Fractional Knapsack Problem in DSA Typescript - Build from Scratch

Fractional Knapsack Problem

📖 Scenario: You are helping a delivery company pack valuable items into a knapsack. Each item has a weight and a value. The knapsack can carry a limited weight. To maximize profit, you can take fractions of items.

🎯 Goal: Build a program that calculates the maximum total value that fits into the knapsack by taking whole or fractional parts of items.

📋 What You'll Learn

Create an array of items with exact weights and values

Add a variable for the knapsack's maximum weight capacity

Implement the fractional knapsack logic to maximize total value

Print the maximum total value with two decimal places

💡 Why This Matters

🌍 Real World

This problem models packing cargo, loading trucks, or resource allocation where partial quantities can be chosen.

💼 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: { weight: 10, value: 60 }, { weight: 20, value: 100 }, { weight: 30, value: 120 }

DSA Typescript

// Your code here

Hint

Use an array of objects with weight and value properties.

2

Set the knapsack capacity

Create a variable called capacity and set it to 50

DSA Typescript

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

Hint

Use a simple number variable for the knapsack's weight limit.

3

Implement fractional knapsack logic

Write code to calculate the maximum total value by sorting items by value per weight, then taking whole or fractional parts until capacity is full. Store the result in a variable called maxValue

DSA Typescript

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

const capacity = 50;

// Your code here

Hint

Sort items by value/weight ratio descending. Use a loop to add full or fractional items until capacity is used.

4

Print the maximum total value

Print the variable maxValue rounded to two decimal places using console.log(maxValue.toFixed(2))

DSA Typescript

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

const capacity = 50;

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

let remainingCapacity = capacity;
let maxValue = 0;

for (const item of items) {
  if (remainingCapacity === 0) break;
  if (item.weight <= remainingCapacity) {
    maxValue += item.value;
    remainingCapacity -= item.weight;
  } else {
    maxValue += item.value * (remainingCapacity / item.weight);
    remainingCapacity = 0;
  }
}

// Your code here

Hint

Use console.log(maxValue.toFixed(2)) to print the result with two decimals.

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 of items selected

C. Select only whole items to maximize value

D. Sort items by weight only

Solution

1. Step 1: Understand problem goal

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

2. Step 2: Compare options

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

4. Quick Check:

   Fractional knapsack = maximize value with fractions [OK]

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

Common Mistakes:

• Thinking only whole items can be taken
• Confusing minimization with maximization
• Ignoring fractional parts of items

2. Which TypeScript syntax correctly declares an array of objects representing items with weight and value for the fractional knapsack?

easy

A. var items = weight: 10, value: 60; weight: 20, value: 100;

B. let items = (weight: 10, value: 60), (weight: 20, value: 100);

C. items = [{10, 60}, {20, 100}];

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

Solution

1. Step 1: Check array and object syntax

   const items = [{weight: 10, value: 60}, {weight: 20, value: 100}]; uses correct array of objects syntax with curly braces and key-value pairs.

2. Step 2: Identify syntax errors in other options

   Options A, B, and D have invalid TypeScript syntax for arrays or objects.

3. Final Answer:

   const items = [{weight: 10, value: 60}, {weight: 20, value: 100}]; -> Option D

4. Quick Check:

   Array of objects syntax = const items = [{weight: 10, value: 60}, {weight: 20, value: 100}]; [OK]

Hint: Use square brackets for arrays and curly braces for objects [OK]

Common Mistakes:

• Using parentheses instead of square brackets for arrays
• Missing key names in objects
• Incorrect object literal syntax

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

const items = [
  {weight: 10, value: 60},
  {weight: 20, value: 100},
  {weight: 30, value: 120}
];
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. 200

B. 220

C. 240

D. 180

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

3. Step 3: Check options

   Matches 240.

4. Final Answer:

   240 -> Option C

5. Quick Check:

   Sum values with fractions = 240 [OK]

Hint: Sort by value/weight ratio, take full items first [OK]

Common Mistakes:

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

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

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

B. Sorting order is ascending instead of descending by value/weight

C. Missing return statement

D. Incorrect fraction calculation in else block

Solution

1. Step 1: Analyze sorting function

   The sort compares (a.value/a.weight) - (b.value/b.weight), which sorts ascending by ratio.

2. Step 2: Understand impact on knapsack

   Fractional knapsack requires descending order to pick highest value/weight first. Ascending order causes wrong selection.

3. Final Answer:

   Sorting order is ascending instead of descending by value/weight -> Option B

4. Quick Check:

   Sort descending by ratio [OK]

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

Common Mistakes:

• Sorting ascending instead of descending
• Ignoring sorting impact on result
• Confusing variable declarations

5. Given items with weights and values: [{weight: 5, value: 30}, {weight: 10, value: 40}, {weight: 20, value: 140}], and a knapsack capacity of 15, what is the maximum value achievable using the fractional knapsack approach?

hard

A. 105

B. 90

C. 120

D. 100

Solution

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

   Ratios: 30/5=6, 40/10=4, 140/20=7.
   Sorted order: item3 (7), item1 (6), item2 (4).

2. Step 2: Fill knapsack capacity 15

   Take item3 partially: since 20 > 15, value = 140 * (15/20) = 105.
   Total value = 105.
   Remaining capacity 0, stop.

3. Final Answer:

   105 -> Option A

4. Quick Check:

   Fractional knapsack max value = 105 [OK]

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

Common Mistakes:

• Not sorting by value/weight ratio
• Trying to take full items exceeding capacity
• Miscomputing fractional values