Big O Complexity in Binary Search Tree(BST)

In the absolute worst case, a binary tree with N elements would be like a linked list.
Hence, there would be N levels, and a search would take N traversals.

                                    ~ Root ~
                                      ____
                                     | 42 |
                                     |____|
                                    /      \
                               ____/        \
                              | 13 |         X
                              |____|
                             /      \
                        ____/        \
                       | 11 |         X
                       |____|
                      /      \
                     /        \
                  ...          X

That’s why it’s O(N) in the worst case.
And this is why we need to balance the trees to achieve O(log N) search.

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