Q$3$: Understanding Binary Search Tree $($BST$)$

$1)$ Explain what a Binary Search Tree $($BST$)$ is$,$ including its key definition and properties.

$2)$ What is the height of a binary search tree in the worst case scenario? How does this affect the time complexity of the search operation in the worst case? Please explain briefly. What is the height of a binary search tree in the best case scenario? What is the corresponding time complexity of the search operation in this case? Provide a brief explanation.

$3)$ Suppose the following sequence of values is inserted into an empty binary search tree in order: $\backslash (5,2,12,1,3,9,21,19,25\backslash ).$ Draw the structure of the tree after all insertions have been completed.

$4)$ In the binary search tree constructed above, explain the process of searching for the value $19,$ describing step by step the sequence of nodes visited.