Fractional Knapsack Problem in DSA Javascript - Build from Scratch

Fractional Knapsack Problem

📖 Scenario: You are helping a delivery company pack valuable items into a truck. The truck can carry a limited weight. Each item has a weight and a value. You want to maximize the total value of items in the truck. You can take fractions of items if needed.

🎯 Goal: Build a program that calculates the maximum value that can fit into the truck using the fractional knapsack method.

📋 What You'll Learn

Create an array called items with objects having value and weight properties

Create a variable called capacity for the truck's weight limit

Sort the items array by value-to-weight ratio in descending order

Calculate the maximum value that fits into the truck using fractional parts of items

Print the maximum value with two decimal places

💡 Why This Matters

🌍 Real World

This problem models packing limited space with valuable goods, useful in logistics and resource allocation.

💼 Career

Understanding greedy algorithms like fractional knapsack is important for optimization tasks in software engineering and data science.

1

Create the items array

Create an array called items with these exact objects: { value: 60, weight: 10 }, { value: 100, weight: 20 }, and { value: 120, weight: 30 }.

DSA Javascript

// Your code here

Hint

Use square brackets to create an array and curly braces for each object with value and weight.

2

Set the truck capacity

Create a variable called capacity and set it to 50.

DSA Javascript

const items = [
  { value: 60, weight: 10 },
  { value: 100, weight: 20 },
  { value: 120, weight: 30 }
];
// Your code here

Hint

Use const capacity = 50; to set the weight limit.

3

Sort items by value-to-weight ratio

Sort the items array in descending order by the ratio of value / weight using items.sort((a, b) => (b.value / b.weight) - (a.value / a.weight)).

DSA Javascript

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

const capacity = 50;
// Your code here

Hint

Use the sort method with a comparison function that compares value-to-weight ratios.

4

Calculate and print maximum value

Create a variable totalValue set to 0. Create a variable remainingCapacity set to capacity. Use a for loop with variable item to go through items. Inside the loop, if item.weight is less than or equal to remainingCapacity, add item.value to totalValue and subtract item.weight from remainingCapacity. Otherwise, add the fractional value item.value * (remainingCapacity / item.weight) to totalValue and break the loop. Finally, print totalValue.toFixed(2).

DSA Javascript

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

const capacity = 50;

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

// Your code here

Hint

Use a loop to add full items if they fit, or fractional part if not. Use toFixed(2) to format the output.

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