图论Dijkstra Algorithm在2D空间平面网格节点图选择最短路径，networkx，Python

（1）Dijkstra Algorithm算法结束后，在代码生成的二维网格图中所有节点的权值即为出发点（源点）到当前节点的最短路径。本例中网格图中所有邻接边权值为1。

（2）通过每个节点中保存的parent指针一路逆行往上迭代查找，直到出发点（源点），即为出发点到当前节点的最短路径。parent指针指向了到当前节点的最短路径父节点。

（3）Dijkstra Algorithm寻路结束后，出发点（源点）到所有可达点的最短距离确定（weight值即为最短路径值）。从中可以得到启发，比如多人对战游戏，一张地图中同一时刻多人需要知道到达某汇聚点的路径，那么这种算法应用场景，Dijkstra Algorithm就很适合（反而A算法在这种应用场景不适合，因为A算法确定的是一个出发点到一个终点的路线。如果是N个人，就需要N次运行A*算法，才能为N个人完成选路），而Dijkstra Algorithm只需一次寻路，就完成所有地图中的点（某个点代表某个人的位置）到某个源点的最短距离。

（4）Dijkstra Algorithm在本例中作为一种广度优先搜索寻找最短路径，在每个节点中加入的parent指针，将其形成一定程度具有深度的寻路思想。这种思想在寻路算法中很普遍，在广度和深度的搜索过程中，通过埋入一个指针parent，可以快速找到出发点到源点的最短路径。

import random

import networkx as nx
import matplotlib.pyplot as plt

WALKABLE = 'walkable'
PARENT = 'parent'
WEIGHT = 'weight'

def my_graph():
    M = 7
    N = 9
    G = nx.grid_2d_graph(m=M, n=N)
    pos = nx.spring_layout(G, iterations=100)

    nx.draw_networkx(G, pos=pos,
                     # labels=labels, #labels = dict(((i, j), 'Phil') for i, j in G.nodes())
                     font_size=8,
                     font_color='white',
                     node_color='green',
                     node_size=500,
                     width=1)

    START = (1, 1)
    GOAL = (M - 1 - 1, N - 1 - 1)

    # 0,随机生成障碍物点
    # 1,精心挑选的障碍物构成陷阱
    OBSTACLE_MODE = 0
    road_closed_nodes = []

    if OBSTACLE_MODE == 0:
        obstacle_number = 20  # 障碍物（断点、不可达点）数量
        road_closed_nodes = obstacle_nodes(G, START, GOAL, obstacle_number, M, N)
    elif OBSTACLE_MODE == 1:
        road_closed_nodes = dummy_nodes(G)

    nx.draw_networkx_nodes(
        G, pos,
        nodelist=road_closed_nodes,
        node_size=500,
        node_color="red",
        node_shape="x",
        # alpha=0.3,
        label='x'
    )

    dijkstra_find_path(G, START, G.number_of_nodes() - len(road_closed_nodes))
    print('G.nodes(data=True) 更新节点权值后', G.nodes(data=True))
    path = find_path_by_parent(G, START, GOAL)
    print('path', path)

    nx.draw_networkx_nodes(
        G, pos,
        nodelist=path,
        node_size=400,
        node_color="red",
        node_shape='o',
        # alpha=0.3,
        # label='NO'
    )

    path_edges = []
    for i in range(len(path)):
        if (i + 1) == len(path):
            break
        path_edges.append((path[i], path[i + 1]))

    print('path_edges', path_edges)
    # 把path着色加粗重新描边
    nx.draw_networkx_edges(G, pos,
                           edgelist=path_edges,
                           width=8,
                           alpha=0.5,
                           edge_color="r")

    plt.axis('off')
    plt.show()

def dijkstra_find_path(G, START, valid_node_number):
    # 设置所有节点的权值为无穷大
    for n in G.nodes():
        G.nodes[n][WEIGHT] = float('inf')

    # 更新出发节点权重为0
    G.nodes[START][WEIGHT] = 0

    print('G.nodes(data=True)', G.nodes(data=True))

    print('起点', START)
    close_list = []

    vertex = START  # 顶点
    while True:
        print('-----')

        if len(close_list) == valid_node_number:
            print('搜索完毕')
            break

        update_weight_from_node(G, vertex, close_list)
        min_node = find_min_nodes(G, vertex, close_list)

        vertex = min_node[0]
        close_list.append(vertex)

def update_weight_from_node(G, cur_node, close_list):
    cur_node_weight = G.nodes[cur_node][WEIGHT]
    neighbors = nx.neighbors(G, cur_node)
    for child in neighbors:
        try:
            walkable = G.nodes[child][WALKABLE]
        except:
            walkable = True

        if (child in close_list) or (not walkable):
            continue

        edge_weight = 1  # 在本例的2D平面图中，邻接的边权都是1
        child_node_weight = G.nodes[child][WEIGHT]
        sum_weight = cur_node_weight + edge_weight
        if sum_weight < child_node_weight:
            G.nodes[child][WEIGHT] = sum_weight
            G.nodes[child][PARENT] = cur_node
            print('更新节点权值', cur_node, '->', child, '新权值为:', sum_weight)

def find_min_nodes(G, vertex, close_list):
    node_list = []
    for node in G.nodes(data=True):
        try:
            walkable = node[1][WALKABLE]
        except:
            walkable = True

        if walkable and (node[0] not in close_list) and (node[0] != vertex):
            node_list.append(node)

    min_node = min(node_list, key=lambda x: x[1][WEIGHT])
    print(vertex, '最小节点', min_node)

    return min_node

def find_path_by_parent(G, START, GOAL):
    t = GOAL
    path = [t]
    is_find = False
    while not is_find:
        for n in G.nodes(data=True):
            if n[0] == t:
                parent = n[1][PARENT]
                path.append(parent)

                if parent == START:
                    is_find = True
                    break

                t = parent

    list.reverse(path)
    return path

# 障碍物点
def obstacle_nodes(G, START, GOAL, obstacle, M, N):
    road_closed_nodes = []
    for i in range(obstacle):
        n = (random.randint(0, M - 1), random.randint(0, N - 1))
        if n == START or n == GOAL:
            continue
        if n in road_closed_nodes:
            continue

        G.nodes[n][WALKABLE] = False
        road_closed_nodes.append(n)

    return road_closed_nodes

def dummy_nodes(G):
    fun_nodes = []

    n0 = (1, 2)
    G.nodes[n0][WALKABLE] = False
    fun_nodes.append(n0)

    n1 = (1, 3)
    G.nodes[n1][WALKABLE] = False
    fun_nodes.append(n1)
    n2 = (1, 4)
    G.nodes[n2][WALKABLE] = False
    fun_nodes.append(n2)
    n3 = (1, 5)
    G.nodes[n3][WALKABLE] = False
    fun_nodes.append(n3)
    n4 = (1, 6)
    G.nodes[n4][WALKABLE] = False
    fun_nodes.append(n4)
    n5 = (2, 6)
    G.nodes[n5][WALKABLE] = False
    fun_nodes.append(n5)
    n6 = (3, 6)
    G.nodes[n6][WALKABLE] = False
    fun_nodes.append(n6)
    n7 = (4, 6)
    G.nodes[n7][WALKABLE] = False
    fun_nodes.append(n7)
    n8 = (5, 6)
    G.nodes[n8][WALKABLE] = False
    fun_nodes.append(n8)
    n9 = (5, 5)
    G.nodes[n9][WALKABLE] = False
    fun_nodes.append(n9)
    n10 = (5, 4)
    G.nodes[n10][WALKABLE] = False
    fun_nodes.append(n10)
    n11 = (5, 3)
    G.nodes[n11][WALKABLE] = False
    fun_nodes.append(n11)
    n12 = (5, 2)
    G.nodes[n12][WALKABLE] = False
    fun_nodes.append(n12)

    return fun_nodes

if __name__ == '__main__':
    my_graph()

运行几轮后的选路截图：

当把障碍物模式切换为1，即特意挑选一批点围成一个围墙，同时把出发点改为(2,2)，看看算法的表现：

算法聪明的规避了围墙，没有跳进凹形陷阱。