算法分析与设计课后练习20

用启发式的方法求0/1背包问题
n=5
(w1,w2,w3,w4,w5)=(2,2,6,5,4)
(p1,p2,p3,p4,p5)=(6,3,5,4,6)
M=10

令L=15
Pleft(0)=24
Pleft(1)=18
Pleft(2)=15
Pleft(3)=10
Pleft(4)=6
Pleft(5)=0
S⁰={(0,0)}
S¹1={(6,2)}
0+ Pleft(1)=18=18>15
S¹={(0,0), (6,2)}
S¹2={(3,2),(9,4)}
0+ Pleft(2)=15
6+ Pleft(2)=21
S²={(0,0),(3,2),(6,2),(9,4)}
S¹3={(5,6),(8,8),(11,8),(14,10)}
0+ Pleft(3)=10
3+ Pleft(3)=13
6+ Pleft(3)=16
9+ Pleft(3)=19
S³={(5,6),(6,2),(8,8),(9,4),(11,8),(14,10)}
S¹4={(9,11),(10,7),(12,13),(13,9),(15,13),(18,15)}
5+ Pleft(4)=9
6+ Pleft(4)=12
8+ Pleft(4)=14
9+ Pleft(4)=15
11+ Pleft(4)=17
14+ Pleft(4)=20
S⁴={(9,4),(10,7),(11,8),(13,9),(14,10)}
S¹4={(15,8),(16,11),(17,12),(19,13),(20,14)}
9+ Pleft(5)=9
10+ Pleft(5)=10
11+ Pleft(5)=11
13+ Pleft(5)=13
14+ Pleft(5)=14
S⁵={(15,8),}
最大代价为15，背包重量8
S⁵中(15,8)∈S¹4，(15-6,8-4)= (9,4)∈S⁴则x5=1
S⁴ 中(9,4)∈S³则x4=0
S³中(9,4)∈S²则x3=0
S²中(9,4)∈S¹2，(9-3,4-2)= (6,2)∈S¹则x2=1
S¹中(6,2)∈S¹1，(6-6,2-2)= (0,0)∈S⁰则x1=1
则Xn={1,1,0,0,1}