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Knapsack Algo

This document defines a knapsack problem as a list of items each with a weight and value. It initializes a table to track solutions and fills it using dynamic programming to find the maximum value for a knapsack of capacity 10. It then traces back through the table to find which items were included for the optimal solution.

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Hanin Bayoud
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54 views1 page

Knapsack Algo

This document defines a knapsack problem as a list of items each with a weight and value. It initializes a table to track solutions and fills it using dynamic programming to find the maximum value for a knapsack of capacity 10. It then traces back through the table to find which items were included for the optimal solution.

Uploaded by

Hanin Bayoud
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as TXT, PDF, TXT or read online on Scribd
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# Define the items as a list of tuples (weight, value)

items = [(2, 6), (3, 5), (4, 8), (5, 9)]

# Define the capacity of the knapsack


capacity = 10

# Initialize the table with zeros


table = [[0 for j in range(capacity + 1)] for i in range(len(items) + 1)]

# Fill in the table using dynamic programming


for i in range(1, len(items) + 1):
for j in range(1, capacity + 1):
weight, value = items[i-1]
if weight <= j:
table[i][j] = max(table[i-1][j], table[i-1][j-weight] + value)
else:
table[i][j] = table[i-1][j]

# Find the items that were included in the solution


i = len(items)
j = capacity
included_items = []
while i > 0 and j > 0:
weight, value = items[i-1]
if table[i][j] != table[i-1][j]:
included_items.append(i-1)
j -= weight
i -= 1

# Reverse the list of included items


included_items = included_items[::-1]

# Print the table and the solution


print("Table:")
for row in table:
print(row)
print("Maximum value:", table[-1][-1])
print("Included items:", included_items)

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