迪克斯特拉'；python中的s算法

我试图使用数组在python中实现Dijkstra的算法。这是我的实现

def extract(Q, w):
    m=0
    minimum=w[0]
    for i in range(len(w)):
        if w[i]<minimum:
            minimum=w[i]
            m=i
    return m, Q[m]

def dijkstra(G, s, t='B'):
    Q=[s]
    p={s:None}
    w=[0]
    d={}
    for i in G:
        d[i]=float('inf')
        Q.append(i)
        w.append(d[i])
    d[s]=0
    S=[]
    n=len(Q)
    while Q:
        u=extract(Q,w)[1]
        S.append(u)
        #w.remove(extract(Q, d, w)[0])
        Q.remove(u)
        for v in G[u]:
            if d[v]>=d[u]+G[u][v]:
                d[v]=d[u]+G[u][v]
                p[v]=u
    return d, p

B='B'
A='A'
D='D'
G='G'
E='E'
C='C'
F='F'
G={B:{A:5, D:1, G:2}, A:{B:5, D:3, E:12, F:5}, D:{B:1, G:1, E:1, A:3}, G:{B:2, D:1, C:2}, C:{G:2, E:1, F:16}, E:{A:12, D:1, C:1, F:2}, F:{A:5, E:2, C:16}}
print "Assuming the start vertex to be B:"
print "Shortest distances", dijkstra(G, B)[0]
print "Parents", dijkstra(G, B)[1]

然而，我得到的答案是：

Assuming the start vertex to be B:
Shortest distances {'A': 4, 'C': 4, 'B': 0, 'E': 2, 'D': 1, 'G': 2, 'F': 10}
Parents {'A': 'D', 'C': 'G', 'B': None, 'E': 'D', 'D': 'B', 'G': 'D', 'F': 'A'}.

---

对于节点F，程序给出了不正确的答案。有人能告诉我为什么吗？

正如其他人所指出的，由于没有使用可理解的变量名，调试代码几乎是不可能的

import sys
import heapq

class Node:

     def __init__(self, name):
        self.name = name
        self.visited = False
        self.adjacenciesList = []
        self.predecessor = None
        self.mindistance = sys.maxsize    

    def __lt__(self, other):
        return self.mindistance < other.mindistance

class Edge:

    def __init__(self, weight, startvertex, endvertex):
        self.weight = weight
        self.startvertex = startvertex
        self.endvertex = endvertex

def calculateshortestpath(vertexlist, startvertex):
    q = []
    startvertex.mindistance = 0
    heapq.heappush(q, startvertex)

    while q:
        actualnode = heapq.heappop(q)
        for edge in actualnode.adjacenciesList:
            tempdist = edge.startvertex.mindistance + edge.weight
            if tempdist < edge.endvertex.mindistance:
                edge.endvertex.mindistance = tempdist
                edge.endvertex.predecessor = edge.startvertex
                heapq.heappush(q,edge.endvertex)
def getshortestpath(targetvertex):
    print("The value of it's minimum distance is: ",targetvertex.mindistance)
    node = targetvertex
    while node:
        print(node.name)
        node = node.predecessor

node1 = Node("A");
node2 = Node("B");
node3 = Node("C");
node4 = Node("D");
node5 = Node("E");
node6 = Node("F");
node7 = Node("G");
node8 = Node("H");

edge1 = Edge(5,node1,node2);
edge2 = Edge(8,node1,node8);
edge3 = Edge(9,node1,node5);
edge4 = Edge(15,node2,node4);
edge5 = Edge(12,node2,node3);
edge6 = Edge(4,node2,node8);
edge7 = Edge(7,node8,node3);
edge8 = Edge(6,node8,node6);
edge9 = Edge(5,node5,node8);
edge10 = Edge(4,node5,node6);
edge11 = Edge(20,node5,node7);
edge12 = Edge(1,node6,node3);
edge13 = Edge(13,node6,node7);
edge14 = Edge(3,node3,node4);
edge15 = Edge(11,node3,node7);
edge16 = Edge(9,node4,node7);

node1.adjacenciesList.append(edge1);
node1.adjacenciesList.append(edge2);
node1.adjacenciesList.append(edge3);
node2.adjacenciesList.append(edge4);
node2.adjacenciesList.append(edge5);
node2.adjacenciesList.append(edge6);
node8.adjacenciesList.append(edge7);
node8.adjacenciesList.append(edge8);
node5.adjacenciesList.append(edge9);
node5.adjacenciesList.append(edge10);
node5.adjacenciesList.append(edge11);
node6.adjacenciesList.append(edge12);
node6.adjacenciesList.append(edge13);
node3.adjacenciesList.append(edge14);
node3.adjacenciesList.append(edge15);
node4.adjacenciesList.append(edge16);

vertexlist = (node1,node2,node3,node4,node5,node6,node7,node8)

calculateshortestpath(vertexlist,node1)
getshortestpath(node7)

在关于Dijkstra算法的wiki文章之后，我们可以按照以下思路（以及无数其他方式）实现它：

这段代码过于冗长，我希望通过比较您的代码和我的代码，您可能会发现一些差异

结果是：

{'E': 2, 'D': 1, 'G': 2, 'F': 4, 'A': 4, 'C': 3, 'B': 0}

---

这不是我的答案——我的教授比我的尝试更有效率。这是他的方法，显然是对重复性任务使用帮助函数

def dijkstra(graph, source):

    vertices, edges = graph
    dist = dict()
    previous = dict()

    for vertex in vertices:
        dist[vertex] = float("inf")
        previous[vertex] = None

    dist[source] = 0
    Q = set(vertices)

    while len(Q) > 0:
        u = minimum_distance(dist, Q)
        print('Currently considering', u, 'with a distance of', dist[u])
        Q.remove(u)

        if dist[u] == float('inf'):
            break

        n = get_neighbours(graph, u)
        for vertex in n:
            alt = dist[u] + dist_between(graph, u, vertex)
            if alt < dist[vertex]:
                dist[vertex] = alt
                previous[vertex] = u

    return previous

def dijkstra（图表，来源）：
顶点，边=图
dist=dict（）
previous=dict（）
对于顶点中的顶点：
距离[顶点]=浮点（“inf”）
上一个[顶点]=无
距离[源]=0
Q=集合（顶点）
当len（Q）>0时：
u=最小距离（距离，Q）
打印（'当前考虑'，u'，距离'，dist[u]）
Q.删除（u）
如果dist[u]==float（'inf'）：
打破
n=获取邻域（图，u）
对于n中的顶点：
alt=dist[u]+dist_之间（图形、u、顶点）
如果alt<距离[顶点]：
距离[顶点]=高度
上一个[顶点]=u
返回上一个

给出一个图表

（{'A'，'B'，'C'，'D'}，{'A'，'B'，5），（'B'，'A'，5），（'B'，'C'，10），（'B'，'D'，6），（'C'，'D'，2），（'D'，'C'，2）}）

命令

print（dijkstra（图形'A'）

产生

当前正在考虑距离为0的

目前正在考虑距离为5的B

目前正在考虑距离为11的D

目前正在考虑距离为13的C

id est:

{'C'：'D'，'D'：'B'，'A'：无，'B'：'A'}=>按随机顺序排列

---

为了让新手更清楚，我用了一种更详细的形式：

def get_parent(pos):
    return (pos + 1) // 2 - 1


def get_children(pos):
    right = (pos + 1) * 2
    left = right - 1
    return left, right


def swap(array, a, b):
    array[a], array[b] = array[b], array[a]


class Heap:

    def __init__(self):
        self._array = []

    def peek(self):
        return self._array[0] if self._array else None

    def _get_smallest_child(self, parent):
        return min([
            it
            for it in get_children(parent)
            if it < len(self._array)
        ], key=lambda it: self._array[it], default=-1)

    def _sift_down(self):
        parent = 0
        smallest = self._get_smallest_child(parent)
        while smallest != -1 and self._array[smallest] < self._array[parent]:
            swap(self._array, smallest, parent)
            parent, smallest = smallest, self._get_smallest_child(smallest)

    def pop(self):
        if not self._array:
            return None
        swap(self._array, 0, len(self._array) - 1)
        node = self._array.pop()
        self._sift_down()
        return node

    def _sift_up(self):
        index = len(self._array) - 1
        parent = get_parent(index)
        while parent != -1 and self._array[index] < self._array[parent]:
            swap(self._array, index, parent)
            index, parent = parent, get_parent(parent)

    def add(self, item):
        self._array.append(item)
        self._sift_up()

    def __bool__(self):
        return bool(self._array)


def backtrack(best_parents, start, end):
    if end not in best_parents:
        return None
    cursor = end
    path = [cursor]
    while cursor in best_parents:
        cursor = best_parents[cursor]
        path.append(cursor)
        if cursor == start:
            return list(reversed(path))
    return None


def dijkstra(weighted_graph, start, end):
    """
    Calculate the shortest path for a directed weighted graph.

    Node can be virtually any hashable datatype.

    :param start: starting node
    :param end: ending node
    :param weighted_graph: {"node1": {"node2": weight, ...}, ...}
    :return: ["START", ... nodes between ..., "END"] or None, if there is no
            path
    """
    distances = {i: float("inf") for i in weighted_graph}
    best_parents = {i: None for i in weighted_graph}

    to_visit = Heap()
    to_visit.add((0, start))
    distances[start] = 0

    visited = set()

    while to_visit:
        src_distance, source = to_visit.pop()
        if src_distance > distances[source]:
            continue
        if source == end:
            break
        visited.add(source)
        for target, distance in weighted_graph[source].items():
            if target in visited:
                continue
            new_dist = distances[source] + weighted_graph[source][target]
            if distances[target] > new_dist:
                distances[target] = new_dist
                best_parents[target] = source
                to_visit.add((new_dist, target))

    return backtrack(best_parents, start, end)

def get_父项（pos）：
返回（位置+1）//2-1
def get_儿童（pos）：
右=（位置+1）*2
左=右-1
向左、向右返回
def交换（阵列、a、b）：
数组[a]，数组[b]=数组[b]，数组[a]
类堆：
定义初始化（自）：
self.\u数组=[]
def peek（自）：
返回self.\u数组[0]如果self.\u数组其他无
定义获取最小的子项（自身、父项）：
返回最小值([
信息技术
在get_children（家长）中为其设置
如果它距离[源]：
持续
如果源==结束：
打破
已访问。添加（源）
对于目标，加权图[source]中的距离。项（）
如果访问了目标：
持续
新距离=距离[源]+加权图[源][目标]
如果距离[目标]>新距离：
距离[目标]=新距离
最佳父母[目标]=来源
添加（（新地区，目标））
返回回溯（最佳父母，开始，结束）

在extract中设置一个断点。您将看到您从Q中删除了条目，但从未从w中删除。其他所有内容都是dict，但Q/w是一个配对数组，您无法保持最新。您必须保持这两个数组的同步，或用dict替换它们。特别注意：最后，在算法运行后，您可能希望用li替换Q/wst的边缘和重新编码的“提取”功能与优先队列（heapq模块）

此外，您将看到，对于源，w的权重始终为0，对于所有其他节点，w的权重始终为“inf”。您完全跳过了更新候选距离的关键步骤

因此，您基本上总是选择遇到的第一条路径，而不是选择最短路径

def get_parent(pos):
    return (pos + 1) // 2 - 1


def get_children(pos):
    right = (pos + 1) * 2
    left = right - 1
    return left, right


def swap(array, a, b):
    array[a], array[b] = array[b], array[a]


class Heap:

    def __init__(self):
        self._array = []

    def peek(self):
        return self._array[0] if self._array else None

    def _get_smallest_child(self, parent):
        return min([
            it
            for it in get_children(parent)
            if it < len(self._array)
        ], key=lambda it: self._array[it], default=-1)

    def _sift_down(self):
        parent = 0
        smallest = self._get_smallest_child(parent)
        while smallest != -1 and self._array[smallest] < self._array[parent]:
            swap(self._array, smallest, parent)
            parent, smallest = smallest, self._get_smallest_child(smallest)

    def pop(self):
        if not self._array:
            return None
        swap(self._array, 0, len(self._array) - 1)
        node = self._array.pop()
        self._sift_down()
        return node

    def _sift_up(self):
        index = len(self._array) - 1
        parent = get_parent(index)
        while parent != -1 and self._array[index] < self._array[parent]:
            swap(self._array, index, parent)
            index, parent = parent, get_parent(parent)

    def add(self, item):
        self._array.append(item)
        self._sift_up()

    def __bool__(self):
        return bool(self._array)


def backtrack(best_parents, start, end):
    if end not in best_parents:
        return None
    cursor = end
    path = [cursor]
    while cursor in best_parents:
        cursor = best_parents[cursor]
        path.append(cursor)
        if cursor == start:
            return list(reversed(path))
    return None


def dijkstra(weighted_graph, start, end):
    """
    Calculate the shortest path for a directed weighted graph.

    Node can be virtually any hashable datatype.

    :param start: starting node
    :param end: ending node
    :param weighted_graph: {"node1": {"node2": weight, ...}, ...}
    :return: ["START", ... nodes between ..., "END"] or None, if there is no
            path
    """
    distances = {i: float("inf") for i in weighted_graph}
    best_parents = {i: None for i in weighted_graph}

    to_visit = Heap()
    to_visit.add((0, start))
    distances[start] = 0

    visited = set()

    while to_visit:
        src_distance, source = to_visit.pop()
        if src_distance > distances[source]:
            continue
        if source == end:
            break
        visited.add(source)
        for target, distance in weighted_graph[source].items():
            if target in visited:
                continue
            new_dist = distances[source] + weighted_graph[source][target]
            if distances[target] > new_dist:
                distances[target] = new_dist
                best_parents[target] = source
                to_visit.add((new_dist, target))

    return backtrack(best_parents, start, end)

import sys
import heapq

class Node:

     def __init__(self, name):
        self.name = name
        self.visited = False
        self.adjacenciesList = []
        self.predecessor = None
        self.mindistance = sys.maxsize    

    def __lt__(self, other):
        return self.mindistance < other.mindistance

class Edge:

    def __init__(self, weight, startvertex, endvertex):
        self.weight = weight
        self.startvertex = startvertex
        self.endvertex = endvertex

def calculateshortestpath(vertexlist, startvertex):
    q = []
    startvertex.mindistance = 0
    heapq.heappush(q, startvertex)

    while q:
        actualnode = heapq.heappop(q)
        for edge in actualnode.adjacenciesList:
            tempdist = edge.startvertex.mindistance + edge.weight
            if tempdist < edge.endvertex.mindistance:
                edge.endvertex.mindistance = tempdist
                edge.endvertex.predecessor = edge.startvertex
                heapq.heappush(q,edge.endvertex)
def getshortestpath(targetvertex):
    print("The value of it's minimum distance is: ",targetvertex.mindistance)
    node = targetvertex
    while node:
        print(node.name)
        node = node.predecessor

node1 = Node("A");
node2 = Node("B");
node3 = Node("C");
node4 = Node("D");
node5 = Node("E");
node6 = Node("F");
node7 = Node("G");
node8 = Node("H");

edge1 = Edge(5,node1,node2);
edge2 = Edge(8,node1,node8);
edge3 = Edge(9,node1,node5);
edge4 = Edge(15,node2,node4);
edge5 = Edge(12,node2,node3);
edge6 = Edge(4,node2,node8);
edge7 = Edge(7,node8,node3);
edge8 = Edge(6,node8,node6);
edge9 = Edge(5,node5,node8);
edge10 = Edge(4,node5,node6);
edge11 = Edge(20,node5,node7);
edge12 = Edge(1,node6,node3);
edge13 = Edge(13,node6,node7);
edge14 = Edge(3,node3,node4);
edge15 = Edge(11,node3,node7);
edge16 = Edge(9,node4,node7);

node1.adjacenciesList.append(edge1);
node1.adjacenciesList.append(edge2);
node1.adjacenciesList.append(edge3);
node2.adjacenciesList.append(edge4);
node2.adjacenciesList.append(edge5);
node2.adjacenciesList.append(edge6);
node8.adjacenciesList.append(edge7);
node8.adjacenciesList.append(edge8);
node5.adjacenciesList.append(edge9);
node5.adjacenciesList.append(edge10);
node5.adjacenciesList.append(edge11);
node6.adjacenciesList.append(edge12);
node6.adjacenciesList.append(edge13);
node3.adjacenciesList.append(edge14);
node3.adjacenciesList.append(edge15);
node4.adjacenciesList.append(edge16);

vertexlist = (node1,node2,node3,node4,node5,node6,node7,node8)

calculateshortestpath(vertexlist,node1)
getshortestpath(node7)

import heapq as hq
import math

def dijkstra(G, s):
    n = len(G)
    visited = [False]*n
    weights = [math.inf]*n
    path = [None]*n
    queue = []
    weights[s] = 0
    hq.heappush(queue, (0, s))
    while len(queue) > 0:
        g, u = hq.heappop(queue)
        visited[u] = True
        for v, w in G[u]:
            if not visited[v]:
                f = g + w
                if f < weights[v]:
                    weights[v] = f
                    path[v] = u
                    hq.heappush(queue, (f, v))
    return path, weights

G = [[(1, 6), (3, 7)],
     [(2, 5), (3, 8), (4, -4)],
     [(1, -2), (4, 7)],
     [(2, -3), (4, 9)],
     [(0, 2)]]

print(dijkstra(G, 0))

import sys
def shortestpath(graph,start,end,visited=[],distances={},predecessors={}):
    """Find the shortest path btw start & end nodes in a graph"""
    # detect if first time through, set current distance to zero
    if not visited: distances[start]=0
    # if we've found our end node, 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]
    # 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 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','a')
    print shortestpath(graph,'a','b')
    """
    Expected Result:
        (0, ['a']) 
        (20, ['a', 'y', 'w', 'b'])
        """

import heapq

def dijkstra(g, s, t):

    q = []
    d = {k: sys.maxint for k in g.keys()}
    p = {}

    d[s] = 0 
    heapq.heappush(q, (0, s))

    while q:
        last_w, curr_v = heapq.heappop(q)
        for n, n_w in g[curr_v]:
            cand_w = last_w + n_w # equivalent to d[curr_v] + n_w 
            # print d # uncomment to see how deltas are updated
            if cand_w < d[n]:
                d[n] = cand_w
                p[n] = curr_v
                heapq.heappush(q, (cand_w, n))

    print "predecessors: ", p 
    print "delta: ", d 
    return d[t]

def test():

    og = {}
    og["s"] = [("t", 10), ("y", 5)]
    og["t"] = [("y", 2), ("x", 1)]
    og["y"] = [("t", 3), ("x", 9), ("z", 2)]
    og["z"] = [("x", 6), ("s", 7)]
    og["x"] = [("z", 4)]

    assert dijkstra(og, "s", "x") == 9 


if __name__ == "__main__":
    test()

Distance from B to C is: 3.00
Path from B to C is: B -> D -> E -> C