求二叉树中距离最远的两个叶子节点间的距离？

问题：给定一棵二叉树（非二叉检索树），求二叉树中距离最远的两个叶子节点间的距离？其中两个叶子间的距离定义为：F(X,Y) = 从节点X到根节点路径上所有节点数据之和 + 从节点Y到根节点路径上所有节点数据之和 - 从X和Y的第一个祖先节点到根节点路径上所有节点数据之和。

该题的主要思路：

1.求出二叉树的所有叶子节点。

2.求任意两个叶子节点的第一个祖先节点。

3.计算具有祖先-子孙关系的两个节点之间的路径，并计算路径上节点数据之和。

#include <iostream>
#include <vector>
using namespace std;

struct Node
{
	Node(int data_) {data = data_; left = NULL; right = NULL;}
	int data;
	Node* left;
	Node* right;
};

bool isExistPath(Node* ancestor, Node* descendant, vector<Node*> &path, int &pathLen)
{
	if(ancestor == NULL)
		return false;
	
	path.push_back(ancestor);
	pathLen++;

	if(ancestor->left == NULL && ancestor->right == NULL)
	{
		if(ancestor == descendant)
		{
			return true;
		}
	}

	bool b1 = isExistPath(ancestor->left,descendant,path,pathLen);
	bool b2 = isExistPath(ancestor->right,descendant,path,pathLen);
	if(!b1 && !b2)
	{
		path.pop_back();
		pathLen--;
		return false;
	}
	return true;
}

int calculateDistance(Node* p, Node* q)
{
	vector<Node*> path;
	int pathLen = 0;
	if(isExistPath(p,q,path,pathLen))
	{
		int res = 0;
		for(int i = 0; i < pathLen; i++)
			res += path[i]->data;
		return res;
	}	
}

static vector<Node*> leafNodes;
void findLeafNodes(Node* root)
{
	if(root->left == NULL && root->right == NULL)
		leafNodes.push_back(root);
	if(root->left)
		findLeafNodes(root->left);
	if(root->right)
		findLeafNodes(root->right);
}

Node* LCA(Node* root, Node* p, Node* q) //least common ancestor
{
	Node *l,*r,*tmp;
	if(root == NULL)
		return NULL;
	if(root->left == p || root->left == q || root->right == p || root->right == q)
		return root;
	else
	{
		l = LCA(root->left,p,q);
		r = LCA(root->right,p,q);
		if(l != NULL && r != NULL)
			return root;
		else
		{
			tmp = (l != NULL) ? l : r;
			return tmp;
		}
	}
}

int main()
{
	Node* root = new Node(5);
	root->left = new Node(4);
	root->left->left = new Node(2);
	root->left->right = new Node(1);
	root->right = new Node(3);
	root->right->left = new Node(6);
	root->right->right = new Node(7);
	root->right->right->left = new Node(8);
		
	int res = 0;
	int max = -1;
	
	findLeafNodes(root);
	for(int i = 0; i < leafNodes.size(); i++)
		for(int j = i+1; j < leafNodes.size(); j++)
		{
			Node* lca = LCA(root,leafNodes[i],leafNodes[j]);
			int d1 = calculateDistance(root,leafNodes[i]);
			int d2 = calculateDistance(lca,leafNodes[j]);
			res = d1 + d2 - lca->data;
			max = res > max ? res : max;
		}
	cout << max << endl;
	return 0;
}