Why are we trying to keep trees balanced

Question

I see many questions that are talking about balanced tree.

For instance R-Tree are better than KD-Tree as they are balanced.

What is the advantage of using a balanced tree over a non-balanced tree?

Answer 1

Searching this tree

O
 \
  O
   \
    O
     \
      O
       \
        O
         \
          O
           \
            O

Is going to take Θ(N) time. Searching this tree

     O
   /   \
  O     O
 / \   / \
O   O O   O

Is going to take Θ(logN) time. Since search time is proportional to the height of the tree.