15.. Find Operations

Now, like binary search you can do iterative version of this, so you start at the root and then so long as it is not nil you trust on the path. So, the current values we return true; otherwise, you walked on to the left are you actually start to the root and you kind of trace a path you can values are that find. And then when you reach are node you say yes, on the other hand if you reach a point where you cannot going further, if you run out of nodes, if you come all the way down and then you say there is no extension, where I can find it then we will safe also. So, this is the simple recursive and iterative version of find.

The find operations are used to determine whether a particular value exists within a binary search tree (BST). These operations can be implemented either recursively or iteratively. In both methods, the search starts at the root of the tree. If the current node is null, it indicates that the value is not in the tree. If the current node matches the target value, the search is successful. Otherwise, the search continues down the left or right subtree depending on whether the target value is less than or greater than the current node's value.

Imagine searching for a book in a library (the binary search tree). You start at the entrance (the root). If you can't find the specific section, you check the next available shelf (next node). If you find a book that matches what you’re looking for, you've succeeded. If you reach an empty shelf and still haven’t found the book, you conclude it isn't available.

The minimum node in the tree is the left most node, in other wards it is the node that you reach if you go and as for as you can follow only left edges. ... So, this is the reason why the left most value in the tree will be the minimum.

To find the minimum value in a binary search tree, you must continuously move to the left child of each node until there are no more left children (i.e., until you reach a node where the left child is null). This is because, in a BST, the smallest value is always located in the leftmost node of the tree, as all nodes to the left of the current node contain smaller values.

It's similar to exploring a street with multiple shops arranged by the height of their signs. The shortest sign (minimum value) will be the first one you see as you walk down the street (leftmost node), assuming you only look left.

Symmetrically the maximum is the right most value on the tree, as you go right you go bigger, if you cannot go right any more this is nothing which is bigger than that node. ... So, this point we have done find minimum and maximum in a search tree.

To find the maximum value in a binary search tree, you need to trace the right child of each node until there's no more right child (when the right child is null). The maximum value is always located at this rightmost node since, in a BST, every node to the right contains larger values.

Think of it like climbing to the top of a staircase where each step represents a value. The top step is the tallest (maximum value), and you can only reach it by moving upwards (tracing the right children) until you can go no higher.

The successor of x in the list, supposed to be the next value, the next smallest value after x the list. ... So, we know that the way that in order works, it prints the left sub tree then it prints x, then it prints right sub tree.

The successor of a given node in a binary search tree is the node with the smallest value that is greater than the value of the given node. If the node has a right subtree, the successor is the minimum value found in that subtree. If the node does not have a right subtree, you must traverse back up the tree using parent pointers until you find the first ancestor that's a left child of its parent, as that ancestor is the successor.

Consider a queue of people waiting for a bus where everyone is lined up by height (like node values). The successor of the person in front is simply the next tallest person behind them in line.

The situation for the predecessor is symmetric, so if we have a left sub tree, then the predecessor is the maximum value in this. ... This is how the predecessor works it is exactly symmetric to the successive function.

The predecessor of a given node in a binary search tree is the node with the largest value that is less than the value of that node. If the node has a left subtree, the predecessor is the maximum value found in that subtree. If it does not have a left subtree, you must traverse back up the tree to find the first ancestor that is a right child of its parent. This ancestor will be the predecessor.

Think of it in terms of a game where points are assigned descendingly, and as you score a new point (the node value), your predecessor is the person who scored just before you (the maximum value in the left subtree).

--