15.1. Finding the Minimum

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.

To find the minimum value in a binary tree, we start our search from the root node. We will repeatedly move to the left child of the current node until we cannot move left anymore. This iterative approach relies on the fact that in a binary search tree, the leftmost node is always the minimum.

Think of searching for the lowest shelf in a multi-level store. Starting at the top (the root), you keep going down (moving left in the tree) to find the shelf that has the lowest items. You don’t need to check every shelf; you just need to keep looking left until you find the one that is at the bottom.

So, we can easily find it recursively, now we will typically use this assuming the trees not empty, it simplifies a little bit of coding. So, assuming the trees not empty we do not have to check any special condition and given a error when it is not empty, when it is empty. So, we assume it is not empty, so if we can go left we can we do, so if the t dot left is nil then this is the minimum value and we return otherwise, we recursively search for the minimum value on the left.

Using recursion, we can efficiently find the minimum value by checking if the left child of the current node exists. If it does, we continue searching down the left subtree. If there is no left child (i.e., it's nil), then we have reached the minimum value, which we can return.

Imagine you are looking for the shortest person in a room full of people. You start with the first person. If you find someone shorter, you continue with that shorter person until you cannot find anyone shorter. The last person you check is the shortest individual.

And again there is the very simple iterative version, we start with the current thing and we keep going left as long as we can. So, long as we do not it will nil and when reach this point why t dot left is nil, we come out with this loop and you return the value at this point.

The iterative method for finding the minimum in a tree uses a loop to traverse left. We start with the root node and continue moving left until we cannot go further. Once we find a node where the left child is nil, we stop and return that node's value as the minimum.

Think of a staircase that only goes down to a basement. You keep going down step by step (moving left in the tree) until there's no more step to take. The last step you stood on before reaching the bottom is like finding the minimum value.

So, 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.

Just as we find the minimum value by moving left, the maximum value is found by moving to the rightmost node of the tree. Each right move leads to a larger value, so once you reach a node that has no right child, that node contains the maximum value.

Imagine you are trying to find the tallest person in a line of people standing on a staircase. Starting from the bottom, every level you go up, you see taller individuals. You keep going up until there are no more steps, and the person you stand next to is the tallest.

And again iterative version of the same, we just follow chase point as to the right. So, as long as right t dot right is not nil, we move from t to t dot right and when we cannot move any more here of the maximum value, so we return that value.

Similar to finding the minimum, the iterative method for finding the maximum involves continuously moving to the right child of the current node until you reach a point where there are no more right children. At that point, you return the value of that node as the maximum.

Think of a game where you have to climb to the top of a tower, trying to find the highest point. As you keep climbing up (moving to the right in the tree), you only stop when you reach the last stair, indicating that you have reached the highest location.

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