Given a binary search tree root, and integers lo and hi, return the count of all nodes in root whose values are between lo and hi (inclusive).
For example, with this tree and lo = 5 and hi = 10, return 3 since only 7, 8, 9 are between [5, 10].
3
/ \
2 9
/ \
7 12
/ \
4 8
Example 1
Input
root = [3, null, [5, null, null]]
lo = 4
hi = 7
Output
1
Our base case is if the node value is 0, we want to return nothing.
Binary Search Trees have 2 properties that interest us:
The left node is smaller than the parent
The right node is larger than or equal to the parent
Therefore if our hi is less than the value, we go to the left. This is because:
lo = 5, hi = 10.
If our hi is less than our value, we want to go to the left. This is because all numbers in the right nodes path will always be larger than hi due to the nature of binary search trees.
If our lo is higher than our value, we want to go to the right. Again, this is because all values in the left hand side are less than our lowest value and due to the nature of binary search trees we want to go to the right.
Eventually, we only go down the paths that have nodes that can possibly be within the appropriate range.
Left is always smaller than current value, right is always equal to or higher than current value.
Otherwise, the current value is within the range and we we add together our 2 recursive calls along with adding + 1 to the counter.
