- #1
Growing More Trees to Sustainable Living
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In summary, the instructor is correct that a complete tree is one in which every level, except possibly the deepest, is entirely filled. At depth $n$, the height of the tree, all nodes are as far left as possible. The number of vertices that have to be added to v4 and v5 is incorrect.
- #2
Evgeny.Makarov
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I come into contact with tree structures only occasionally, so I don't remember all definitions. Besides, some concepts have been used in different senses in different sources.
1a) This is correct if levels are counted from 1. I think it is more likely that the root has level 0.
1b-d) Correct.
2) Correct.
3) According to NIST, a complete tree is one "in which every level, except possibly the deepest, is entirely filled. At depth $n$, the height of the tree, all nodes are as far left as possible". This grouping to the left means that no only a child has to be added to v1, but also it must have three children of its own. The problem statement does not make it clear how to write this. A similar observation applies to v2: if children are added to the left of v6, then they themselves have to have three children each.
Also, there is more than one way to turn this tree into a complete one: for example, one could add from 0 to 3 children grouped left to v7 and 0 children to v8 and v9. One could add 0 or 1 child to v6 (zero if no children are added to v7--v9). As for v10 and v11, they should definitely not have children.
This problem does not seem to be formulated very well. Perhaps you have a different definition of a complete tree.
Edit: Forgot 4) and 5). I am not sure what T(v3) denotes and what the difference is with (T, v3). You should review the definition of tree height in your source, but I think it's the maximum number of edges from the root to a leave. Then the height of the whole tree in the second picture is 2.
1a) This is correct if levels are counted from 1. I think it is more likely that the root has level 0.
1b-d) Correct.
2) Correct.
3) According to NIST, a complete tree is one "in which every level, except possibly the deepest, is entirely filled. At depth $n$, the height of the tree, all nodes are as far left as possible". This grouping to the left means that no only a child has to be added to v1, but also it must have three children of its own. The problem statement does not make it clear how to write this. A similar observation applies to v2: if children are added to the left of v6, then they themselves have to have three children each.
Also, there is more than one way to turn this tree into a complete one: for example, one could add from 0 to 3 children grouped left to v7 and 0 children to v8 and v9. One could add 0 or 1 child to v6 (zero if no children are added to v7--v9). As for v10 and v11, they should definitely not have children.
This problem does not seem to be formulated very well. Perhaps you have a different definition of a complete tree.
Edit: Forgot 4) and 5). I am not sure what T(v3) denotes and what the difference is with (T, v3). You should review the definition of tree height in your source, but I think it's the maximum number of edges from the root to a leave. Then the height of the whole tree in the second picture is 2.
- #3
johng1
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Hi,
I agree with Markov; the definition of complete tree is as specified in his link. Also unless you have misinterpreted the definitions, your text/instructor is "marching to his own drummer". For example, the height of a tree with one node is 0. The following tree is the result of augmenting your original tree to a complete tree; the color coding indicates the nodes which are added.
I agree with Markov; the definition of complete tree is as specified in his link. Also unless you have misinterpreted the definitions, your text/instructor is "marching to his own drummer". For example, the height of a tree with one node is 0. The following tree is the result of augmenting your original tree to a complete tree; the color coding indicates the nodes which are added.
- #4
- #5
Evgeny.Makarov
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The number of vertices that have to be added to v4 and v5 is incorrect. I repeat the remarks that one must add leaves to some added vertices and that this tree can be made complete in several ways. Also, as I said in post #2,
What do you denote by (T, v3) and T(v3)?Evgeny.Makarov said:
FAQ: Growing More Trees to Sustainable Living
What is the importance of planting more trees?
Planting more trees is crucial for several reasons. Trees provide oxygen, filter air and water pollution, prevent soil erosion, and provide habitats for a variety of plants and animals. They also have a positive impact on human health by reducing stress and improving air quality.
How do trees help combat climate change?
Trees play a significant role in mitigating climate change. They absorb carbon dioxide, a greenhouse gas that contributes to global warming, and store it in their trunks, branches, and leaves. Trees also release oxygen, which is essential for all living beings.
What are the benefits of reforestation?
Reforestation, or the act of replanting trees in an area where they previously existed, has numerous benefits. It helps restore biodiversity, improves soil quality, and provides economic opportunities through timber production and ecotourism. Reforestation also helps mitigate the effects of deforestation and climate change.
What can individuals do to support "More Trees" initiatives?
There are several ways individuals can support the planting and preservation of more trees. They can participate in community tree-planting events, donate to organizations that focus on reforestation, and reduce their own carbon footprint by using public transportation, conserving energy, and recycling. Individuals can also educate themselves and others about the importance of trees and the impact of deforestation.
How can we ensure the sustainability of "More Trees" efforts?
To ensure the sustainability of "More Trees" initiatives, it is essential to involve all stakeholders, including governments, businesses, and local communities. There should also be a focus on choosing the right tree species for the given location, proper maintenance and care of the trees, and monitoring and evaluation of the reforestation efforts. Additionally, sustainable logging practices and responsible consumption of timber products can help maintain a healthy balance between tree growth and harvest.