How does a weight balanced tree differ from a height balanced tree in terms of balancing criterion?a)It focuses on the total number of nodes in the tree.b)It considers the weight of the edges in the tree.c)It minimizes the absolute difference in height between subtrees.d)It maximizes the height of the tree.
Question
How does a weight balanced tree differ from a height balanced tree in terms of balancing criterion?a)It focuses on the total number of nodes in the tree.b)It considers the weight of the edges in the tree.c)It minimizes the absolute difference in height between subtrees.d)It maximizes the height of the tree.
Solution
A weight balanced tree and a height balanced tree differ in their balancing criteria as follows:
a) A weight balanced tree focuses on the total number of nodes in the tree. This means that it tries to distribute the nodes in the tree in such a way that the number of nodes in the left and right subtrees of every node differs by at most one. This is different from a height balanced tree, which focuses on the heights of the subtrees.
b) The weight balanced tree does not consider the weight of the edges in the tree. The term "weight" in a weight balanced tree refers to the number of nodes, not the weight of the edges.
c) A height balanced tree minimizes the absolute difference in height between subtrees. This means that for every node in the tree, the height of the left subtree and the right subtree should not differ by more than one. This is different from a weight balanced tree, which focuses on the number of nodes in the subtrees.
d) Neither a weight balanced tree nor a height balanced tree aims to maximize the height of the tree. Both types of trees aim to minimize the height of the tree to ensure that operations like insertion, deletion, and search can be performed efficiently.
Similar Questions
The weight balance criterion in a weight-balanced tree ensures a proportional relationship between the weight of a subtree and the _____ of the subtree.a)depthb)widthc)valued)height
In a weight-balanced tree, the _____ of a node is defined as the number of nodes in its left subtree divided by the number of nodes in its right subtree.
What does the absolute difference of height between left and right subtrees indicate in a height balanced tree?a)Balance of the treeb)Maximum height of the treec)Total number of nodes in the treed)Minimum height of the tree
In a weight-balanced tree, the _____ of a node is defined as the number of nodes in its left subtree divided by the number of nodes in its right subtree.a)rotation factorb)constant factorc)weight balance factord)depth ratio
In a weight-balanced tree, a new node with a large weight is inserted as the right child of a node with a small weight.How might the tree adapt to maintain balance, and what rotation operation is likely to be involved?a)No action is needed.b)The left subtree's weight increases; left rotation is performed.c)The right subtree's weight increases; right rotation is performed.d)The left subtree's weight decreases; double rotation is performed.
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