Add kruskals algorithm
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@ -168,7 +168,7 @@ See examples of what the engine for the exam template can do here: [exam_templat
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- [X] Output a graph to a matrix
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- [X] Draw an undirected graph
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- [X] Draw a directed graph
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- [ ] Find a minimal spanning tree with Kruskals algorithm
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- [X] Find a minimal spanning tree with Kruskals algorithm
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#### Chapter 8. Finite state automata
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@ -68,7 +68,7 @@ class Graph:
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return \
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f'Nodes: {" ".join(self.nodes)}\n' \
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+ f'Edges: {" ".join(x+y for x,y in (self.undirectedEdgeSet() if self.isUndirected() else self.edges))}'
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@classmethod
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def fromMatrix(cls, matrix):
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return matrix.toGraph()
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@ -136,12 +136,14 @@ class Graph:
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new_connected_subgraphs = [subgraph_v.union(x) if u in x else x for x in new_connected_subgraphs]
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return new_connected_subgraphs
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sorted_edges = [ e for e in sorted(self.edges, key=lambda e: weigths[str(e)]) ]
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sorted_edges = [ e for e in sorted(self.edges, key=lambda e: weigths[e[0] + e[1]]) ]
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for u,v in sorted_edges:
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if find_subgraph_containing(u) != find_subgraph_containing(v):
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edges += [(u, v)]
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connected_subgraphs = merge_subgraphs_that_contains(u, v)
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edges += [(y,x) for x,y in edges]
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return Graph(self.nodes, edges)
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@ -161,6 +163,15 @@ class Graph:
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return (nodeString, edgeString)
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def toLaTeXWithWeights(self, weights):
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zippedNodes = zip(self.nodes, generateNodeCoords(len(self.nodes)))
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nodeString = '\n'.join(f'\\node ({name}) at ({x},{y}) {{${name}$}};' for name,(x,y) in zippedNodes)
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if self.isUndirected():
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edgeString = '\n'.join(f'\\draw ({x}) -- ({y}) node [midway, above, sloped] (Tx{x+y}) {{{weights[x+y]}}};' for x,y in self.undirectedEdgeSet())
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return (nodeString, edgeString)
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def generateLoopInOutAngle(node, nodes):
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baseAngle = 360 / len(nodes)
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@ -186,11 +197,37 @@ def generateNodeCoords(n):
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return nodeCoords
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def extractWeights(string):
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weights = dict()
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lines = string.split('\n')
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for i in range(4, len(lines)):
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edge, weight = lines[i].split(' ')
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weights[edge] = int(weight)
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weights[edge[1] + edge[0]] = int(weight)
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lines[i] = edge
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return ('\n'.join(lines), weights)
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def processFileContent(raw):
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lines = raw.split('\n')
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lines.pop(1)
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outputType = lines.pop(0)
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if lines[0] == 'kruskals':
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lines[0] = 'undirected'
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string, weights = extractWeights('\n'.join(lines))
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graph1 = Graph.fromString(string)
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graph2 = graph1.getKruskalsSpanningTree(weights)
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return replaceContent(
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(graph1.toLaTeXWithWeights(weights), graph2.toLaTeXWithWeights(weights)),
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'Kruskals',
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replaceF = lambda temp, cont:
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temp.replace('%NODES1', cont[0][0])
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.replace('%EDGES1', cont[0][1])
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.replace('%NODES2', cont[1][0])
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.replace('%EDGES2', cont[1][1])
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)
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graph = Graph.fromString('\n'.join(lines))
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print(graph)
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@ -207,11 +244,14 @@ def processFileContent(raw):
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content = graph.toMatrix().toLaTeX()
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return replaceContent(content, 'Matrix')
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if __name__ == '__main__':
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pass
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# matrix = Matrix([[False, False, True], [True, False, True], [True, False, False]])
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# print(matrix)
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# print(matrix.toGraph())
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# print(matrix.toGraph().isUndirected())
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g = Graph.fromString('complete\n\n6')
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print(g)
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import random
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d = dict()
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for e in g.edges:
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d[str(e)] = random.randint(0, 10)
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print(g.getKruskalsSpanningTree(d))
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@ -0,0 +1,37 @@
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\begin{mgraphbox}[width=\linewidth]
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\begin{figure}[H]
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\begin{center}
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\begin{tikzpicture}
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\begin{scope}[every node/.style={shape=circle, fill=white, draw, inner sep=2pt}]
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%NODES1
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\end{scope}
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\begin{scope}[every draw/.style={}]
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%EDGES1
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\end{scope}
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\end{tikzpicture}
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\end{center}
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\end{figure}
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\end{mgraphbox}
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Minimal spanning tree:
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\begin{mgraphbox}[width=\linewidth]
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\begin{figure}[H]
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\begin{center}
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\begin{tikzpicture}
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\begin{scope}[every node/.style={shape=circle, fill=white, draw, inner sep=2pt}]
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%NODES2
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\end{scope}
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\begin{scope}[every draw/.style={}]
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%EDGES2
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\end{scope}
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\end{tikzpicture}
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\end{center}
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\end{figure}
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\end{mgraphbox}
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@ -0,0 +1,67 @@
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\begin{mgraphbox}[width=\linewidth]
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\begin{figure}[H]
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\begin{center}
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\begin{tikzpicture}
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\begin{scope}[every node/.style={shape=circle, fill=white, draw, inner sep=2pt}]
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\node (A) at (0,4.0) {$A$};
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\node (B) at (-2.82843,2.82843) {$B$};
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\node (C) at (-4.0,0.0) {$C$};
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\node (D) at (-2.82843,-2.82843) {$D$};
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\node (E) at (-0.0,-4.0) {$E$};
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\node (F) at (2.82843,-2.82843) {$F$};
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\node (G) at (4.0,-0.0) {$G$};
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\node (H) at (2.82843,2.82843) {$H$};
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\end{scope}
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\begin{scope}[every draw/.style={}]
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\draw (A) -- (B) node [midway, above, sloped] (TxAB) {1};
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\draw (A) -- (C) node [midway, above, sloped] (TxAC) {2};
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\draw (A) -- (H) node [midway, above, sloped] (TxAH) {11};
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\draw (B) -- (C) node [midway, above, sloped] (TxBC) {7};
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\draw (B) -- (F) node [midway, above, sloped] (TxBF) {12};
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\draw (C) -- (D) node [midway, above, sloped] (TxCD) {3};
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\draw (C) -- (H) node [midway, above, sloped] (TxCH) {14};
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\draw (D) -- (E) node [midway, above, sloped] (TxDE) {9};
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\draw (D) -- (F) node [midway, above, sloped] (TxDF) {6};
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\draw (D) -- (G) node [midway, above, sloped] (TxDG) {10};
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\draw (F) -- (G) node [midway, above, sloped] (TxFG) {8};
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\end{scope}
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\end{tikzpicture}
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\end{center}
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\end{figure}
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\end{mgraphbox}
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Minimal spanning tree:
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\begin{mgraphbox}[width=\linewidth]
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\begin{figure}[H]
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\begin{center}
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\begin{tikzpicture}
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\begin{scope}[every node/.style={shape=circle, fill=white, draw, inner sep=2pt}]
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\node (A) at (0,4.0) {$A$};
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\node (B) at (-2.82843,2.82843) {$B$};
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\node (C) at (-4.0,0.0) {$C$};
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\node (D) at (-2.82843,-2.82843) {$D$};
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\node (E) at (-0.0,-4.0) {$E$};
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\node (F) at (2.82843,-2.82843) {$F$};
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\node (G) at (4.0,-0.0) {$G$};
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\node (H) at (2.82843,2.82843) {$H$};
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\end{scope}
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\begin{scope}[every draw/.style={}]
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\draw (A) -- (B) node [midway, above, sloped] (TxAB) {1};
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\draw (A) -- (C) node [midway, above, sloped] (TxAC) {2};
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\draw (A) -- (H) node [midway, above, sloped] (TxAH) {11};
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\draw (C) -- (D) node [midway, above, sloped] (TxCD) {3};
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\draw (D) -- (E) node [midway, above, sloped] (TxDE) {9};
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\draw (D) -- (F) node [midway, above, sloped] (TxDF) {6};
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\draw (F) -- (G) node [midway, above, sloped] (TxFG) {8};
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\end{scope}
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\end{tikzpicture}
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\end{center}
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\end{figure}
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\end{mgraphbox}
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@ -0,0 +1,19 @@
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# Graph
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kruskals
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A B C D E F G H
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AB 1
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AC 2
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CD 3
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DE 4
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HA 5
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FD 6
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CB 7
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FG 8
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DE 9
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DG 10
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AH 11
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FB 12
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HC 13
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CH 14
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@ -95,6 +95,8 @@
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\verbatimInput{undirectedGraphToMatrix}
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\verbatimDiagram{directedFromMatrix}
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\verbatimInput{kruskals}
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\section{Finite state automata}
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@ -17,7 +17,8 @@
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\contentsline {subsection}{\numberline {5.4}adjacency}{12}{subsection.5.4}%
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\contentsline {subsection}{\numberline {5.5}undirectedGraphToMatrix}{13}{subsection.5.5}%
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\contentsline {subsection}{\numberline {5.6}directedFromMatrix}{14}{subsection.5.6}%
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\contentsline {section}{\numberline {6}Finite state automata}{15}{section.6}%
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\contentsline {subsection}{\numberline {6.1}automata}{15}{subsection.6.1}%
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\contentsline {section}{\numberline {7}Raw python}{16}{section.7}%
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\contentsline {subsection}{\numberline {7.1}python}{16}{subsection.7.1}%
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\contentsline {subsection}{\numberline {5.7}kruskals}{15}{subsection.5.7}%
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\contentsline {section}{\numberline {6}Finite state automata}{17}{section.6}%
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\contentsline {subsection}{\numberline {6.1}automata}{17}{subsection.6.1}%
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\contentsline {section}{\numberline {7}Raw python}{18}{section.7}%
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\contentsline {subsection}{\numberline {7.1}python}{18}{subsection.7.1}%
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