Demo AS Discrete Questions

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1 emo S iscrete Questions Please answer on file paper. : ind the Minimum Spanning Tree using Prim's lgorithm starting from vertex : rcs/length: rcs/length: : ind the Minimum Spanning Tree using Prim's lgorithm starting from vertex : rcs: Total length= rcs: Total length= ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

2 : ind the Minimum Spanning Tree using Kruskal's lgorithm: J rcs/length: rcs/length: : ind the shortest route from to the ringed vertex using ijkstra's lgorithm: Route/Length: Route/Length: J ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

3 : ind the shortest route starting and finishing at which includes every edge. Pairings/est solution: Pairings/est solution: : ind a amiltonian cycle using the Nearest Neighbour algorithm (start at the ringed vertex): ycle/length: ycle/length: ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

4 : ind a lower bound for the Travelling Salesperson Problem (remove the ringed vertex): Lower ound: Lower ound: : Use the first fit algorithm to pack these objects into bins: (in size ) (in size ) : Use the first fit decreasing algorithm to pack these objects into bins: (in size ) (in size ) : Use the full bin algorithm to pack these objects into bins: (in size ) (in size ) : rrange the following lists in ascending order using ubble Sort: : rrange the following lists in ascending order using Shuttle Sort: : ind the order of each algorithm, given its efficiency: Time taken = n + n + n + n + n! Time taken = n : Solve the following: n algorithm has order n and takes seconds to solve a problem of size. stimate the time taken to solve a problem of size. n algorithm has order n and takes seconds to solve a problem of size. stimate the time taken to solve a problem of size. ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

5 : ive the following Linear Programming terms: ind the smallest value of The statement of a problem as a function to be optimised, with a set of inequalities c) The function to be optimised (minimised or maximised) d) quantity that can be changed in the problem (e.g. representing a physical quantity) : Maximise each objective function: P = x + y P = x + y : Solve using the Simplex algorithm: P x y s t value P x y s t value : Solve using the Simplex algorithm: P x y z s t u value P x y z s t u value ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

6 nswers: emo S iscrete Questions : rcs:,,,,,,,. Total length= rcs:,,,,,. Total length= : rcs:,,,,,. Total length= rcs:,,,,. Total length= ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

7 : J rcs:, J,,, J,,,,. Total length= rcs:,,,,,. Total length= :, Route:. Length=,,, Route: J. Length=,, J ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

8 : Pairings: : : Tot: : : Tot: Poss. route: Length: + = Pairings: : : Tot: : : Tot: : : Tot: : : Tot: Poss. route: Length: + = : ycle:. Length= ycle:. Length= ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

9 : Length = + = Length = + = : (in size ) in : [] in : [] in : [] in : [] (in size ) in : [] in : [] in : [] in : [] : (in size ) in : [] in : [] in : [] in : [] in : [] in : [] (in size ) in : [] in : [] in : [] in : [] ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

10 : (in size ) (in size ) in : [] in : [] in : [] in : [] in : [] in : [] in : [] in : [] in : [] : : : Order n! Order n : seconds seconds : Minimise Linear Programming (LP) formulation c) Objective function d) ontrol variable ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

11 : Max value = at (, ) Max value = at (, ) : teration : teration : P x y s t value P x y s t value Optimal solution: P x y s t value P =, x =, y = teration : P x y s t value Optimal solution: P x y s t value P =, x =, y = ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

12 : teration : P x y z s t u value teration : P x y z s t u value Optimal solution: P x y z s t u value P =, x =, y = ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

13 teration : P x y z s t u value Optimal solution: P x y z s t u value P =, x =, y = ree worksheet created by MTSprint. emo S iscrete Questions: MTSprint,

Demo AS Discrete Questions

Demo AS Discrete Questions emo S iscrete Questions Please answer on file paper. www.mathsprint.co.uk : ind the Minimum Spanning Tree using Prim's lgorithm starting from vertex : J rcs/length: rcs/length: : ind the Minimum Spanning