Detailed description and Implementation of Dynamic Planning ideas, detailed examples of Dynamic Planning

Detailed description and Implementation of Dynamic Planning ideas, detailed examples of Dynamic Planning

This article uses two examples to describe the concept of dynamic planning algorithm design. It mainly refers to the introduction to algorithms in the Bible, and adds some understanding of it. It mainly includes some specific implementation processes, so I hope it will help you.

# _ * _ Coding: UTF-8 _*_

Import numpy as np

Def MemoizedCutRodAux (p, n, r, s ):

If r [n]> = 0:

Return r [n]

If n = 0:

Q = 0

C = 0

Else:

Q =-1

C =-1

For I in range (1, n + 1 ):

If q <(p [I] + MemoizedCutRodAux (p, n-I, r, s )):

Q = p [I] + MemoizedCutRodAux (p, n-I, r, s)

C = I

R [n] = q

S [n] = c

Return q

Def MemoizedCutRod (p, n ):

R =-np. ones (n + 1)

S =-np. ones (n + 1)

MemoizedCutRodAux (p, n, r, s)

Return r, s

If _ name __= = '_ main __':

P = np. array ([,])

R, s = MemoizedCutRod (p, 10)

Print r

Print s

 

Result output:

R = [0. 1. 5. 8. 10. 13. 17. 18. 22. 25. 30.]

S = [0. 1. 2. 3. 2. 6. 1. 2. 3. 10.]

Import numpy as np

Def BottomUpCutRod (p, n ):

R =-np. ones (n + 1)

S =-np. ones (n + 1)

R [0] = 0

S [0] = 0

Q =-1

For j in range (1, n + 1 ):

For I in range (1, j + 1 ):

If q <(p [I] + r [j-I]):

Q = p [I] + r [j-I]

S [j] = I

R [j] = q

Return r, s

If _ name __= = '_ main __':

P = np. array ([0, 1, 5, 8, 9, 10, 17, 17, 20, 24, 30])

R, s = BottomUpCutRod (p, 10)

Print r

Print s

★Step 3: Use the bottom-up iteration method to calculate the optimal value

Import numpy as np

Def MatrixChain (p ):

N = p. size-1

M = np. ones (n + 1, n + 1) * np. inf

S = np. zeros (n + 1, n + 1 ))

For I in range (n + 1 ):

M [I, I] = 0

For lenth in range (2, n + 1 ):

For I in range (1, n-lenth + 2 ):

J = I + lenth-1

For k in range (I, j ):

Q = m [I, k] + m [k + 1, j] + p [I-1] * p [k] * p [j]

If q <m [I, j]:

M [I, j] = q

S [I, j] = k

Return m, s

If _ name __= = '_ main __':

P = np. array ([50, 10, 40, 30, 5])

M, s = MatrixChain (p)

Print m

Print s

 

Result output:

 

M = [[0. inf]

[Inf 0. 20000. 27000. 10500.]

[Inf 0. 12000. 8000.]

[Inf 0. 6000.]

[Inf 0.]

S = [[0. 0. 0. 0. 0.]

[0. 0. 1. 1. 1.]

[0. 0. 0. 2. 2.]

[0. 0. 0. 0. 3.]

[0. 0. 0. 0. 0.]

 

 

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This article is the author's original, where the code can be run through (Python), hope to help