Greedy choice

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  • Given a connected, undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together. A single graph can have many different spanning trees. We can also assign a weight to each edge, which is a number representing how unfavorable it is, and use this to assign a weight to a spanning tree by computing the sum of the weights of the edges in that spanning tree.

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  • The greedy algorithm is one of the simplest approaches to solve the optizmization problem in which we want to determine the global optimum of a given function by a sequence of steps where at each stage we can make a choice among a class of possible decisions. In the greedy method the choice of the optimal decision is made on the information at hand without worrying about the effect these decisions may have in the future.

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  • The definition of a tree accepted by science and the forestry industry is “A woody plant (arboreal perennial) usually with a single columnar stem capable of reaching six metres in height”. Less than six metres (21ft) of potential height is regarded as a shrub.This definition is not absolute; gardeners contest the height threshold, some preferring five metres (17ft) and others choosing a threshold of three metres (13ft). It is likely that bonsai enthusiasts would entirely dismiss any figures suggested.

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