Question

For a given real-world problem like the one below, which algorithm will you use to solve it? How would you map the input information into the input required by the algorithm? What computational complexity the chosen algorithm has? Blizzard has come over the whole state, covering all highways with 40 inches of snow. To keep the distribution of food, roads between major cities need to be cleared, so that each major city can be reached from each other. But getting rid of the snow from a highway is expensive - $1000 per mile. You, member of the Emergency Services, need to devise a plan that keeps all major cities connected through cleared roads, with the cost of clearing as small as possible. You are given the list of distances (in miles) of direct connections (i.e. not going through any other major city) between the major cities. You have to do the math, and choose which of those connections should be cleared.

Answer 1

An algorithm is a written formula that is part of software that, when triggered, tells the tech what to do to solve a problem. Computer algorithms work with input and output.

What is an algorithm's most basic definition?

An algorithm is a method for doing calculations or locating issues. Algorithms function as a precise set of instructions that carry out preset tasks consecutively in either machine or development tools programs. Algorithms play a significant role in every role of information technology.

What kind of algorithm would that be?

The approach we use to answer a long division problem, the process of doing laundry, and the functioning of a search engine are all examples of common examples of an

Briefing:

Minimal Spanning Tree(MST):

We also called this as a minimum weight spanning tree. It is the subset of the edges of connected vertices.

What is a spanning tree?

A graph is a sub graph that contains all the vertices and is a tree. Graph might have many spanning trees.

   o---o

   |\ /|

   | X |

   |/ \|

   o---o

So the above graph has below spanning trees.

    o---o    o---o    o   o    o---o

    |   |    |        |   |        |

    |   |    |        |   |        |

    |   |    |        |   |        |

    o   o    o---o    o---o    o---o

   

    o---o    o   o    o   o    o   o

     \ /     |\ /      \ /      \ /|

      X      | X        X        X |

     / \     |/ \      / \      / \|

    o   o    o   o    o---o    o   o

   

    o   o    o---o    o   o    o---o

    |\  |       /     |  /|     \

    | \ |      /      | / |      \

    |  \|     /       |/  |       \

    o   o    o---o    o   o    o---o

   

    o---o    o   o    o   o    o---o

    |\       |  /      \  |       /|

    | \      | /        \ |      / |

    |  \     |/          \|     /  |

    o   o    o---o    o---o    o   o

So these are possible spanning trees from the given graph.

Now what is Minimum Spanning Tree?

Now take your graph you have weights or length are given in it.

The Weight of the whole trees is:  Sum of the weight of the edges.

Now, we have to find the minimum length spanning tree in the given graph.

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