), (100, 20), (50, 10), (60, 12)] and knapsack capacity 30, what is the maximum value achievable using fractional knapsack?

hard

A. 180

B. 160

C. 190

D. 200

Solution

1. Step 1: Calculate value-to-weight ratios and sort

   Ratios:
   (40/2)=20, (100/20)=5, (50/10)=5, (60/12)=5
   Sorted order: (40,2), (100,20), (50,10), (60,12)

2. Step 2: Pick items to maximize value within capacity 30

   Take full (40,2): value=40, remaining=28
   Take full (100,20): value=140, remaining=8
   Next (50,10): only 8 weight left, fraction=8/10=0.8, value added=50*0.8=40
   Total value=40+100+40=180

3. Step 3: Check if next item can add value

   Last item (60,12) cannot be taken as capacity is full.

4. Final Answer:

   180 -> Option A

5. Quick Check:

   Sum values with fractions = 180 [OK]

Hint: Pick highest ratio items fully, then fractionally fill remaining [OK]

Common Mistakes:

• Ignoring highest ratio item first
• Taking items in wrong order
• Not calculating fraction correctly