Add kruskals algorithm
This commit is contained in:
parent
f2a26807c1
commit
bc1609c549
|
|
@ -168,7 +168,7 @@ See examples of what the engine for the exam template can do here: [exam_templat
|
|||
- [X] Output a graph to a matrix
|
||||
- [X] Draw an undirected graph
|
||||
- [X] Draw a directed graph
|
||||
- [ ] Find a minimal spanning tree with Kruskals algorithm
|
||||
- [X] Find a minimal spanning tree with Kruskals algorithm
|
||||
|
||||
#### Chapter 8. Finite state automata
|
||||
|
||||
|
|
|
|||
|
|
@ -68,7 +68,7 @@ class Graph:
|
|||
return \
|
||||
f'Nodes: {" ".join(self.nodes)}\n' \
|
||||
+ f'Edges: {" ".join(x+y for x,y in (self.undirectedEdgeSet() if self.isUndirected() else self.edges))}'
|
||||
|
||||
|
||||
@classmethod
|
||||
def fromMatrix(cls, matrix):
|
||||
return matrix.toGraph()
|
||||
|
|
@ -136,12 +136,14 @@ class Graph:
|
|||
new_connected_subgraphs = [subgraph_v.union(x) if u in x else x for x in new_connected_subgraphs]
|
||||
return new_connected_subgraphs
|
||||
|
||||
sorted_edges = [ e for e in sorted(self.edges, key=lambda e: weigths[str(e)]) ]
|
||||
sorted_edges = [ e for e in sorted(self.edges, key=lambda e: weigths[e[0] + e[1]]) ]
|
||||
|
||||
for u,v in sorted_edges:
|
||||
if find_subgraph_containing(u) != find_subgraph_containing(v):
|
||||
edges += [(u, v)]
|
||||
connected_subgraphs = merge_subgraphs_that_contains(u, v)
|
||||
|
||||
edges += [(y,x) for x,y in edges]
|
||||
|
||||
return Graph(self.nodes, edges)
|
||||
|
||||
|
|
@ -161,6 +163,15 @@ class Graph:
|
|||
|
||||
return (nodeString, edgeString)
|
||||
|
||||
def toLaTeXWithWeights(self, weights):
|
||||
zippedNodes = zip(self.nodes, generateNodeCoords(len(self.nodes)))
|
||||
nodeString = '\n'.join(f'\\node ({name}) at ({x},{y}) {{${name}$}};' for name,(x,y) in zippedNodes)
|
||||
|
||||
if self.isUndirected():
|
||||
edgeString = '\n'.join(f'\\draw ({x}) -- ({y}) node [midway, above, sloped] (Tx{x+y}) {{{weights[x+y]}}};' for x,y in self.undirectedEdgeSet())
|
||||
|
||||
return (nodeString, edgeString)
|
||||
|
||||
|
||||
def generateLoopInOutAngle(node, nodes):
|
||||
baseAngle = 360 / len(nodes)
|
||||
|
|
@ -186,11 +197,37 @@ def generateNodeCoords(n):
|
|||
|
||||
return nodeCoords
|
||||
|
||||
def extractWeights(string):
|
||||
weights = dict()
|
||||
lines = string.split('\n')
|
||||
for i in range(4, len(lines)):
|
||||
edge, weight = lines[i].split(' ')
|
||||
weights[edge] = int(weight)
|
||||
weights[edge[1] + edge[0]] = int(weight)
|
||||
lines[i] = edge
|
||||
return ('\n'.join(lines), weights)
|
||||
|
||||
def processFileContent(raw):
|
||||
lines = raw.split('\n')
|
||||
lines.pop(1)
|
||||
outputType = lines.pop(0)
|
||||
|
||||
if lines[0] == 'kruskals':
|
||||
lines[0] = 'undirected'
|
||||
string, weights = extractWeights('\n'.join(lines))
|
||||
graph1 = Graph.fromString(string)
|
||||
graph2 = graph1.getKruskalsSpanningTree(weights)
|
||||
return replaceContent(
|
||||
(graph1.toLaTeXWithWeights(weights), graph2.toLaTeXWithWeights(weights)),
|
||||
'Kruskals',
|
||||
replaceF = lambda temp, cont:
|
||||
temp.replace('%NODES1', cont[0][0])
|
||||
.replace('%EDGES1', cont[0][1])
|
||||
.replace('%NODES2', cont[1][0])
|
||||
.replace('%EDGES2', cont[1][1])
|
||||
)
|
||||
|
||||
|
||||
graph = Graph.fromString('\n'.join(lines))
|
||||
|
||||
print(graph)
|
||||
|
|
@ -207,11 +244,14 @@ def processFileContent(raw):
|
|||
content = graph.toMatrix().toLaTeX()
|
||||
return replaceContent(content, 'Matrix')
|
||||
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
pass
|
||||
# matrix = Matrix([[False, False, True], [True, False, True], [True, False, False]])
|
||||
# print(matrix)
|
||||
# print(matrix.toGraph())
|
||||
# print(matrix.toGraph().isUndirected())
|
||||
g = Graph.fromString('complete\n\n6')
|
||||
print(g)
|
||||
|
||||
import random
|
||||
|
||||
d = dict()
|
||||
for e in g.edges:
|
||||
d[str(e)] = random.randint(0, 10)
|
||||
|
||||
print(g.getKruskalsSpanningTree(d))
|
||||
|
|
@ -0,0 +1,37 @@
|
|||
\begin{mgraphbox}[width=\linewidth]
|
||||
\begin{figure}[H]
|
||||
\begin{center}
|
||||
\begin{tikzpicture}
|
||||
|
||||
\begin{scope}[every node/.style={shape=circle, fill=white, draw, inner sep=2pt}]
|
||||
%NODES1
|
||||
\end{scope}
|
||||
|
||||
\begin{scope}[every draw/.style={}]
|
||||
%EDGES1
|
||||
\end{scope}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
\end{figure}
|
||||
\end{mgraphbox}
|
||||
|
||||
Minimal spanning tree:
|
||||
|
||||
\begin{mgraphbox}[width=\linewidth]
|
||||
\begin{figure}[H]
|
||||
\begin{center}
|
||||
\begin{tikzpicture}
|
||||
|
||||
\begin{scope}[every node/.style={shape=circle, fill=white, draw, inner sep=2pt}]
|
||||
%NODES2
|
||||
\end{scope}
|
||||
|
||||
\begin{scope}[every draw/.style={}]
|
||||
%EDGES2
|
||||
\end{scope}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
\end{figure}
|
||||
\end{mgraphbox}
|
||||
|
|
@ -0,0 +1,67 @@
|
|||
\begin{mgraphbox}[width=\linewidth]
|
||||
\begin{figure}[H]
|
||||
\begin{center}
|
||||
\begin{tikzpicture}
|
||||
|
||||
\begin{scope}[every node/.style={shape=circle, fill=white, draw, inner sep=2pt}]
|
||||
\node (A) at (0,4.0) {$A$};
|
||||
\node (B) at (-2.82843,2.82843) {$B$};
|
||||
\node (C) at (-4.0,0.0) {$C$};
|
||||
\node (D) at (-2.82843,-2.82843) {$D$};
|
||||
\node (E) at (-0.0,-4.0) {$E$};
|
||||
\node (F) at (2.82843,-2.82843) {$F$};
|
||||
\node (G) at (4.0,-0.0) {$G$};
|
||||
\node (H) at (2.82843,2.82843) {$H$};
|
||||
\end{scope}
|
||||
|
||||
\begin{scope}[every draw/.style={}]
|
||||
\draw (A) -- (B) node [midway, above, sloped] (TxAB) {1};
|
||||
\draw (A) -- (C) node [midway, above, sloped] (TxAC) {2};
|
||||
\draw (A) -- (H) node [midway, above, sloped] (TxAH) {11};
|
||||
\draw (B) -- (C) node [midway, above, sloped] (TxBC) {7};
|
||||
\draw (B) -- (F) node [midway, above, sloped] (TxBF) {12};
|
||||
\draw (C) -- (D) node [midway, above, sloped] (TxCD) {3};
|
||||
\draw (C) -- (H) node [midway, above, sloped] (TxCH) {14};
|
||||
\draw (D) -- (E) node [midway, above, sloped] (TxDE) {9};
|
||||
\draw (D) -- (F) node [midway, above, sloped] (TxDF) {6};
|
||||
\draw (D) -- (G) node [midway, above, sloped] (TxDG) {10};
|
||||
\draw (F) -- (G) node [midway, above, sloped] (TxFG) {8};
|
||||
\end{scope}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
\end{figure}
|
||||
\end{mgraphbox}
|
||||
|
||||
Minimal spanning tree:
|
||||
|
||||
\begin{mgraphbox}[width=\linewidth]
|
||||
\begin{figure}[H]
|
||||
\begin{center}
|
||||
\begin{tikzpicture}
|
||||
|
||||
\begin{scope}[every node/.style={shape=circle, fill=white, draw, inner sep=2pt}]
|
||||
\node (A) at (0,4.0) {$A$};
|
||||
\node (B) at (-2.82843,2.82843) {$B$};
|
||||
\node (C) at (-4.0,0.0) {$C$};
|
||||
\node (D) at (-2.82843,-2.82843) {$D$};
|
||||
\node (E) at (-0.0,-4.0) {$E$};
|
||||
\node (F) at (2.82843,-2.82843) {$F$};
|
||||
\node (G) at (4.0,-0.0) {$G$};
|
||||
\node (H) at (2.82843,2.82843) {$H$};
|
||||
\end{scope}
|
||||
|
||||
\begin{scope}[every draw/.style={}]
|
||||
\draw (A) -- (B) node [midway, above, sloped] (TxAB) {1};
|
||||
\draw (A) -- (C) node [midway, above, sloped] (TxAC) {2};
|
||||
\draw (A) -- (H) node [midway, above, sloped] (TxAH) {11};
|
||||
\draw (C) -- (D) node [midway, above, sloped] (TxCD) {3};
|
||||
\draw (D) -- (E) node [midway, above, sloped] (TxDE) {9};
|
||||
\draw (D) -- (F) node [midway, above, sloped] (TxDF) {6};
|
||||
\draw (F) -- (G) node [midway, above, sloped] (TxFG) {8};
|
||||
\end{scope}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
\end{figure}
|
||||
\end{mgraphbox}
|
||||
|
|
@ -0,0 +1,19 @@
|
|||
# Graph
|
||||
kruskals
|
||||
|
||||
A B C D E F G H
|
||||
|
||||
AB 1
|
||||
AC 2
|
||||
CD 3
|
||||
DE 4
|
||||
HA 5
|
||||
FD 6
|
||||
CB 7
|
||||
FG 8
|
||||
DE 9
|
||||
DG 10
|
||||
AH 11
|
||||
FB 12
|
||||
HC 13
|
||||
CH 14
|
||||
|
|
@ -95,6 +95,8 @@
|
|||
\verbatimInput{undirectedGraphToMatrix}
|
||||
|
||||
\verbatimDiagram{directedFromMatrix}
|
||||
|
||||
\verbatimInput{kruskals}
|
||||
|
||||
\section{Finite state automata}
|
||||
|
||||
|
|
|
|||
|
|
@ -17,7 +17,8 @@
|
|||
\contentsline {subsection}{\numberline {5.4}adjacency}{12}{subsection.5.4}%
|
||||
\contentsline {subsection}{\numberline {5.5}undirectedGraphToMatrix}{13}{subsection.5.5}%
|
||||
\contentsline {subsection}{\numberline {5.6}directedFromMatrix}{14}{subsection.5.6}%
|
||||
\contentsline {section}{\numberline {6}Finite state automata}{15}{section.6}%
|
||||
\contentsline {subsection}{\numberline {6.1}automata}{15}{subsection.6.1}%
|
||||
\contentsline {section}{\numberline {7}Raw python}{16}{section.7}%
|
||||
\contentsline {subsection}{\numberline {7.1}python}{16}{subsection.7.1}%
|
||||
\contentsline {subsection}{\numberline {5.7}kruskals}{15}{subsection.5.7}%
|
||||
\contentsline {section}{\numberline {6}Finite state automata}{17}{section.6}%
|
||||
\contentsline {subsection}{\numberline {6.1}automata}{17}{subsection.6.1}%
|
||||
\contentsline {section}{\numberline {7}Raw python}{18}{section.7}%
|
||||
\contentsline {subsection}{\numberline {7.1}python}{18}{subsection.7.1}%
|
||||
|
|
|
|||
Loading…
Reference in New Issue