A binary tree is either an empty tree (represented by an empty pointer) or a node consisting of a single integer value and two binary trees called the left subtree and right subtree.
A binary tree T is given. A path in tree T is a non-empty sequence of nodes of tree T such that each consecutive node in the sequence is a subtree of its preceding node.
A path P in tree T is given. The amplitude of path P is the maximum difference between values of nodes on path P. The amplitude of tree T is the maximum amplitude of paths in T. If tree T is empty, then it does not have any paths and its amplitude is assumed to be 0.
For example, consider the following tree T consisting of nine nodes:
5
/ \
8 9
/ \ | \
12 2 8 4
| |
2 5
Sequence [9, 8, 2] is a path in this tree. Sequence [12, 8, 2] is not a path in this tree. Path [5, 8, 2] has amplitude 6. Paths [9, 8, 2] and [5, 8, 12] have amplitude 7. The amplitude of the tree is 7, as no path in it has amplitude greater than [9, 8, 2] or [5, 8, 12].
Assume that the following declarations are given:
class Tree {
public int x;
public Tree l;
public Tree r;
}
Write a function:
class Solution { public int solution(Tree T); }
that, given a tree T consisting of N nodes, returns the amplitude of T.
For example, given tree T shown in the example above, the function should return 7.
Assume that:
· N is an integer within the range [0..1,000,000];
· each element of tree T is an integer within the range [-1,000,000,000..1,000,000,000].
