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AS level OCR Maths D1
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Terms in this set (26)
Bubble sort
The largest number sinks to the bottom after each pass
One final pass is needed to ensure the sorting is finished
Shuttle sort
Numbers can move up more than one place in a pass
There are fewer comparisons than bubble sort
Maximum number of comparisons and swaps
½n(n-1)
First-fit algorithm
Place each object in turn in the first available space
Simple graph
A graph without loops and multiple arcs
Complete graph
A graph in which each node is connected by one arc to every other node
Complete bipartite graph
Every node in one set is connected to every node in the other set
Trail
Closed trail
A sequence of arcs
Initial and final nodes are the same
Path
A trail where no node is passed more than once
Cycle
A closed trail where only the initial and final nodes are the same
Order of a node
The number of arcs meeting at that node
Eulerian graph
A connected graph which has a closed trail containing every arc once
Every node has even order
Semi-Eulerian
A connected graph is Eulerian if precisely two nodes have odd order
Tree
Connected graph with no cycles
Spanning tree
Any tree which connects all the nodes of a graph
For a connected graph with n nodes, each spanning tree has n-1 arcs
Prim's algorithm
Finds minimum spanning tree
Choose the lowest arcs until every node is on the graph
Kruskal's algorithm
Choose the arcs of least weight that do not form a cycle until n-1 arcs have been chosen
Matrix formulation of Prim's algorithm
Cross out the row corresponding to a circled node
Dijkstra's algorithm
Temporary labels are replaced when a shorter path is found
When there is no shorter route use a permanent label
Drawback of Dijkstra's algorithm
Cannot be used if any weights are negative
Chinese postman algorithm
Length of all streets + length of repeated streets
Assumes the original graph has an even number of nodes of odd order
All graphs have...
an even number of nodes of odd order
Hamiltonian cycle
A tour which contains every node precisely once
For n nodes the number of Hamiltonian cycles is ½(n-1)!
Nearest neighbour algorithm
Finds a Hamiltonian cycle
At each stage, it visits the nearest node which has not already been visited
The lower bound algorithm
Narrows the range within which the weight of the minimum Hamiltonian cycle must lie
Tour improvement algorithm
Lowers the weight of a Hamiltonian tour
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