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For each of the following statements about red-black trees, determine whether it

ID: 3774371 • Letter: F

Question

For each of the following statements about red-black trees, determine whether it is true or false. If you think it is true, provide a justification. If you think it is false, give a counterexample. a. A subtree of a red-black tree is itself a red-black tree. b. The sibling of an external node is either external or it is red. c. Given a red-black tree T, there is an unique (2,4) tree T associated with T. d. Given a (2,4) tree T, there is a unique red-black tree T associated with T.
/*IF YOU WRITE CODE, PLEASE PROVIDE COMMENTS*/ I need to understand For each of the following statements about red-black trees, determine whether it is true or false. If you think it is true, provide a justification. If you think it is false, give a counterexample. a. A subtree of a red-black tree is itself a red-black tree. b. The sibling of an external node is either external or it is red. c. Given a red-black tree T, there is an unique (2,4) tree T associated with T. d. Given a (2,4) tree T, there is a unique red-black tree T associated with T.
/*IF YOU WRITE CODE, PLEASE PROVIDE COMMENTS*/ I need to understand For each of the following statements about red-black trees, determine whether it is true or false. If you think it is true, provide a justification. If you think it is false, give a counterexample. a. A subtree of a red-black tree is itself a red-black tree. b. The sibling of an external node is either external or it is red. c. Given a red-black tree T, there is an unique (2,4) tree T associated with T. d. Given a (2,4) tree T, there is a unique red-black tree T associated with T.
/*IF YOU WRITE CODE, PLEASE PROVIDE COMMENTS*/ I need to understand

Explanation / Answer

Answer :

For each of the following statements about red-black trees, determine whether it is true or false. If you think it is true, provide a justification. If you think it is false, give a counterexample.

a. A subtree of a red-black tree is itself a red-black tree.

b. The sibling of an external node is either external or it is red.

c. Given a red-black tree T, there is an unique (2,4) tree T associated with T.

d. Given a (2,4) tree T, there is a unique red-black tree T associated with T.

Answer :

a. A subtree of a red-black tree is itself a red-black tree.

Answer :

False

Explanation :

A subtree of a red-black tree is itself a red-black tree.

No,Because the definition of RB trees,A subtree with a red root is not a red-black tree.Definition says that the root is always black.

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b. The sibling of an external node is either external or it is red.

Answer :

True

Explanation :

If an external node had ablack internal sibling then these 2 siblings would not have the same black depth,which would combinations of statements the property of red black trees that all leaves must have the same black depth.

c. Given a red-black tree T, there is an unique (2,4) tree T associated with T.

Answer :

True

Explanation :

All three types of nodes in a (2,4) tree can be directly converted to corresponding red-black nodes.Every node in the red-black tree with 2 red children is uniquely represented as a 4-node in T.Merge each block node with its red children to form either 2-node,4-node.So,It is true for Given a red-black tree T, there is an unique (2,4) tree T associated with T.

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d. Given a (2,4) tree T, there is a unique red-black tree T associated with T.

Answer :

False.

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