数据结构与算法 动态规划.pdf
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3
3.1
3-1 [] 1 2 - 2s = 1d= 5
2 34 3 35 35
135 3 2 5 (9 ) 15
1 3 2 5 (11 ) 3 4 515 1 3 4 5 (9)
v v v d
3-2 [0/1] 1 3 . 40 / 1x 1 .. xn i = 1 2 . n
xi x 1 = 0 2 3 . n c x 1 = 1
c-w1 r ? {c c-w1 }
r x 1 01 [x2 . xn ]
[y 2 . y n ] [x 1 y 2 . y n ]
n=3, w=[100,14,10], p =[20,18,15], c= 11 6 x 1 = 1 r= 116-100=16 [x2 x3 ]=[0,1]
1 5 [x2 x3 ]= [1 0] 1 8 [x2 x3 ] = [ 0 1]
x= [ 1 0 1] x= [ 1 1 0 ] x 1 = 0 11 6
[x2 x3 ][x 1 x2 x3 ]
3-3 [] $ 1 0 0 $ 2 0
$ 2 0
$ 1 0 0 $ 2 0 0
$ 1 4 0 -
-
t a g t a g0t a g1
网
0
d y n a m i c -programming recurrence equation
赛
3-4 [0/1] 3 - 2 0 / 1f (i,y ) 1 5 - 2y
竞
i i + 1 . n f f ( 1 ,c)
1 5 - 2 f ( 1 ,c) f (n, * )f (n, * ) 1 5 - 11 5 - 2
学
f (i,*) ( i=n- 1 n- 2 . 2 ) 1 5 - 2f ( 1 ,c)
1 5 - 2 0≤y 1 0 f ( 3 ,y ) = 0 y ≥1 0 f ( 3 ,y ) = 1 5 1 5 - 2f (2, y ) = 0 ( 0≤y 10
息
) f 2 y = 1 5 1 0≤y 1 4f 2 y = 1 8 1 4≤y 2 4 f 2 y = 3 3 y ≥2 4 f ( 1 , 11 6 ) = m a x {f 2 11
6 f 2 11 6 - w1 + p 1 } = m a x {f 2 11 6f 2 1 6+ 2 0 } = m a x { 3 3 3 8 } = 3 8
信
xi f ( 1 ,c) =f ( 2 ,c) x 1 = 0 x 1 = 1 c-w1 f (2, c-w1)
xi (i= 1 .n)
华
f ( 2 , 11 6 ) = 3 3≠f ( 1 , 11 6 ) x 1 = 1 3 8 -p 1=18 x2 x3 r = 11 6 -w1 = 1 6 f (
2 , 1 6 ) = 1 8 f ( 3 , 1 6 ) = 1 4≠f ( 2 , 1 6 ) x2 = 1 r= 1 6 -w2 = 2 f (3,2) =0 x3 = 0
中
principle of optimality
t r a c
e b a c k
3.2
3.2.1 0/1
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1.
3 - 4 1 5 - 21 5 - 1
p w n p F(1,c) f ( 1 ,c)
15-1
int F(int i, int y)
{// f ( i , y ) .
if (i == n) return (y w[n]) ? 0
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