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import unittest
from collections import deque
################################################################################
# Solution
################################################################################
class GraphNode:
def __init__(self, label):
self.label = label
self.neighbors = set()
self.color = None
# color_graph :: G(V, E) -> Set(Color) -> IO ()
def color_graph(graph, colors):
q = deque()
seen = set()
q.append(graph[0])
while q:
node = q.popleft()
illegal = {n.color for n in node.neighbors}
for x in colors:
if x not in illegal:
node.color = x
seen.add(node)
for x in node.neighbors:
if x not in seen:
q.append(x)
# TODO: Is this the best way to traverse separate graphs?
for x in graph:
if x not in seen:
q.append(x)
return 0
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def setUp(self):
self.colors = frozenset([
'red',
'green',
'blue',
'orange',
'yellow',
'white',
])
def assertGraphColoring(self, graph, colors):
self.assertGraphHasColors(graph, colors)
self.assertGraphColorLimit(graph)
for node in graph:
self.assertNodeUniqueColor(node)
def assertGraphHasColors(self, graph, colors):
for node in graph:
msg = 'Node %r color %r not in %r' % (node.label, node.color,
colors)
self.assertIn(node.color, colors, msg=msg)
def assertGraphColorLimit(self, graph):
max_degree = 0
colors_found = set()
for node in graph:
degree = len(node.neighbors)
max_degree = max(degree, max_degree)
colors_found.add(node.color)
max_colors = max_degree + 1
used_colors = len(colors_found)
msg = 'Used %d colors and expected %d at most' % (used_colors,
max_colors)
self.assertLessEqual(used_colors, max_colors, msg=msg)
def assertNodeUniqueColor(self, node):
for adjacent in node.neighbors:
msg = 'Adjacent nodes %r and %r have the same color %r' % (
node.label,
adjacent.label,
node.color,
)
self.assertNotEqual(node.color, adjacent.color, msg=msg)
def test_line_graph(self):
node_a = GraphNode('a')
node_b = GraphNode('b')
node_c = GraphNode('c')
node_d = GraphNode('d')
node_a.neighbors.add(node_b)
node_b.neighbors.add(node_a)
node_b.neighbors.add(node_c)
node_c.neighbors.add(node_b)
node_c.neighbors.add(node_d)
node_d.neighbors.add(node_c)
graph = [node_a, node_b, node_c, node_d]
tampered_colors = list(self.colors)
color_graph(graph, tampered_colors)
self.assertGraphColoring(graph, self.colors)
def test_separate_graph(self):
node_a = GraphNode('a')
node_b = GraphNode('b')
node_c = GraphNode('c')
node_d = GraphNode('d')
node_a.neighbors.add(node_b)
node_b.neighbors.add(node_a)
node_c.neighbors.add(node_d)
node_d.neighbors.add(node_c)
graph = [node_a, node_b, node_c, node_d]
tampered_colors = list(self.colors)
color_graph(graph, tampered_colors)
self.assertGraphColoring(graph, self.colors)
def test_triangle_graph(self):
node_a = GraphNode('a')
node_b = GraphNode('b')
node_c = GraphNode('c')
node_a.neighbors.add(node_b)
node_a.neighbors.add(node_c)
node_b.neighbors.add(node_a)
node_b.neighbors.add(node_c)
node_c.neighbors.add(node_a)
node_c.neighbors.add(node_b)
graph = [node_a, node_b, node_c]
tampered_colors = list(self.colors)
color_graph(graph, tampered_colors)
self.assertGraphColoring(graph, self.colors)
def test_envelope_graph(self):
node_a = GraphNode('a')
node_b = GraphNode('b')
node_c = GraphNode('c')
node_d = GraphNode('d')
node_e = GraphNode('e')
node_a.neighbors.add(node_b)
node_a.neighbors.add(node_c)
node_b.neighbors.add(node_a)
node_b.neighbors.add(node_c)
node_b.neighbors.add(node_d)
node_b.neighbors.add(node_e)
node_c.neighbors.add(node_a)
node_c.neighbors.add(node_b)
node_c.neighbors.add(node_d)
node_c.neighbors.add(node_e)
node_d.neighbors.add(node_b)
node_d.neighbors.add(node_c)
node_d.neighbors.add(node_e)
node_e.neighbors.add(node_b)
node_e.neighbors.add(node_c)
node_e.neighbors.add(node_d)
graph = [node_a, node_b, node_c, node_d, node_e]
tampered_colors = list(self.colors)
color_graph(graph, tampered_colors)
self.assertGraphColoring(graph, self.colors)
def test_loop_graph(self):
node_a = GraphNode('a')
node_a.neighbors.add(node_a)
graph = [node_a]
tampered_colors = list(self.colors)
with self.assertRaises(Exception):
color_graph(graph, tampered_colors)
unittest.main(verbosity=2)
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