class TestSquareMatrix(unittest.TestCase):
def setUp(self):
self.matrix = SquareMatrix(5)
def test_empty(self):
for i in range(5):
for j in range(5):
element = self.matrix.get(i, j)
self.assertTrue(element == 0)
def test_set_get(self):
self.matrix.set(3, 3, 1)
elem = self.matrix.get(3, 3)
self.assertTrue(elem == 1)
def test_sizes(self):
size = self.matrix.size()
self.assertTrue(size == 5)
def test_clone(self):
self.matrix.set(2, 2, 1)
clone = self.matrix.clone()
self.matrix.set(3, 3, 1)
clone.set(4, 4, 1)
orig_before_cloning = self.matrix.get(2, 2)
self.assertTrue(orig_before_cloning == 1)
orig_after_cloning = self.matrix.get(3, 3)
matching_clone_elem = clone.get(3, 3)
self.assertTrue(orig_after_cloning == 1)
self.assertTrue(matching_clone_elem == 0)
modified_clone = clone.get(4, 4)
matching_orig_elem = self.matrix.get(4, 4)
self.assertTrue(modified_clone == 1)
self.assertTrue(matching_orig_elem == 0)
class TestSquareMatrix(unittest.TestCase):
def setUp(self):
self.matrix = SquareMatrix(5)
def test_empty(self):
for i in range(5):
for j in range(5):
element = self.matrix.get(i, j)
self.assertTrue(element == 0)
def test_set_get(self):
self.matrix.set(3, 3, 1)
elem = self.matrix.get(3, 3)
self.assertTrue(elem == 1)
def test_sizes(self):
size = self.matrix.size()
self.assertTrue(size == 5)
def test_clone(self):
self.matrix.set(2, 2, 1)
clone = self.matrix.clone()
self.matrix.set(3, 3, 1)
clone.set(4, 4, 1)
orig_before_cloning = self.matrix.get(2, 2)
self.assertTrue(orig_before_cloning == 1)
orig_after_cloning = self.matrix.get(3, 3)
matching_clone_elem = clone.get(3, 3)
self.assertTrue(orig_after_cloning == 1)
self.assertTrue(matching_clone_elem == 0)
modified_clone = clone.get(4, 4)
matching_orig_elem = self.matrix.get(4, 4)
self.assertTrue(modified_clone == 1)
self.assertTrue(matching_orig_elem == 0)
class UndirectedGraph:
def __init__(self, size):
self.adj_matrix = SquareMatrix(size)
def vertexCount(self):
return self.adj_matrix.size()
def addEdge(self, vertex1, vertex2):
self.adj_matrix.set(vertex1, vertex2, True)
self.adj_matrix.set(vertex2, vertex1, True)
def areConnected(self, vertex1, vertex2):
return self.adj_matrix.get(vertex1, vertex2)
def adjacentEdges(self, vertex):
adj_edges = []
for vertex2 in range(0, self.adj_matrix.size()):
if self.areConnected(vertex, vertex2):
adj_edges.append(Edge(vertex, vertex2))
return adj_edges
def edgeCandidates(self, tree):
"""Returns a list of edges of this graph where one vertex of the edge
is contained in the given tree and the other vertex is not."""
matrix_copy = self.adj_matrix.clone()
# remove edges already in tree from adjacency matrix
for edge in tree.edges:
matrix_copy.set(edge.vertex1, edge.vertex2, False)
matrix_copy.set(edge.vertex2, edge.vertex1, False)
for vertex_1 in range(0, self.adj_matrix.size()):
# skip edges where the first vertex would have degree 0 in the tree
if tree.vertexDegrees()[vertex_1] == 0:
continue
for vertex_2 in range(0, self.adj_matrix.size()):
# skip edges that would create cycle in the tree
if tree.vertexDegrees()[vertex_2] != 0:
continue
if matrix_copy.get(vertex_1, vertex_2):
yield Edge(vertex_1, vertex_2)
def __str__(self):
result = " |"
for col in range(0, self.vertexCount()):
result += " {0}".format(col)
result += "\n"
result += "-|"
for i in range(0, self.vertexCount()):
result += "--"
result += "-\n"
for row in range(0, self.vertexCount()):
result += "{0}|".format(row)
for col in range(0, self.vertexCount()):
value = self.adj_matrix.get(row, col)
result += " {0}".format(int(value))
result += "\n"
return result
class UndirectedGraph:
def __init__(self, size):
self.adj_matrix = SquareMatrix(size)
def vertexCount(self):
return self.adj_matrix.size()
def addEdge(self, vertex1, vertex2):
self.adj_matrix.set(vertex1, vertex2, True)
self.adj_matrix.set(vertex2, vertex1, True)
def areConnected(self, vertex1, vertex2):
return self.adj_matrix.get(vertex1, vertex2)
def adjacentEdges(self, vertex):
adj_edges = []
for vertex2 in range(0, self.adj_matrix.size()):
if self.areConnected(vertex, vertex2):
adj_edges.append(Edge(vertex, vertex2))
return adj_edges
def edgeCandidates(self, tree):
"""Returns a list of edges of this graph where one vertex of the edge
is contained in the given tree and the other vertex is not."""
matrix_copy = self.adj_matrix.clone()
# remove edges already in tree from adjacency matrix
for edge in tree.edges:
matrix_copy.set(edge.vertex1, edge.vertex2, False)
matrix_copy.set(edge.vertex2, edge.vertex1, False)
for vertex_1 in range(0, self.adj_matrix.size()):
# skip edges where the first vertex would have degree 0 in the tree
if tree.vertexDegrees()[vertex_1] == 0:
continue
for vertex_2 in range(0, self.adj_matrix.size()):
# skip edges that would create cycle in the tree
if tree.vertexDegrees()[vertex_2] != 0:
continue
if matrix_copy.get(vertex_1, vertex_2):
yield Edge(vertex_1, vertex_2)
def __str__(self):
result = " |"
for col in range(0, self.vertexCount()):
result += " {0}".format(col)
result += "\n"
result += "-|"
for i in range(0, self.vertexCount()):
result += "--"
result += "-\n"
for row in range(0, self.vertexCount()):
result += "{0}|".format(row)
for col in range(0, self.vertexCount()):
value = self.adj_matrix.get(row, col)
result += " {0}".format(int(value))
result += "\n"
return result
class UndirectedGraph:
"""Undirected unweighted graph for representing graph structure only. Does not store any values in vertices.
Vertices are numbered starting with zero.
"""
def __init__(self, size):
"""Creates a new graph with specified number of vertices. The number of vertices is immutable..
:param size: number of vertices in the graph.
"""
self.adj_matrix = SquareMatrix(size)
def vertexCount(self):
"""
:return: number of vertices in the graph.
"""
return self.adj_matrix.size()
def addEdge(self, vertex1, vertex2):
"""Adds an edge to the graph. The order of vertices doesn't matter.
:param vertex1: first node of the edge (from 0 to size - 1).
:param vertex2: second node of the edge (from 0 to size - 1).
"""
self.adj_matrix.set(vertex1, vertex2, True)
self.adj_matrix.set(vertex2, vertex1, True)
def areConnected(self, vertex1, vertex2):
"""Checks if there is an edge between two vertices. The order of vertices doesn't matter.
:param vertex1: first vertex (from 0 to size - 1).
:param vertex2: second vertex (from 0 to size - 1).
:return: True if the edge exists in the graph, false otherwise.
"""
return self.adj_matrix.get(vertex1, vertex2)
def adjacentEdges(self, vertex):
"""Returns a set of edges adjacent to the given vertex.
:param vertex: endpoint vertex.
:return: set of edges adjacent to the vertex.
"""
adj_edges = set()
for vertex2 in range(0, self.adj_matrix.size()):
if self.areConnected(vertex, vertex2):
adj_edges.add(Edge(vertex, vertex2))
return adj_edges
def edgeCandidates(self, tree):
"""Given a spanning tree, returns a set of new edge candidates for the spanning tree.
In other words, returns a subset of the edges of this graph where each edge has exactly one
of its vertices contained in the spanning tree.
:param tree: Existing spanning tree for this graph. An instance of SpanningTree.
:return: set of new spanning tree edge candidates.
"""
matrix_copy = self.adj_matrix.clone()
# remove edges already present in tree from the adjacency matrix
for edge in tree.edges:
matrix_copy.set(edge.vertex1, edge.vertex2, False)
matrix_copy.set(edge.vertex2, edge.vertex1, False)
candidates = set()
for vertex_1 in range(self.adj_matrix.size()):
# skip edges where the first vertex would have degree 0 in the tree
if tree.vertexDegrees()[vertex_1] == 0:
continue
for vertex_2 in range(0, self.adj_matrix.size()):
# skip edges that would create cycle in the tree
if tree.vertexDegrees()[vertex_2] != 0:
continue
if matrix_copy.get(vertex_1, vertex_2):
candidates.add(Edge(vertex_1, vertex_2))
return candidates
def __str__(self):
result = " |"
for col in range(0, self.vertexCount()):
result += " {0}".format(col)
result += "\n"
result += "-|"
for i in range(0, self.vertexCount()):
result += "--"
result += "-\n"
for row in range(0, self.vertexCount()):
result += "{0}|".format(row)
for col in range(0, self.vertexCount()):
value = self.adj_matrix.get(row, col)
result += " {0}".format(int(value))
result += "\n"
return result
class UndirectedGraph:
"""Undirected unweighted graph for representing graph structure only. Does not store any values in vertices.
Vertices are numbered starting with zero.
"""
def __init__(self, size):
"""Creates a new graph with specified number of vertices. The number of vertices is immutable..
:param size: number of vertices in the graph.
"""
self.adj_matrix = SquareMatrix(size)
def vertexCount(self):
"""
:return: number of vertices in the graph.
"""
return self.adj_matrix.size()
def addEdge(self, vertex1, vertex2):
"""Adds an edge to the graph. The order of vertices doesn't matter.
:param vertex1: first node of the edge (from 0 to size - 1).
:param vertex2: second node of the edge (from 0 to size - 1).
"""
self.adj_matrix.set(vertex1, vertex2, True)
self.adj_matrix.set(vertex2, vertex1, True)
def areConnected(self, vertex1, vertex2):
"""Checks if there is an edge between two vertices. The order of vertices doesn't matter.
:param vertex1: first vertex (from 0 to size - 1).
:param vertex2: second vertex (from 0 to size - 1).
:return: True if the edge exists in the graph, false otherwise.
"""
return self.adj_matrix.get(vertex1, vertex2)
def adjacentEdges(self, vertex):
"""Returns a set of edges adjacent to the given vertex.
:param vertex: endpoint vertex.
:return: set of edges adjacent to the vertex.
"""
adj_edges = set()
for vertex2 in range(0, self.adj_matrix.size()):
if self.areConnected(vertex, vertex2):
adj_edges.add(Edge(vertex, vertex2))
return adj_edges
def edgeCandidates(self, tree):
"""Given a spanning tree, returns a set of new edge candidates for the spanning tree.
In other words, returns a subset of the edges of this graph where each edge has exactly one
of its vertices contained in the spanning tree.
:param tree: Existing spanning tree for this graph. An instance of SpanningTree.
:return: set of new spanning tree edge candidates.
"""
matrix_copy = self.adj_matrix.clone()
# remove edges already present in tree from the adjacency matrix
for edge in tree.edges:
matrix_copy.set(edge.vertex1, edge.vertex2, False)
matrix_copy.set(edge.vertex2, edge.vertex1, False)
candidates = set()
for vertex_1 in range(self.adj_matrix.size()):
# skip edges where the first vertex would have degree 0 in the tree
if tree.vertexDegrees()[vertex_1] == 0:
continue
for vertex_2 in range(0, self.adj_matrix.size()):
# skip edges that would create cycle in the tree
if tree.vertexDegrees()[vertex_2] != 0:
continue
if matrix_copy.get(vertex_1, vertex_2):
candidates.add(Edge(vertex_1, vertex_2))
return candidates
def __str__(self):
result = " |"
for col in range(0, self.vertexCount()):
result += " {0}".format(col)
result += "\n"
result += "-|"
for i in range(0, self.vertexCount()):
result += "--"
result += "-\n"
for row in range(0, self.vertexCount()):
result += "{0}|".format(row)
for col in range(0, self.vertexCount()):
value = self.adj_matrix.get(row, col)
result += " {0}".format(int(value))
result += "\n"
return result