<｜begin▁of▁sentence｜>### Instruction:
Given a weighted tree with node weights {1: 2, 2: 1, 3: 3, 4: 4, 5: 5} and edge weights {(1, 2): 0.5, (1, 3): 1.5, (2, 4): 1.0, (3, 5): 2.0}, how would you partition this tree using the Lukes algorithm such that each partition does not exceed a total node weight of 5 and the weight of the edges cut is minimized?
### Response:
import networkx as nx
from networkx.algorithms import tree

# Create a tree with integer node weights
T = nx.Graph()
T.add_nodes_from([(1, {'weight': 2}), (2, {'weight': 1}), (3, {'weight': 3}), (4, {'weight': 4}), (5, {'weight': 5})])
T.add_weighted_edges_from([(1, 2, 0.5), (1, 3, 1.5), (2, 4, 1.0), (3, 5, 2.0)])

# Run Lukes partitioning algorithm with a max partition size of 5
partition = tree.lukes_partitioning(T, max_size=5, edge_weight='weight', node_weight='weight')
print(partition)
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