Fractional Knapsack Problem in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

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

DSA Javascript

const ratio = items.map(item => item.value [1] item.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 the 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 Javascript

items.sort((a, b) => b.[1] - a.[1]);

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

Aweight

Bratio

Cvalue

Dindex

Attempts:

3 left

💡 Hint

Common Mistakes

Sorting by value or weight alone instead of ratio.

Sorting in ascending order instead of descending.

We sort by the ratio property to get items with highest value per weight first.

3fill in blank

hard

Fix the error in the loop condition to correctly process all items.

DSA Javascript

for (let 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 never runs the loop.

The loop should run while i is less than items.length to avoid going out of bounds.

4fill in blank

hard

Fill both blanks to correctly calculate the fraction of the item to take and update capacity.

DSA Javascript

const fraction = Math.min(1, capacity [1] item.weight);
capacity [2]= fraction * item.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 for fraction.

Adding to capacity instead of subtracting.

Fraction is capacity divided by item weight, and capacity is reduced by fraction times item weight.

5fill in blank

hard

Fill all three blanks to update total value and print the final result.

DSA Javascript

totalValue [1]= fraction * item.[2];
console.log('Total value: ' + totalValue.toFixed([3]));

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

A+=

Bvalue

C2

D-=

Attempts:

3 left

💡 Hint

Common Mistakes

Using -= instead of += causing wrong total.

Using weight instead of value for calculation.

Not formatting output or using wrong decimal places.

Add fraction times item value to totalValue and print with 2 decimal places.

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. Maximize total weight without considering value

C. Select only whole items to maximize value

D. Minimize the number of items selected

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

   Maximize total value by taking fractions of items within weight limit correctly states maximizing value by taking fractions. Others ignore fractions or value maximization.

3. Final Answer:

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

4. Quick Check:

   Fractional knapsack = maximize value with fractions [OK]

Hint: Remember: fractions allowed to maximize value [OK]

Common Mistakes:

• Thinking only whole items can be taken
• Ignoring value and focusing on weight
• Confusing with 0/1 knapsack problem

2. Which of the following JavaScript code snippets correctly sorts items by value-to-weight ratio for the fractional knapsack?

easy

A. items.sort((a, b) => (b.value / b.weight) - (a.value / a.weight));

B. items.sort((a, b) => (a.weight / a.value) - (b.weight / b.value));

C. items.sort((a, b) => a.value - b.value);

D. items.sort((a, b) => a.weight - b.weight);

Solution

1. Step 1: Identify sorting criteria

   We must sort items by descending value-to-weight ratio (value/weight) to pick best items first.

2. Step 2: Check each code snippet

   items.sort((a, b) => (b.value / b.weight) - (a.value / a.weight)); sorts descending by (value/weight). Others sort incorrectly by inverse or by value or weight alone.

3. Final Answer:

   items.sort((a, b) => (b.value / b.weight) - (a.value / a.weight)); -> Option A

4. Quick Check:

   Sort by descending value/weight ratio [OK]

Hint: Sort items by (value/weight) descending [OK]

Common Mistakes:

• Sorting by weight or value alone
• Sorting ascending instead of descending
• Using inverse ratio (weight/value)

3. What is the output of the following JavaScript code?

const items = [
  {value: 60, weight: 10},
  {value: 100, weight: 20},
  {value: 120, weight: 30}
];
const capacity = 50;

function fractionalKnapsack(items, capacity) {
  items.sort((a, b) => (b.value / b.weight) - (a.value / a.weight));
  let totalValue = 0;
  let remaining = capacity;
  for (const item of items) {
    if (item.weight <= remaining) {
      totalValue += item.value;
      remaining -= item.weight;
    } else {
      totalValue += item.value * (remaining / item.weight);
      break;
    }
  }
  return totalValue;
}

console.log(fractionalKnapsack(items, capacity));

medium

A. 220

B. 240

C. 180

D. 200

Solution

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

   Ratios: 60/10=6, 100/20=5, 120/30=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 fraction of item3: (20/30)*120 = 80.
   Total value = 60 + 100 + 80 = 240.

3. Final Answer:

   240 -> Option B

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 without fractions
• Miscomputing fraction value

4. Find the error in this fractional knapsack code snippet:

function fractionalKnapsack(items, capacity) {
  items.sort((a, b) => (a.value / a.weight) - (b.value / b.weight));
  let totalValue = 0;
  let remaining = capacity;
  for (const item of items) {
    if (item.weight <= remaining) {
      totalValue += item.value;
      remaining -= item.weight;
    } else {
      totalValue += item.value * (remaining / item.weight);
      break;
    }
  }
  return totalValue;
}

medium

A. Incorrect fraction calculation formula

B. Using 'let' instead of 'const' for totalValue

C. Missing return statement

D. Sorting is ascending; should be descending by value/weight ratio

Solution

1. Step 1: Analyze sorting order

   The code sorts items ascending by value/weight ratio, but we need descending to pick best items first.

2. Step 2: Check other parts

   Return statement exists, fraction formula is correct, 'let' is appropriate for totalValue.

3. Final Answer:

   Sorting is ascending; should be descending by value/weight ratio -> Option D

4. Quick Check:

   Sort descending by ratio to maximize value [OK]

Hint: Sort descending by value/weight ratio [OK]

Common Mistakes:

• Sorting ascending instead of descending
• Ignoring fraction calculation correctness
• Confusing variable declarations

5. Given items with values and weights:

items = [
  {value: 40, weight: 2},
  {value: 100, weight: 20},
  {value: 50, weight: 10},
  {value: 60, weight: 12}
];
capacity = 30;

What is the maximum total value achievable using the fractional knapsack approach?

hard

A. 190

B. 160

C. 180

D. 200

Solution

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

   Ratios:
   Item1: 40/2=20
   Item2: 100/20=5
   Item3: 50/10=5
   Item4: 60/12=5
   Sorted order: Item1, then Items 2,3,4 (equal ratio 5).

2. Step 2: Pick items until capacity 30

   Take Item1 fully: weight 2, value 40, remaining 28.
   Next, take Item2 fully: weight 20, value 100, remaining 8.
   Then take fraction of Item3: fraction = 8/10 = 0.8, value = 50 * 0.8 = 40.
   Total value = 40 + 100 + 40 = 180.

3. Step 3: Check if taking Item4 fraction is better

   Item4 has same ratio as Item3, but we already used remaining capacity on Item3 fraction.
   So total value remains 180.

4. Final Answer:

   180 -> Option C

5. Quick Check:

   Sum values with fractions = 180 [OK]

Hint: Pick highest ratio items first, then fractions [OK]

Common Mistakes:

• Ignoring highest ratio item first
• Not taking fractions correctly
• Adding values without considering capacity