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102 lines
2.9 KiB
Python
102 lines
2.9 KiB
Python
import heapq
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import sys
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# First implementation of johnson algorithm
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# Steps followed to implement this algorithm is given in the below link:
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# https://brilliant.org/wiki/johnsons-algorithm/
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class JohnsonGraph:
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def __init__(self):
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self.edges = []
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self.graph = {}
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# add vertices for a graph
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def add_vertices(self, u):
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self.graph[u] = []
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# assign weights for each edges formed of the directed graph
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def add_edge(self, u, v, w):
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self.edges.append((u, v, w))
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self.graph[u].append((v, w))
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# perform a dijkstra algorithm on a directed graph
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def dijkstra(self, s):
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distances = {vertex: sys.maxsize - 1 for vertex in self.graph}
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pq = [(0, s)]
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distances[s] = 0
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while pq:
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weight, v = heapq.heappop(pq)
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if weight > distances[v]:
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continue
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for node, w in self.graph[v]:
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if distances[v] + w < distances[node]:
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distances[node] = distances[v] + w
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heapq.heappush(pq, (distances[node], node))
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return distances
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# carry out the bellman ford algorithm for a node and estimate its distance vector
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def bellman_ford(self, s):
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distances = {vertex: sys.maxsize - 1 for vertex in self.graph}
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distances[s] = 0
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for u in self.graph:
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for u, v, w in self.edges:
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if distances[u] != sys.maxsize - 1 and distances[u] + w < distances[v]:
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distances[v] = distances[u] + w
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return distances
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# perform the johnson algorithm to handle the negative weights that
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# could not be handled by either the dijkstra
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# or the bellman ford algorithm efficiently
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def johnson_algo(self):
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self.add_vertices("#")
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for v in self.graph:
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if v != "#":
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self.add_edge("#", v, 0)
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n = self.bellman_ford("#")
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for i in range(len(self.edges)):
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u, v, weight = self.edges[i]
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self.edges[i] = (u, v, weight + n[u] - n[v])
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self.graph.pop("#")
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self.edges = [(u, v, w) for u, v, w in self.edges if u != "#"]
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for u in self.graph:
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self.graph[u] = [(v, weight) for x, v, weight in self.edges if x == u]
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distances = []
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for u in self.graph:
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new_dist = self.dijkstra(u)
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for v in self.graph:
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if new_dist[v] < sys.maxsize - 1:
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new_dist[v] += n[v] - n[u]
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distances.append(new_dist)
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return distances
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g = JohnsonGraph()
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# this a complete connected graph
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g.add_vertices("A")
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g.add_vertices("B")
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g.add_vertices("C")
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g.add_vertices("D")
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g.add_vertices("E")
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g.add_edge("A", "B", 1)
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g.add_edge("A", "C", 3)
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g.add_edge("B", "D", 4)
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g.add_edge("D", "E", 2)
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g.add_edge("E", "C", -2)
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optimal_paths = g.johnson_algo()
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print("Print all optimal paths of a graph using Johnson Algorithm")
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for i, row in enumerate(optimal_paths):
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print(f"{i}: {row}")
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