Further Mathematics · Pearson Edexcel 9FM0 · Option D2 · Topic 4

Dynamic programming

Dynamic programming: solving multi-stage problems by working backwards through stages and states.

1 sub-topic
Taught in Year 13
12 practice questions
1 animated lesson

Practice questions (12) Lessons Worksheets All Edexcel Further Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

4.1Dynamic programmingY13

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Easy and hard questions from this topic, each with a worked solutions and the mark for every step. All 12 questions in this topic, free, no account needed.

Dynamic programming

Not needed for Year 12Easy

Bellman's principle · Year 13 · 1 mark

What is Bellman's principle of optimality?
(1)

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This is why dynamic programming can work backwards from the final stage, keeping only the best option from each state. $B$ : Any part of an optimal path is itself an optimal path

Total1

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Dynamic programming

Not needed for Year 12Hard

Dynamic programming · Year 13 · 6 marks

A journey goes from

S

T

through one of

A

B

C

and then one of

D

E

F

. The values on the possible stages are:

S

A

: 6;

S

B

: 9;

S

C

: 10;

A

D

: 5;

A

E

: 5;

A

F

: 2;

B

D

: 2;

B

E

: 11;

B

F

: 6;

C

D

: 5;

C

F

: 4;

D

T

: 9;

E

T

: 11;

F

T

: 4.

Use dynamic programming, working backwards from $T$ , to find the route that minimises the total value. Show your stages, states and values.
(6)

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Stage 1 (states D, E, F): D 9, E 11, F 4.
For each state take the least action value + value of the next state.Stage 2 (states A, B, C): A 6, B 10, C 8.
Stage 3 (state S): 12.
$SAFT, \ \text{total} = 12$

Total6

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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