Procedure

---

Step 1: User Input Configuration

1.1 Enter the Knapsack Capacity

• Enter the Knapsack Capacity (M) in the corresponding input field.
• This represents the maximum weight the knapsack can hold.
• Input Constraint: Knapsack Capacity should be ≤ 200.

1.2 Enter Item Weights

• Enter the Item Weights as a comma-separated list of positive numbers.
• Input Constraint: Maximum 15 items are allowed and each item’s weight should be ≤ 100.

1.3 Enter Item Values

• Enter the Item Values as a comma-separated list corresponding to each item’s weight.
• Input Constraint: Each item’s value should be ≤ 2000.

1.4 Input Validation

Ensure that:

• The number of weights and values are equal.
• Ensure that all the inputs are positive numbers and within the specified constraint ranges.

(Optional)

• Click the Randomize button to automatically generate sample weights and values.

---

Step 2: Initialization of the Fractional Knapsack Algorithm

2.1 Start the Simulation

• Click the Auto Play or Next Step button to initialize the simulation.

2.2 Ratio Computation

• The algorithm computes the Value-to-Weight ratio (V/W) for each item.

2.3 Reset Visualization

• All visualization panels, result tables, knapsack fill indicator, and execution logs are reset to their initial states.

2.4 Knapsack Initialization

• The knapsack is initialized with zero filled weight and zero total value.

2.5 Sorting Preparation

• The algorithm prepares to process items in descending order of their value-to-weight ratio.

---

Step 3: Selection of Execution Mode

Choose one of the following execution modes:

(a) Manual Mode

• Click the Next Step button to execute the algorithm step-by-step.

For each step:

• The next item with the highest value-to-weight ratio is selected.
• The algorithm checks whether the item can be fully accommodated in the knapsack.
• The active algorithm step is highlighted in the Algorithm Steps panel.

If the item fits completely:

• The full item is added to the knapsack.
• The knapsack fill level increases accordingly.

If the item does not fit completely:

• A fraction of the item is added to exactly fill the remaining capacity.

Additional control:

• Click the Previous Step button to revisit earlier steps without affecting the final result.

(b) Automatic Mode

• Click the Auto Play button to allow the algorithm to execute automatically.

• Items are processed sequentially based on decreasing value-to-weight ratio.
• Knapsack filling is animated smoothly to visually represent full or fractional inclusion.
• Execution logs update dynamically to describe each decision taken by the algorithm.
• The simulation pauses automatically after the knapsack reaches full capacity.

---

Step 4: Visualization of Knapsack Filling

• Observe the Items Panel, where items are displayed in sorted order of value-to-weight ratio.

• Track the gradual filling of the Knapsack Panel, represented by a coloured progress fill.

Notice:

• Full items increase the fill proportionally to their weight.
• Fractional items partially fill the remaining space.
• The current weight and maximum capacity are updated in real time.
• The result table records the fraction of each item taken along with its contribution to the total value.

---

Step 5: Result Analysis and Completion

• Once the knapsack reaches its maximum capacity, the simulation displays Completed.
• The Total Value obtained is shown in the Results panel.

• The Auto Play button is disabled to indicate the completion of the experiment.
• The final state of the knapsack remains visible for verification.
• Click the Reset button to clear all inputs and restart the experiment.

---