This document discusses the knapsack problem and provides an algorithm to solve it. It introduces the knapsack problem as trying to find the maximum value that can be stored within a knapsack of limited weight/space. It then shows an example problem with 5 items, each with a value and weight. The algorithm involves sorting the items by their value/weight ratio and selecting items in that order until the knapsack is full. It provides code to implement the knapsack algorithm and runs through an example solution.

1. Hello Everyone.

2. PRITAM GOLDER
ID: 172-15-9879

4. What is it ?

5. Bag???What is it ?

6. Bag???
No, It’s a Knapsack.
What is it ?

7. Value: 25
Value: 40 Value: 50
Value: 15Value: 20
Weight: 4
Weight: 1Weight: 2
Weight: 3
Weight: 5Space: 6(weight)
Value: ????
Get the Maximum Value:
store

8. Get the Maximum Value:
Now, We are facing a big problem.
There are many options to get the maximum value.
This problem is called
knapsack problem.
Good thing is. There is an algorithm to solve this.
Today, we are going to learn this

9. Solve Knapsack Problem:
• Firstly, create a table store the data.
Item 1 2 3 4 5
Value 25 20 15 40 50
Weight 3 2 1 4 5
• Secondly, get the ratio value/weight.
Item 1 2 3 4 5
Value 25 20 15 40 50
Weight 3 2 1 4 5
Value/weight 8.3 10 15 10 10

10. Solve Knapsack Problem:
Item 1 2 3 4 5
Value 25 20 15 40 50
Weight 3 2 1 4 5
Value/weight 8.3 10 15 10 10
• Now, sort the values on the basis of ratio.
Item 3 2 4 5 1
Value 15 20 40 50 25
Weight 1 2 4 5 3
Value/weight 15 10 10 10 8.3
Sort

11. Solve Knapsack Problem:
• Now, We have to keep taking items till the knapsack filled up.
Item 3 2 4 5 1
Value 15 20 40 50 25
Weight 1 2 4 5 3
Value/weight 15 10 10 10 8.3
Item Weight Value Space remaining
3 1 15 5
2 2 20 3
4 3 30 0 Fractional
Total value: 65

12. Code of Knapsack Algorithm

13. Run Knapsack Algorithm

14. That’s All.
Thank you.