Created
June 13, 2012 18:43
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| import sys | |
| def shortestpath(graph,start,end,visited=[],distances={},predecessors={}): | |
| """Find the shortest path between start and end nodes in a graph""" | |
| # we've found our end node, now find the path to it, and return | |
| if start==end: | |
| path=[] | |
| while end != None: | |
| path.append(end) | |
| end=predecessors.get(end,None) | |
| return distances[start], path[::-1] | |
| # detect if it's the first time through, set current distance to zero | |
| if not visited: distances[start]=0 | |
| # process neighbors as per algorithm, keep track of predecessors | |
| for neighbor in graph[start]: | |
| if neighbor not in visited: | |
| neighbordist = distances.get(neighbor,sys.maxint) | |
| tentativedist = distances[start] + graph[start][neighbor] | |
| if tentativedist < neighbordist: | |
| distances[neighbor] = tentativedist | |
| predecessors[neighbor]=start | |
| # neighbors processed, now mark the current node as visited | |
| visited.append(start) | |
| # finds the closest unvisited node to the start | |
| unvisiteds = dict((k, distances.get(k,sys.maxint)) for k in graph if k not in visited) | |
| closestnode = min(unvisiteds, key=unvisiteds.get) | |
| # now we can take the closest node and recurse, making it current | |
| return shortestpath(graph,closestnode,end,visited,distances,predecessors) | |
| if __name__ == "__main__": | |
| graph = {'a': {'w': 14, 'x': 7, 'y': 9}, | |
| 'b': {'w': 9, 'z': 6}, | |
| 'w': {'a': 14, 'b': 9, 'y': 2}, | |
| 'x': {'a': 7, 'y': 10, 'z': 15}, | |
| 'y': {'a': 9, 'w': 2, 'x': 10, 'z': 11}, | |
| 'z': {'b': 6, 'x': 15, 'y': 11}} | |
| print shortestpath(graph,'a','b') | |
| """ | |
| Result: | |
| (20, ['a', 'y', 'w', 'b']) | |
| """ |
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