在问题81中,您只能向右或向下移动.因此,您的Dijkstra算法需要一个有向图.如果您将字典用作图,则该字典中的每个值(列表)都不得超过2个节点(您只能在2个方向上移动-> 2个邻居).您可以删除@AustinHastings的最后一段代码中的前两个if块.否则,您将向四个方向移动,并且将获得不同的结果.这是问题81中示例的解决方案.我使用了networkx和jupyter notebook软件包：
import networkx as nx
import numpy as np
import collections
a = np.matrix("""131 673 234 103 18;
201 96 342 965 150;
630 803 746 422 111;
537 699 497 121 956;
805 732 524 37 331""")
rows, columns = a.shape
# Part of @AustinHastings solution
graph = collections.defaultdict(list)
for r in range(rows):
for c in range(columns):
if c < columns - 1:
# get the right neighbor
graph[(r, c)].append((r, c+1))
if r < rows - 1:
# get the bottom neighbor
graph[(r, c)].append((r+1, c))
G = nx.from_dict_of_lists(graph, create_using=nx.DiGraph)
weights = {(row, col): {'weight': num} for row, r in enumerate(a.tolist()) for col, num in enumerate(r)}
nx.set_node_attributes(G, values=weights)
def weight(u, v, d):
return G.nodes[u].get('weight')/2 + G.nodes[v].get('weight')/2
target = tuple(i - 1 for i in a.shape)
path = nx.dijkstra_path(G, source=(0, 0), target=target, weight=weight)
print('Path: ', [a.item(i) for i in path])
%matplotlib inline
color_map = ['green' if n in path else 'red' for n in G.nodes()]
labels = nx.get_node_attributes(G, 'weight')
pos = {(r, c): (c, -r) for r, c in G.nodes()}
nx.draw(G, pos=pos, with_labels=True, node_size=1500, labels = labels, node_color=color_map)
输出：
Path: [131, 201, 96, 342, 746, 422, 121, 37, 331]
