Knapsack problem of Greedy method [ understand with real life example].

Knapsack problem of Greedy method [ understand with real life example].

Knapsack Problem using Greedy Method — with Real-Life Example

What is the Knapsack Problem?

It’s a classic optimization problem where:

• You have a bag (knapsack) that can carry up to a certain weight/capacity.

• You have items, each with a weight and a value.

• The goal is to maximize total value without exceeding the capacity.

Greedy Method (Fractional Knapsack)

In the Greedy approach, you:

• Choose items with the highest value per unit weight (value/weight ratio) first.

• You can take fractions of items (not whole only).

• It’s optimal for fractional knapsack, not for 0/1 version.

Real-Life Example: Emergency Relief Backpack

Imagine you’re packing an emergency relief bag during a disaster. The bag can hold up to 15 kg. You have these items:

Step-by-step Greedy Method:

1. Sort items by value/weight ratio:

   • All have 20.0, except flashlight (15.0)

2. Start filling the bag with items of highest ratio:

• Take First Aid Kit (3 kg) → total weight = 3 kg, value = 60

• Take Bottled Water (5 kg) → total weight = 8 kg, value = 160

• Take Food Pack (7 kg) → total weight = 15 kg (max), value = 300

Total weight used = 15 kg
Total value gained = 300
(No room for Flashlight)

If only 2 kg space left for Food Pack?

Take 2/7 of it:
→ Value = (2/7) × 140 = 40

Why Greedy Works Here?

• Fractional choices are allowed.

• Maximizing value per kg works best when dividing is allowed.

Where Greedy Fails?

In 0/1 Knapsack (items can’t be split), greedy may not give the best solution. There, Dynamic Programming is better.

Summary:

Concept	Greedy Approach Works
Fractional items	Yes
0/1 items	Not always optimal
Real-life fit	Packing, resource loading

Would you like:

• A visual chart of this example?

• Practice problems with solutions?

• A version for 0/1 knapsack?

Knapsack problem of Greedy method [ understand with real life example].

Greedy solution method for knapsack problems with R