Complete the sentence to explain why balancing is important in data structures.
Balancing a data structure helps keep its height [1], which improves performance.Balancing keeps the height minimal, which ensures operations like search, insert, and delete stay efficient.
Complete the sentence to describe the worst-case height of an unbalanced binary search tree.
In the worst case, an unbalanced binary search tree can have height [1], making operations slow.Without balancing, the tree can become a linked list with height n, causing slow operations.
Fix the error in the explanation about balancing trees.
Balancing trees ensures that the height is always [1], which is equal to the number of nodes.The height is logarithmic in the number of nodes, not equal to the number of nodes, which prevents worst-case degradation.
Fill both blanks to complete the explanation of balancing benefits.
Balancing a tree keeps its height around [1], so operations take [2] time instead of linear time.
Balanced trees have height about log n, so operations like search take logarithmic time, much faster than linear time.
Fill all three blanks to explain how balancing prevents worst-case degradation.
When a tree is balanced, its height is about [1], which means search takes [2] steps, much better than [3] steps in an unbalanced tree.
Balanced trees have height about log n, so search takes logarithmic steps, which is much faster than linear steps (n) in unbalanced trees.