3.8 圖3.28是五個城市的交通圖,城市之間的連線旁邊的數字是城市之間路程的費用。要求從A城出發,通過其餘各城一次僅且一次,最後回到A城,請找出一條最優路線。spa
解:五個城市能夠組成如下路徑:blog
(1)A-B-C-D-E-A,代價=10+8+3+9+11=41. (2)A-B-C-E-D-A,代價=10+8+8+9+9=44.im
(3)A-B-D-C-E-A,代價=10+12+3+8+11=44. (4)A-B-D-E-C-A,代價=10+12+9+8+2=41.img
(5)A-B-E-C-D-A,代價=10+6+8+3+9=36. (6)A-B-E-D-C-A,代價=10+6+9+3+2=30.co
(7)A-C-B-D-E-A,代價=2+8+12+9+11=42. (8)A-C-B-E-D-A,代價=2+8+6+9+9=34.數字
(9)A-C-D-B-E-A,代價=2+3+12+6+11=34. (10)A-C-D-E-B-A,代價=2+3+9+6+10=30.ps
(11)A-C-E-B-D-A,代價=2+8+6+12+9=37. (12)A-C-E-D-B-A,代價=2+8+9+12+10=41.ab
(13)A-D-B-C-E-A,代價=9+12+8+8+11=48. (14)A-D-B-E-C-A,代價=9+12+6+8+2=37.
(15)A-D-C-B-E-A,代價=9+3+8+6+11=37. (16)A-D-C-E-B-A,代價=9+3+8+6+10=36.
(17)A-D-E-C-B-A,代價=9+9+8+8+10=44. (18)A-D-E-B-C-A,代價=9+9+6+8+2=34.
(19)A-E-B-C-D-A,代價=11+6+8+3+9=37. (20)A-E-B-D-C-A,代價=11+6+12+3+2=34.
(21)A-E-C-B-D-A,代價=11+8+8+12+9=48. (22)A-E-C-D-B-A,代價=11+8+3+12+10=44.
(23)A-E-D-B-C-A,代價=11+9+12+8+2=42. (24)A-E-D-C-B-A,代價=11+9+3+8+10=41.
能夠看出最短路徑是 (6)A-B-E-D-C-A 和(10)A-C-D-E-B-A,他們是同一條路徑。