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AndrewTrieu
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<!doctype html>
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<html>
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<head>
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<title>Week 9 Programming Assignments (8 points)</title>
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<meta charset="utf-8">
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</head>
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<body>
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<div>
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<h4><span>Assignment 9.1: Creating a Graph</span> <span style="font-weight: normal;">(4 points)</span><br></h4>
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</div>
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<div><span class="" style="color: rgb(239, 69, 64);"></span>Your task is to create a class <strong>Graph</strong> in python which stores a weighted directed or undirected graph structure. The initializer method takes a \(V \times V\) weighted adjacency matrix as an input value (\(V\) sized list of \(V\) sized lists).
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The class must have following methods:</div>
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<ul>
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<ul>
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<li><strong>df_print(start: int)</strong>: prints out the graph in depth-first order from the start vertex (vertex numbers separated by space).</li>
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<li><strong>bf_print(start: int)</strong>: prints out the graph in breadth-first order from the start vertex.</li>
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<li><strong>weight(vertex1: int, vertex2: int)</strong>: returns the weight from vertex1 to vertex2, returns -1 if there is no edge between the vertices.</li>
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</ul>
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</ul>
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<div>where start vertex is labeled between \(0\ ...\ V-1\).</div>
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<p></p>
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<div>Feel free to store the graph structure to your class as you wish as long as the given functions above work as intended. You can use the adjacency matrix
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or create a adjacency list to keep track of neighbors of each vertex (or even both).</div>
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<div><br>
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</div>
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<div><strong><span class="" style="background-color: rgb(255, 255, 255); color: rgb(239, 69, 64);">Note: </span></strong><span class="" style="background-color: rgb(255, 255, 255); color: rgb(239, 69, 64);">This graph class will be used in following assignments related to graphs so it is recommended to complete this assignment before moving to others.</span></div>
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<p></p>
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<div><span>A code template with an example program </span>for the directed graph below:</div>
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<p></p>
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<!-- Add other path in Moodle! --> <img src="data/examplegraph.png?time=1657884314459" alt="Example Graph" class="img-responsive atto_image_button_text-bottom" width="306" height="239">
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<p></p>
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<div style="border:2px solid black">
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<pre>class Graph:
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# TODO
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if __name__ == "__main__":
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matrix = [
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# 0 1 2 3 4 5
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[0, 0, 7, 0, 9, 0], # 0
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[0, 0, 0, 0, 0, 0], # 1
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[0, 5, 0, 1, 0, 2], # 2
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[6, 0, 0, 0, 0, 2], # 3
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[0, 0, 0, 0, 0, 1], # 4
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[0, 6, 0, 0, 0, 0] # 5
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]
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graph = Graph(matrix)
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graph.df_print(0) # 0 2 1 3 5 4
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graph.bf_print(0) # 0 2 4 1 3 5
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print(graph.weight(0, 2)) # 7
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print(graph.weight(3, 4)) # -1
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</pre>
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</div>
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<p></p>
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<div>Submit your solution in CodeGrade as <strong>graph.py</strong>.</div>
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<br>
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<br>
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<div>
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<h4><span><span>Assignment 9.2: Dijkstra's Algoritmh</span></span> <span style="font-weight: normal;">(4 points)</span><br></h4>
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</div>
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<div>With Dijkstra's algorithm we not only get the shortest paths from the start vertex to other vertices but we can build a new
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graph with only the arcs that constructs those paths.</div>
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<br>
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<div>Create a function <strong>dijkstragraph(graph: Graph, start: int)</strong> that takes a Graph object and the start vertex as an input value. The function
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returns a new Graph object that has only the arcs that constructs the shortest paths computed by Dijkstra's algorithm. The new graph will be directed despite
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whether the original graph was directed or undirected.</div>
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<br>
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<div>For example the on the left we have the original directed graph and on the right we have a graph that the function produces, starting from vertex \(0\).</div>
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<br>
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<p> <img src="data/dijkstra.png?time=1657884289742" alt="Example Graph" class="img-responsive atto_image_button_text-bottom" width="776" height="240">
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</p><br>
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<div><span>A code template with an example program </span>for the graph:</div>
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<br>
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<div style="border:2px solid black">
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<pre>from graph import Graph
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def dijkstragraph(graph, start):
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# TODO
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if __name__ == "__main__":
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matrix = [
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[0, 25, 6, 0, 0, 0, 0, 0, 0, 0],
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[0, 0, 0, 10, 3, 0, 0, 0, 0, 0],
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[0, 0, 0, 7, 0, 25, 0, 0, 0, 0],
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[0, 0, 0, 0, 12, 15, 4, 15, 20, 0],
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[0, 0, 0, 0, 0, 0, 0, 2, 0, 0],
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[0, 0, 0, 0, 0, 0, 0, 0, 2, 0],
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[0, 0, 0, 0, 0, 0, 0, 8, 13, 15],
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[0, 0, 0, 0, 0, 0, 0, 0, 0, 5],
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[0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
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[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
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]
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graph = Graph(matrix)
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new_graph = dijkstragraph(graph, 0)
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new_graph.df_print(0) # 0 1 2 3 4 5 6 7 9 8
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new_graph.bf_print(0) # 0 1 2 3 4 5 6 7 8 9
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print(new_graph.weight(3, 6)) # 4
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print(new_graph.weight(5, 8)) # -1
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</pre>
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</div>
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<br>
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<div>Submit your solution in CodeGrade as <strong>dijkstra.py</strong> including your graph class in <strong>graph.py</strong> (Assignment 9.1).</div>
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<br>
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<div>Hint: try to do the Dijkstra's algorithm and new graph construction separately. What other information can we get while running Dijkstra's algorithm?</div>
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</body>
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</html>
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class Graph:
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def __init__(self, adj_matrix):
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self.adj_matrix = adj_matrix
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self.V = len(adj_matrix)
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def df_print(self, start):
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visited = [False] * self.V
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self.dfs(start, visited)
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print()
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def dfs(self, start, visited):
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visited[start] = True
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print(start, end=' ')
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for i in range(self.V):
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if self.adj_matrix[start][i] > 0 and not visited[i]:
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self.dfs(i, visited)
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def bf_print(self, start):
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visited = [False] * self.V
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queue = []
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queue.append(start)
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visited[start] = True
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while queue:
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start = queue.pop(0)
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print(start, end=' ')
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for i in range(self.V):
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if self.adj_matrix[start][i] > 0 and not visited[i]:
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queue.append(i)
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visited[i] = True
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print()
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def weight(self, vertex1, vertex2):
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return self.adj_matrix[vertex1][vertex2] if self.adj_matrix[vertex1][vertex2] > 0 else -1
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if __name__ == "__main__":
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matrix = [
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# 0 1 2 3 4 5
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[0, 0, 7, 0, 9, 0], # 0
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[0, 0, 0, 0, 0, 0], # 1
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[0, 5, 0, 1, 0, 2], # 2
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[6, 0, 0, 0, 0, 2], # 3
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[0, 0, 0, 0, 0, 1], # 4
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[0, 6, 0, 0, 0, 0] # 5
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]
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graph = Graph(matrix)
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graph.df_print(0) # 0 2 1 3 5 4
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graph.bf_print(0) # 0 2 4 1 3 5
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print(graph.weight(0, 2)) # 7
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print(graph.weight(3, 4)) # -1
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