US5249+Networks

[] =Use networks to find optimal solutions to problems.= =1.1 The method chosen is appropriate to the problem.= =1.2 An optimal solution is found which is consistent with the problem.=

Geometry (Exploring networks), [Old Document] -choose an appropriate network to organise and visually represent information; -systematically develop, and critically evaluate, optimal solutions using networks; The standard must be met in project management (critical path analysis) and at least two from the following list: shortest path; traversability; minimum spanning tree. Calculators and computers can be used in achievement of credit for this unit standard.

=M7-5: Choose appropriate networks to find optimal solutions. [new document]= "*" below means they have been covered in class. Solves problems which can be modelled by networks. Uses trial and improve methods to develop algorithms for solving network problems. =*Traversability (all even nodes or exactly 2 odd nodes, starting and ending on the odd nodes)= -Euler circuits and paths -Hamilton circuits and paths -Shortest path -Chinese postman problem [] -Weighted paths -Minimum length connect network (for example, cabling, water pipes) =*Minimum spanning tree (take out the longest paths, if they are part of a polygon).= [] [] [] =MST Game:= [] []

=Practical contexts include:= Delivery routes Minimum length of phone, power, cables

From: http://nzmaths.co.nz/elaborations-level-seven-mathematics-0?parent_node=

[] [] [] []

media type="custom" key="9868831"

media type="youtube" key="Leb5x6Nhlao" height="279" width="448"media type="youtube" key="OWfeZ9uDhdw" height="279" width="313"

Vocab arc = line = edge (many of these make up a path) and could represent a road, path, tramping track, cable node = vertex = dot = point and could represent a house, tramping hut, computer graph = diagram of nodes and paths cycle = circuit and is a closed path Hamiltonian Cycle - like a wonky circle Kruskal's minimum spanning tree algorithm - start with the shortest arc, and go through the arc's in order, include them as long as they do not form a polygon (or closed shape = cycle) Traversability = trace every arc just once and visit all nodes (all even nodes or exactly 2 odd nodes) Valency = number of arcs leaving the node Shortest Path = you may wish to label your nodes to help you find the shortest path Critical Path Analysis = plan a complex project by representing tasks as nodes []

You can use the files beside this video to solve the problem yourself. media type="youtube" key="bjckuVtk1zs" height="209" width="336"

media type="custom" key="9898367"

media type="custom" key="9897779"