Mixing
What type of tree is this?
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
The checkmarks I've drawn means that the branch ends or a node with the same number allready exists in the tree. I.e it means it reaches some cycle or ends the branching.
I don't know if this is even called a tree? But if so, what kind of specific tree is it? I would like to study this more, but don't know where to find literature on the specifics of this. (This tree has nodes with actual binary values but I used decimal for better visualization).
And also there are two "roots". But some of the nodes could have been connected, like node: 10, but I don't want to clutter the structure too much, or maybe I should redraw the tree-structure altogheter?
Updated: I've improved the nodes. Now it looks more like a graph. So the question is now is it a digraph and/or what can I derive from this?
terminology trees decision-trees
asked Jul 29 at 12:48
Natural Number Guy
362315
 |Â
show 7 more comments
up vote
0
down vote
favorite
The checkmarks I've drawn means that the branch ends or a node with the same number allready exists in the tree. I.e it means it reaches some cycle or ends the branching.
I don't know if this is even called a tree? But if so, what kind of specific tree is it? I would like to study this more, but don't know where to find literature on the specifics of this. (This tree has nodes with actual binary values but I used decimal for better visualization).
And also there are two "roots". But some of the nodes could have been connected, like node: 10, but I don't want to clutter the structure too much, or maybe I should redraw the tree-structure altogheter?
Updated: I've improved the nodes. Now it looks more like a graph. So the question is now is it a digraph and/or what can I derive from this?
terminology trees decision-trees
asked Jul 29 at 12:48
Natural Number Guy
362315
A tree is connected. This would be a forest.
– user578878
Jul 29 at 12:54
Tree is a connected graph with no cycles, so your picture represents two trees. I do not understand what do you mean by some of the nodes could have been connected
– Antoine
Jul 29 at 12:55
This seems to be a data structure you've invented for some purpose. I doubt that it has appeared before, and that it has a name. Describe it carefully in your paper or computer program and choose an appropriate name.
– Ethan Bolker
Jul 29 at 13:00
Ok @Antoine: I mean that each node has a decision in it, to go left or right. But the route it takes doesn't mean some of the other nodes are connected in a practical sense. Hard to explain.
– Natural Number Guy
Jul 29 at 13:01
@EthanBolker The purpose is that it is invented for studying the Collatz Conjecture. Thanks for the answers.
– Natural Number Guy
Jul 29 at 13:04
 |Â
show 7 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
The checkmarks I've drawn means that the branch ends or a node with the same number allready exists in the tree. I.e it means it reaches some cycle or ends the branching.
I don't know if this is even called a tree? But if so, what kind of specific tree is it? I would like to study this more, but don't know where to find literature on the specifics of this. (This tree has nodes with actual binary values but I used decimal for better visualization).
And also there are two "roots". But some of the nodes could have been connected, like node: 10, but I don't want to clutter the structure too much, or maybe I should redraw the tree-structure altogheter?
Updated: I've improved the nodes. Now it looks more like a graph. So the question is now is it a digraph and/or what can I derive from this?
terminology trees decision-trees
asked Jul 29 at 12:48
Natural Number Guy
362315
The checkmarks I've drawn means that the branch ends or a node with the same number allready exists in the tree. I.e it means it reaches some cycle or ends the branching.
I don't know if this is even called a tree? But if so, what kind of specific tree is it? I would like to study this more, but don't know where to find literature on the specifics of this. (This tree has nodes with actual binary values but I used decimal for better visualization).
And also there are two "roots". But some of the nodes could have been connected, like node: 10, but I don't want to clutter the structure too much, or maybe I should redraw the tree-structure altogheter?
Updated: I've improved the nodes. Now it looks more like a graph. So the question is now is it a digraph and/or what can I derive from this?
terminology trees decision-trees
asked Jul 29 at 12:48
Natural Number Guy
362315
edited Jul 29 at 17:04
asked Jul 29 at 12:48
Natural Number Guy
362315
asked Jul 29 at 12:48
Natural Number Guy
362315
asked Jul 29 at 12:48
Natural Number Guy
362315
362315
A tree is connected. This would be a forest.
– user578878
Jul 29 at 12:54
Tree is a connected graph with no cycles, so your picture represents two trees. I do not understand what do you mean by some of the nodes could have been connected
– Antoine
Jul 29 at 12:55
This seems to be a data structure you've invented for some purpose. I doubt that it has appeared before, and that it has a name. Describe it carefully in your paper or computer program and choose an appropriate name.
– Ethan Bolker
Jul 29 at 13:00
Ok @Antoine: I mean that each node has a decision in it, to go left or right. But the route it takes doesn't mean some of the other nodes are connected in a practical sense. Hard to explain.
– Natural Number Guy
Jul 29 at 13:01
@EthanBolker The purpose is that it is invented for studying the Collatz Conjecture. Thanks for the answers.
– Natural Number Guy
Jul 29 at 13:04
 |Â
show 7 more comments
A tree is connected. This would be a forest.
– user578878
Jul 29 at 12:54
Tree is a connected graph with no cycles, so your picture represents two trees. I do not understand what do you mean by some of the nodes could have been connected
– Antoine
Jul 29 at 12:55
This seems to be a data structure you've invented for some purpose. I doubt that it has appeared before, and that it has a name. Describe it carefully in your paper or computer program and choose an appropriate name.
– Ethan Bolker
Jul 29 at 13:00
Ok @Antoine: I mean that each node has a decision in it, to go left or right. But the route it takes doesn't mean some of the other nodes are connected in a practical sense. Hard to explain.
– Natural Number Guy
Jul 29 at 13:01
@EthanBolker The purpose is that it is invented for studying the Collatz Conjecture. Thanks for the answers.
– Natural Number Guy
Jul 29 at 13:04
A tree is connected. This would be a forest.
– user578878
Jul 29 at 12:54
A tree is connected. This would be a forest.
– user578878
Jul 29 at 12:54
Tree is a connected graph with no cycles, so your picture represents two trees. I do not understand what do you mean by some of the nodes could have been connected
– Antoine
Jul 29 at 12:55
Tree is a connected graph with no cycles, so your picture represents two trees. I do not understand what do you mean by some of the nodes could have been connected
– Antoine
Jul 29 at 12:55
This seems to be a data structure you've invented for some purpose. I doubt that it has appeared before, and that it has a name. Describe it carefully in your paper or computer program and choose an appropriate name.
– Ethan Bolker
Jul 29 at 13:00
This seems to be a data structure you've invented for some purpose. I doubt that it has appeared before, and that it has a name. Describe it carefully in your paper or computer program and choose an appropriate name.
– Ethan Bolker
Jul 29 at 13:00
Ok @Antoine: I mean that each node has a decision in it, to go left or right. But the route it takes doesn't mean some of the other nodes are connected in a practical sense. Hard to explain.
– Natural Number Guy
Jul 29 at 13:01
Ok @Antoine: I mean that each node has a decision in it, to go left or right. But the route it takes doesn't mean some of the other nodes are connected in a practical sense. Hard to explain.
– Natural Number Guy
Jul 29 at 13:01
@EthanBolker The purpose is that it is invented for studying the Collatz Conjecture. Thanks for the answers.
– Natural Number Guy
Jul 29 at 13:04
@EthanBolker The purpose is that it is invented for studying the Collatz Conjecture. Thanks for the answers.
– Natural Number Guy
Jul 29 at 13:04
 |Â
show 7 more comments
2 Answers
2
active
oldest
votes
up vote
0
down vote
I can not fully understand what do the brach ends mean. But if we will ignore them, then we will get a forest, which includes two binary trees. These trees are called binary because each node has two children (and a binary tree is a tree in which each node has at most two children). I don't think you can say anything interesting about the two trees besides the fact that they are binary.
The definitions of tree and forest:
Tree - an undirected graph in which any two vertices are connected by exactly one path.
Another definition: Connected graph without cycles.
Forest - graph without cycles.
(I am sorry for the English, I know it is not perfect)
answered Jul 29 at 13:04
Eulerrr
1646
add a comment |Â
up vote
0
down vote
Assuming I understand what you have tried to show in your image, you have a directed graph (digraph) with a loop and nodes of outdegree two. There may be other structure that you can endow your digraph with if you need it. You don't have a tree because there are directed cycles, for example, $ 4 to 10 to 4. $ You can try to find spanning trees of the digraph if you need it. You can try to use it as the basis for a nondeterministic finite automaton.
answered Jul 29 at 14:20
Somos
11k1831
I might have been unclear about how the structure works, but you seem to partly answer my question. I don't think I want a tree (or forest) because path-tracing the branches may or may not enter a cycle. So I can't eliminate edges. A more difficult question is wether a path will enter an infinite cycle in Collatz iterations. I think digraph is close to what i need yes, since there are definite directions.
– Natural Number Guy
Jul 29 at 15:37
Updated the thing now, so it looks more like a graph.
– Natural Number Guy
Jul 29 at 16:30
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
I can not fully understand what do the brach ends mean. But if we will ignore them, then we will get a forest, which includes two binary trees. These trees are called binary because each node has two children (and a binary tree is a tree in which each node has at most two children). I don't think you can say anything interesting about the two trees besides the fact that they are binary.
The definitions of tree and forest:
Tree - an undirected graph in which any two vertices are connected by exactly one path.
Another definition: Connected graph without cycles.
Forest - graph without cycles.
(I am sorry for the English, I know it is not perfect)
answered Jul 29 at 13:04
Eulerrr
1646
add a comment |Â
up vote
0
down vote
I can not fully understand what do the brach ends mean. But if we will ignore them, then we will get a forest, which includes two binary trees. These trees are called binary because each node has two children (and a binary tree is a tree in which each node has at most two children). I don't think you can say anything interesting about the two trees besides the fact that they are binary.
The definitions of tree and forest:
Tree - an undirected graph in which any two vertices are connected by exactly one path.
Another definition: Connected graph without cycles.
Forest - graph without cycles.
(I am sorry for the English, I know it is not perfect)
answered Jul 29 at 13:04
Eulerrr
1646
add a comment |Â
up vote
0
down vote
up vote
0
down vote
I can not fully understand what do the brach ends mean. But if we will ignore them, then we will get a forest, which includes two binary trees. These trees are called binary because each node has two children (and a binary tree is a tree in which each node has at most two children). I don't think you can say anything interesting about the two trees besides the fact that they are binary.
The definitions of tree and forest:
Tree - an undirected graph in which any two vertices are connected by exactly one path.
Another definition: Connected graph without cycles.
Forest - graph without cycles.
(I am sorry for the English, I know it is not perfect)
answered Jul 29 at 13:04
Eulerrr
1646
I can not fully understand what do the brach ends mean. But if we will ignore them, then we will get a forest, which includes two binary trees. These trees are called binary because each node has two children (and a binary tree is a tree in which each node has at most two children). I don't think you can say anything interesting about the two trees besides the fact that they are binary.
The definitions of tree and forest:
Tree - an undirected graph in which any two vertices are connected by exactly one path.
Another definition: Connected graph without cycles.
Forest - graph without cycles.
(I am sorry for the English, I know it is not perfect)
answered Jul 29 at 13:04
Eulerrr
1646
answered Jul 29 at 13:04
Eulerrr
1646
answered Jul 29 at 13:04
Eulerrr
1646
answered Jul 29 at 13:04
Eulerrr
1646
1646
add a comment |Â
add a comment |Â
up vote
0
down vote
Assuming I understand what you have tried to show in your image, you have a directed graph (digraph) with a loop and nodes of outdegree two. There may be other structure that you can endow your digraph with if you need it. You don't have a tree because there are directed cycles, for example, $ 4 to 10 to 4. $ You can try to find spanning trees of the digraph if you need it. You can try to use it as the basis for a nondeterministic finite automaton.
answered Jul 29 at 14:20
Somos
11k1831
I might have been unclear about how the structure works, but you seem to partly answer my question. I don't think I want a tree (or forest) because path-tracing the branches may or may not enter a cycle. So I can't eliminate edges. A more difficult question is wether a path will enter an infinite cycle in Collatz iterations. I think digraph is close to what i need yes, since there are definite directions.
– Natural Number Guy
Jul 29 at 15:37
Updated the thing now, so it looks more like a graph.
– Natural Number Guy
Jul 29 at 16:30
add a comment |Â
up vote
0
down vote
Assuming I understand what you have tried to show in your image, you have a directed graph (digraph) with a loop and nodes of outdegree two. There may be other structure that you can endow your digraph with if you need it. You don't have a tree because there are directed cycles, for example, $ 4 to 10 to 4. $ You can try to find spanning trees of the digraph if you need it. You can try to use it as the basis for a nondeterministic finite automaton.
answered Jul 29 at 14:20
Somos
11k1831
I might have been unclear about how the structure works, but you seem to partly answer my question. I don't think I want a tree (or forest) because path-tracing the branches may or may not enter a cycle. So I can't eliminate edges. A more difficult question is wether a path will enter an infinite cycle in Collatz iterations. I think digraph is close to what i need yes, since there are definite directions.
– Natural Number Guy
Jul 29 at 15:37
Updated the thing now, so it looks more like a graph.
– Natural Number Guy
Jul 29 at 16:30
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Assuming I understand what you have tried to show in your image, you have a directed graph (digraph) with a loop and nodes of outdegree two. There may be other structure that you can endow your digraph with if you need it. You don't have a tree because there are directed cycles, for example, $ 4 to 10 to 4. $ You can try to find spanning trees of the digraph if you need it. You can try to use it as the basis for a nondeterministic finite automaton.
answered Jul 29 at 14:20
Somos
11k1831
Assuming I understand what you have tried to show in your image, you have a directed graph (digraph) with a loop and nodes of outdegree two. There may be other structure that you can endow your digraph with if you need it. You don't have a tree because there are directed cycles, for example, $ 4 to 10 to 4. $ You can try to find spanning trees of the digraph if you need it. You can try to use it as the basis for a nondeterministic finite automaton.
answered Jul 29 at 14:20
Somos
11k1831
edited Jul 30 at 2:28
answered Jul 29 at 14:20
Somos
11k1831
answered Jul 29 at 14:20
Somos
11k1831
answered Jul 29 at 14:20
Somos
11k1831
11k1831
I might have been unclear about how the structure works, but you seem to partly answer my question. I don't think I want a tree (or forest) because path-tracing the branches may or may not enter a cycle. So I can't eliminate edges. A more difficult question is wether a path will enter an infinite cycle in Collatz iterations. I think digraph is close to what i need yes, since there are definite directions.
– Natural Number Guy
Jul 29 at 15:37
Updated the thing now, so it looks more like a graph.
– Natural Number Guy
Jul 29 at 16:30
add a comment |Â
I might have been unclear about how the structure works, but you seem to partly answer my question. I don't think I want a tree (or forest) because path-tracing the branches may or may not enter a cycle. So I can't eliminate edges. A more difficult question is wether a path will enter an infinite cycle in Collatz iterations. I think digraph is close to what i need yes, since there are definite directions.
– Natural Number Guy
Jul 29 at 15:37
Updated the thing now, so it looks more like a graph.
– Natural Number Guy
Jul 29 at 16:30
I might have been unclear about how the structure works, but you seem to partly answer my question. I don't think I want a tree (or forest) because path-tracing the branches may or may not enter a cycle. So I can't eliminate edges. A more difficult question is wether a path will enter an infinite cycle in Collatz iterations. I think digraph is close to what i need yes, since there are definite directions.
– Natural Number Guy
Jul 29 at 15:37
I might have been unclear about how the structure works, but you seem to partly answer my question. I don't think I want a tree (or forest) because path-tracing the branches may or may not enter a cycle. So I can't eliminate edges. A more difficult question is wether a path will enter an infinite cycle in Collatz iterations. I think digraph is close to what i need yes, since there are definite directions.
– Natural Number Guy
Jul 29 at 15:37
Updated the thing now, so it looks more like a graph.
– Natural Number Guy
Jul 29 at 16:30
Updated the thing now, so it looks more like a graph.
– Natural Number Guy
Jul 29 at 16:30
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2866049%2fwhat-type-of-tree-is-this%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
A tree is connected. This would be a forest.
– user578878
Jul 29 at 12:54
Tree is a connected graph with no cycles, so your picture represents two trees. I do not understand what do you mean by some of the nodes could have been connected
– Antoine
Jul 29 at 12:55
This seems to be a data structure you've invented for some purpose. I doubt that it has appeared before, and that it has a name. Describe it carefully in your paper or computer program and choose an appropriate name.
– Ethan Bolker
Jul 29 at 13:00
Ok @Antoine: I mean that each node has a decision in it, to go left or right. But the route it takes doesn't mean some of the other nodes are connected in a practical sense. Hard to explain.
– Natural Number Guy
Jul 29 at 13:01
@EthanBolker The purpose is that it is invented for studying the Collatz Conjecture. Thanks for the answers.
– Natural Number Guy
Jul 29 at 13:04