python et le calcul du chemin le plus court

un petit bout de code bien sympathique pour calculer le chemin le plus court entre deux points via une matrice d’évaluation des distances et l’algo de Dijkstra.

En gros on donne une valeur pour la distance entre 2 points (A -> B a une valeur, B -> A en a une autre) Puis on lance le calcul

# file
# Priority dictionary using binary heaps
# David Eppstein, UC Irvine, 8 Mar 2002
# extract on

from __future__ import generators

class priorityDictionary(dict):
    def __init__(self):
        '''Initialize priorityDictionary by creating binary heap
        of pairs (value,key).  Note that changing or removing a dict entry will
        not remove the old pair from the heap until it is found by smallest() or
        until the heap is rebuilt.'''
        self.__heap = []

    def smallest(self):
        '''Find smallest item after removing deleted items from heap.'''
        if len(self) == 0:
            raise IndexError, "smallest of empty priorityDictionary"
        heap = self.__heap
        while heap[0][1] not in self or self[heap[0][1]] != heap[0][0]:
            lastItem = heap.pop()
            insertionPoint = 0
            while 1:
                smallChild = 2*insertionPoint+1
                if smallChild+1 < len(heap) and \
                        heap[smallChild] > heap[smallChild+1]:
                    smallChild += 1
                if smallChild >= len(heap) or lastItem <= heap[smallChild]:
                    heap[insertionPoint] = lastItem
                heap[insertionPoint] = heap[smallChild]
                insertionPoint = smallChild
        return heap[0][1]

    def __iter__(self):
        '''Create destructive sorted iterator of priorityDictionary.'''
        def iterfn():
            while len(self) > 0:
                x = self.smallest()
                yield x
                del self[x]
        return iterfn()

    def __setitem__(self,key,val):
        '''Change value stored in dictionary and add corresponding
        pair to heap.  Rebuilds the heap if the number of deleted items grows
        too large, to avoid memory leakage.'''
        heap = self.__heap
        if len(heap) > 2 * len(self):
            self.__heap = [(v,k) for k,v in self.iteritems()]
            self.__heap.sort()  # builtin sort likely faster than O(n) heapify
            newPair = (val,key)
            insertionPoint = len(heap)
            while insertionPoint > 0 and \
                    newPair < heap[(insertionPoint-1)//2]:
                heap[insertionPoint] = heap[(insertionPoint-1)//2]
                insertionPoint = (insertionPoint-1)//2
            heap[insertionPoint] = newPair

    def setdefault(self,key,val):
        '''Reimplement setdefault to call our customized __setitem__.'''
        if key not in self:
            self[key] = val
        return self[key]

# file
# Dijkstra's algorithm for shortest paths
# David Eppstein, UC Irvine, 4 April 2002
# extract on

from priodict import priorityDictionary

def Dijkstra(G,start,end=None):
            D = {}  # dictionary of final distances
    P = {}  # dictionary of predecessors
    Q = priorityDictionary()   # est.dist. of non-final vert.
    Q[start] = 0

    for v in Q:
        D[v] = Q[v]
        if v == end: break

        for w in G[v]:
            vwLength = D[v] + G[v][w]
            if w in D:
                if vwLength < D[w]:
                    raise ValueError, \
"Dijkstra: found better path to already-final vertex"
            elif w not in Q or vwLength < Q[w]:
                Q[w] = vwLength
                P[w] = v

    return (D,P)

def shortestPath(G,start,end):
    Find a single shortest path from the given start vertex
    to the given end vertex.
    The input has the same conventions as Dijkstra().
    The output is a list of the vertices in order along
    the shortest path.

    D,P = Dijkstra(G,start,end)
    Path = []
    while 1:
        if end == start: break
        end = P[end]
    return Path

if __name__ == "__main__":
    #G = {'s':{'u':10, 'x':5}, 'u':{'v':1, 'x':2}, 'v':{'y':4}, 'x':{'u':3, 'v':9, 'y':2},
    # 'y':{'s':7, 'v':6}, 'w':{}}
    #print shortestPath(G,'s','w')
    G = {'MSK100':{'MPLIE':1, 'MPSFT':1, 'MPCLG':1,'MRE100':1},
        'MRE100':{'MSK100':1, 'MPDSC':1,'MMO100':1, 'MPCLG2':1, 'MPCCP':1, 'MPFCO':1},
        'MMO100':{'MPCLT':1, 'MPPLA':1},
    print shortestPath(G,'MSK100','MPPLA')