D1 – Minimum Connectors
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D1 – Minimum Connectors
A minimum spanning tree shows the shortest set of edges connecting a
number of vertices.
For n vertices there are n – 1 edges in a minimum spanning tree.
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Prim’s algorithm adds the nearest vertex to the current tree.
- must have start vertex
- find nearest vertex to existing tree
- add vertex to tree
- don’t make a cycle
- continue until all vertices part of tree
Prim’s algorithm can be applied to a matrix.
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Kruskal’s algorithm adds edges to a tree in order of size.
- start with shortest edge
- find next shortest edge
- add vertex to tree
- don’t’ make cycles
- continue until all vertices part of tree.
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D1 – Shortest Path Problem
A minimum spanning tree shows the shortest set of edges connecting a
number of vertices.
For n vertices there are n – 1 edges in a minimum spanning tree.
Prim’s algorithm adds the nearest vertex to the current tree.
- must have start vertex
- find nearest vertex to existing tree
- add vertex to tree
- don’t make a cycle
- continue until all vertices part of tree
Prim’s algorithm can be applied to a matrix.
Kruskal’s algorithm adds edges to a tree in order of size.
- start with shortest edge
- find next shortest edge
- add vertex to tree
- don’t’ make cycles
- continue until all vertices part of tree.
D1 – Shortest Path Problem
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Real-life problems may not obey the triangle inequality.
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Real-life problems may not obey the triangle inequality.
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Dijkstra’s algorithm enables the shortest path between two points to be
found.
- label start vertex as 0, box this number
- at each vertex connected to start vertex list distance
- box smallest number
- from this vertex, list all distances connected to this vertex
- if distance is less than a value at this vertex, cross out and write
new value
- box the smallest number shown at any vertex
- continue until destination is boxed.
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Dijkstra’s algorithm enables the shortest path between two points to be
found.
- label start vertex as 0, box this number
- at each vertex connected to start vertex list distance
- box smallest number
- from this vertex, list all distances connected to this vertex
- if distance is less than a value at this vertex, cross out and write
new value
- box the smallest number shown at any vertex
- continue until destination is boxed.
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Dijkstra’s algorithm is equally valid when used backwards through a network
(i.e. this is necessary when there are multiple starting points.)
Dijkstra’s algorithm fails if there are negative edges in the network.
Tracing a route through a network can be easily found if careful labelling of
Dijkstra’s algorithm is used.
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Dijkstra’s algorithm is equally valid when used backwards through a network
(i.e. this is necessary when there are multiple starting points.)
Dijkstra’s algorithm fails if there are negative edges in the network.
Tracing a route through a network can be easily found if careful labelling of
Dijkstra’s algorithm is used.
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