def knapsack_with_mandatory(capacity, file_sizes, mandatory_index):
n = len(file_sizes)
mandatory_size = file_sizes[mandatory_index]
# Convert all sizes to integers (bytes) to avoid floating point issues
capacity = int(capacity * 1000) # Convert MB to KB
file_sizes = [int(size * 1000) for size in file_sizes] # Convert MB to KB
mandatory_size = file_sizes[mandatory_index]
# Reduce capacity by the size of the mandatory file
remaining_capacity = capacity - mandatory_size
# Create a new list without the mandatory file
remaining_files = file_sizes[:mandatory_index] + file_sizes[mandatory_index+1:]
dp = [[0 for _ in range(remaining_capacity + 1)] for _ in range(n)]
for i in range(1, n):
for w in range(1, remaining_capacity + 1):
if remaining_files[i-1] <= w:
dp[i][w] = max(remaining_files[i-1] + dp[i-1][w-remaining_files[i-1]], dp[i-1][w])
else:
dp[i][w] = dp[i-1][w]
# Backtrack to find which files were included
w = remaining_capacity
included_files = [mandatory_index] # Start with the mandatory file
for i in range(n-1, 0, -1):
if dp[i][w] != dp[i-1][w]:
if i >= mandatory_index:
included_files.append(i+1)
else:
included_files.append(i)
w -= remaining_files[i-1]
return (dp[n-1][remaining_capacity] + mandatory_size) / 1000, included_files[::-1] # Convert KB back to MB
# File sizes in MB
file_sizes = [33.7, 16.2, 1.5, 1.0, 1.8, 2.7, .9,
6.6, 5.2, 2.0, 1.8, 1.1, 5.1, 6.4, 7.3]
capacity = 20 # Hard drive capacity in MB
mandatory_file = 14 # Index of file 15 (remember, Python uses 0-based indexing)
total_size, selected_files = knapsack_with_mandatory(capacity, file_sizes, mandatory_file)
print(f"Maximum total size: {total_size:.1f} MB")
print("Selected files:")
for i in selected_files:
print(f"File {i+1}: {file_sizes[i]} MB")
print(f"Total size of selected files: {sum([file_sizes[i] for i in selected_files]):.1f} MB")
print(f"Unused space: {capacity - sum([file_sizes[i] for i in selected_files]):.1f} MB")Benefits of TheCodeground Online IDE
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