截断切割图论

权值 33.75 20
30
20
12
9
58 40 58
弧 20,23 21,24 22,23 22,25 23,24 23,26 24,27 25,26 26,27
权值 16
12 30 40 30 16
12
8
8
弧 权值
弧 权值
弧 权值
弧 权值
弧 权值
弧 权值
1,2 275.5
4,7 190 8,9 38 12,15 30 15,24 180 20,23 16
87
57 65.25 142.5
弧 4,7 4,13 5,6 5,8 5,14 6,9 6,15 7,8 7,16
权值 190 112.5 142.5 76
45
57 33.75 38
30
弧 8,9 8,17 9,18 10,11 10,13 10,19 11,12 11,14 11,20
权值 38
12
#r=1,e=0
edge_length1 = [ 275.5,190,145,275.5,76,58, 57,
43.5,142.5,
190,75,142.5,76,30,57,22.5,38,20,
38,8,6,145,100,145,145,40,58,
30,43.5,75,100,75,75,40,30,30,
plt.show()
编程实现——Python代码（r=1.5,e=2）
import networkx as nx
graph = nx.DiGraph() nodes_list = [i for i in range(1,28)] edges_list=[(1,2),(1,4),(1,10),(2,3),(2,5),(2,11),(3,6),(3,12),(4,5), (4,7),(4,13),(5,6),(5,8),(5,14),(6,9),(6,15),(7,8),(7,16), (8,9),(8,17),(9,18),(10,11),(10,13),(10,19),(11,12),(11,14),(11,20), (12,15),(12,21),(13,14),(13,16),(13,22),(14,15),(14,17),(14,23),(1 5,18), (15,24),(16,17),(16,25),(17,18),(17,26),(18,27),(19,20),(19,22),(2 0,21), (20,23),(21,24),(22,23),(22,25),(23,24),(23,26),(24,27),(25,26),(2 6,27)]
1,4 190 4,13 600 8,17 64 12,21 34.8 16,17 20 21,24 12
1,10 1160 5,6 142.5 9,18 48 13,14 75 16,25 160 22,23 30
2,3 275.5
5,8 76 10,11 145 13,16 100 17,18 20 22,25 40
p = nx.shortest_path(graph,source=1,target=27,weight='weight') d = nx.shortest_path_length(graph, source=1,target=27,weight='weight') print("r=1,e=0:") print("V1到 V27 的最短路径为:", p) print("V1到 V27的最短距离为:", d) p2 = nx.shortest_path(graph2,source=1,target=27,weight='weight') d2 = nx.shortest_path_length(graph2, source=1,target=27,weight='weight') print("r=1.5,e=0:") print("V1到 V27 的最短路径为:", p2) print("V1到 V27的最短距离为:", d2) p3 = nx.shortest_path(graph3,source=1,target=27,weight='weight') d3 = nx.shortest_path_length(graph3, source=1,target=27,weight='weight') print("r=8,e=0:") print("V1到 V27 的最短路径为:", p3) print("V1到 V27的最短距离为:", d3) #边和节点信息 node_name=['v'+str(i) for i in range(1,28)] labels=dict({i+1:node_name[i] for i in range(27)}) #生成节点位置 pos=nx.spring_layout(graph) #把节点画出来 nx.draw_networkx_nodes(graph,pos,node_color='g',node_size=500,alpha=0.8) #把边画出来 nx.draw_networkx_edges(graph,pos,width=1.0,alpha=0.5,edge_color='b') #把节点的标签画出来 nx.draw_networkx_labels(graph,pos,labels,font_color='w')
(12,15),(12,21),(13,14),(13,16),(13,22),(14,15),(14,17),(14,23),(15,18),
(15,24),(16,17),(16,25),(17,18),(17,26),(18,27),(19,20),(19,22),(20,21),
(20,23),(21,24),(22,23),(22,25),(23,24),(23,26),(24,27),(25,26),(26,27)]
权值 275.5 190 145 275.5 76
58
57 43.5 142.5
弧 4,7 4,13 5,6 5,8 5,14 6,9 6,15 7,8 7,16
权值 190 75 142.5 76
30
57 22.5 38
20
弧 8,9 8,17 9,18 10,11 10,13 10,19 11,12 11,14 11,20
2,5 76 5,14 240 10,13 100 13,22 600 17,26 64 23,24 30
2,11 464 6,9 57 10,19 1160 14,15 75 18,27 48 23,26 16
3,6 57 6,15 180 11,12 145 14,17 40 19,20 58 24,27 12
V10 (10,14.5,10) V11 (4,14.5,10) V12 (3,14.5,10) V13(10, 7.5,10) V14 (4, 7.5,10) V15 (3, 7.5,10) V16 (10, 2,10)
V17 (4, 2,10) V18 (3, 2,10)
V19 (10,14.5, 4) V20 (4,14.5, 4) V21(3,14.5, 4) V22 (10, 7.5, 4) V23 (4, 7.5, 4) V24 (3, 7.5, 4) V25 (10, 2, 4)
edges_list=[(1,2),(1,4),(1,10),(2,3),(2,5),(2,11),(3,6),(3,12),(4,5),
(4,7),(4,13),(5,6),(5,8),(5,14),(6,9),(6,15),(7,8),(7,16),
(8,9),(8,17),(9,18),(10,11),(10,13),(10,19),(11,12),(11,14),(11,20),
38,12,9,145,100,217.5,145,40,87,
30,65.25,75,100,112.5,75,40,45,30,
33.75,20,30,20,12,9,58,40,58,
16,12,30,40,30,16,12,8,8]
#r=8,e=0
edge_length3=[275.5,190,1160,275.5,76,464,57,248,142.5,
编程实现——Python代码（e=0）
for n in nodes_list: graph.add_node(n) graph2.add_node(n) graph3.add_node(n)
for i, e in enumerate(edges_list): graph.add_edge(*e, weight = edge_length1[i]) graph2.add_edge(*e, weight = edge_length2[i]) graph3.add_edge(*e, weight = edge_length3[i])
有向路路径 (0,1, z) (0, 2, z) (1, 2, z) (2, 2, z) (1,0, z) (2,0, z) (2,1, z) (2, 2, z) (0,1, z) (1,1, z) (2,1, z) (2, 2, z) (1,0, z) (1,1, z) (1, 2, z) (2, 2, z) (0,1, z) (1,1,0) (1, 2, z) (2, 2, z) (1,0, z) (1,1, z) (2,1, z) (2, 2, z)
9 145 100 217.5 145 40 87
弧 12,15 12,21 13,14 13,16 13,22 14,15 14,17 14,23 15,18
权值 30 65.25 75 100 112.5 75
40
45
30
弧 15,24 16,17 16,25 17,18 17,26 18,27 19,20 19,22 20,21
[1, 10, 13, 14, 23, 26, 27] [u5,u3,u1,u6,u4,u2]
各顶点的剩余长方体的长、宽、高。
V1(10,14.5,19) V2 (4,14.5,19) V3 (3,14.5,19) V4 (10, 7.5,19)
V5 (4, 7.5,19) V6 (3, 7.5,19) V7 (10, 2,19) V8 (4, 2,19) V9 (3, 2,19)
22.5,20,20,20,8,6,58,40,58,
16,12,30,40,30,16,12,8,8 ]
#r=1.5,e=0
edge_length2 = [ 275.5,190,217.5,275.5,76,87,57,65.25,142.5,
190,112.5,142.5,76,45,57,33.75,38,30,
编程实现——Python代码（e=0）
import networkx as nx import matplotlib.pyplot as plt
graph = nx.DiGraph()
graph2=nx.DiGraph()
graph3=nx.DiGraph()
nodes_list = [i for i in range(1,28)]
190,600,142.5,76,240,57,180,38,160,
38,64,48,145,100,1160,145,40,46.4,
30,34.8,75,100,600,75,40,200,30,
180,20,160,20,64,48,58,40,58,
16,12,30,40,30,16,12,8,8]
3,12 248 7,8 38 11,14 40 14,23 200 19,22 40 25,26
8
4,5 142.5 7,16 160 11,20 46.4 15,18
30 20,21
58 26,27
8
来自百度文库
垂直切割的顺序安排可分为6种情况，如下表所示：
垂直切割顺序 M1 M2 M3 M4 M3 M4 M1 M2 M1 M3 M4 M2 M3 M1 M2 M4 M1 M3 M2 M4 M3 M1 M4 M2
权值 38
8
6
145 100 145 145 40
58
弧 12,15 12,21 13,14 13,16 13,22 14,15 14,17 14,23 15,18
权值 30 43.5 75 100 75
75
40
30
30
弧 15,24 16,17 16,25 17,18 17,26 18,27 19,20 19,22 20,21
权值 22.5 20
20
20
8
6
58
40
58
弧 20,23 21,24 22,23 22,25 23,24 23,26 24,27 25,26 26,27
权值 16
12
30
40
30
16
12
8
8
弧 1,2 1,4 1,10 2,3 2,5 2,11 3,6 3,12 4,5
权值 275.5 190 217.5 275.5 76
V26 (4, 2, 4) V27 (3, 2, 4)
sj,k bj cj p sj,k aj cj p s j,k (a j bj ) pr
(k j 1) (k j 3) (k j 9)
弧 1,2 1,4 1,10 2,3 2,5 2,11 3,6 3,12 4,5