Lesson 4D.4.1
4D.4.1 Principles of dynamic programming Quiz: Pearson Edexcel Further Maths, Unit 43
20 questions
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Lesson 4D.4.1, Principles of dynamic programming: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 43: Dynamic programming, written with Revision Ninja.
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The 20 questions
-
Which dynamic programming principle states that any subpath of an optimal path must also be optimal?
- Max-flow theorem
- Optimality principle
- Greedy choice
- Route inversion
-
In a dynamic programming network, what defines a stage?
- Total arc weight
- Maximum flow value
- Set of decision vertices
- Single final destination
-
In dynamic programming, what is a state?
- Condition at a stage
- The final answer
- A stage number
- An optimal route
-
What does a minimax route minimise in a network?
- Minimum arc length
- Number of vertices
- Maximum arc length
- Total route length
-
What does a maximin route maximise in a network?
- Number of stages
- Total route length
- Minimum arc length
- Maximum arc length
-
What is a table formulation used for in dynamic programming?
- Deleting redundant nodes
- Finding network capacity
- Recording stage values
- Checking game payoffs
-
Which principle allows dynamic programming to ignore suboptimal routes at intermediate stages?
- Maximum flow
- Greedy choice
- Optimality principle
- Critical path
-
In the network with arcs A-B (2), A-C (4), B-C (1), B-D (5), C-D (2), C-E (6), D-F (3) and E-F (1), all directed from A towards F, what is the length of the shortest route from A to F?
- 10
- 8
- 9
- 11
-
Which route from A to F is the shortest in that network?
- A, C, E, F
- A, C, D, F
- A, B, C, D, F
- A, B, D, F
-
In the same network, what is the length of the longest route from A to F?
- 10
- 9
- 12
- 11
-
Which route from A to F is the longest in that network?
- A, B, D, F
- A, C, E, F
- A, C, D, F
- A, B, C, E, F
-
In that network, what is the value of the minimax route from A to F, measured as the largest arc on the route?
- 5
- 6
- 3
- 2
-
Which route is the minimax route from A to F in that network?
- A, B, C, D, F
- A, B, D, F
- A, C, D, F
- A, C, E, F
-
In that network, what is the shortest route length from B to F?
- 8
- 9
- 6
- 7
-
In that network, what is the shortest route length from A to E?
- 9
- 12
- 7
- 10
-
In network routing, what is typically true when a minimax route equals the shortest path?
- Criteria agree
- Unique stage
- Negative cycle
- Network loops
-
What property allows dynamic programming to break a large route problem into stages?
- Linear ordering
- Cyclic symmetry
- Optimal substructure
- Random pairing
-
In the same network, if the best route to E is extended, what is the shortest route from A to F that passes through E?
- 12
- 11
- 9
- 10
-
In the same network, if the arc C to D is changed from 2 to 9, what is the new shortest route length from A to F?
- 10
- 16
- 11
- 15
-
What kind of structure must a problem have for dynamic programming to apply?
- Single state
- Staged structure
- Random walk
- Continuous domain
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