#include <iostream>
#include <vector>
#include <map>
#include <set>

using namespace std;

struct Node
{
	int val;
	vector<int> chlidren;
	Node(int v):val(v){}
};

class UnSet
{
public:
	UnSet(int n):capacity(n)
	{
		father = new int[n];
		for(int i = 0; i < n ;i++)
		{
			father[i] = i;
		}
	}
	~UnSet()
	{
		delete [] father;
	}
	int find(int i)
	{
		return (father[i] == i)?i:(father[i] = find(father[i]));
	}
	void unionSet(int a, int b)
	{
		a = find(a);
		b = find(b);
		father[b] = a;
	}
	int size()
	{
		return capacity;
	}
	int * father;
private:
	int capacity;

};

class LCA
{
public:
	LCA(Node tree[], int n):fatSet(n),capacity(n)//root is tree[0]
	{
		hasVisit = new bool[n];
		memset(hasVisit,false,n*sizeof(bool));
		this->tree = tree;
	}
	map<pair<int,int>,int> calLCA(vector<pair<int,int> > query)
	{
		map<int,set<int> > queryMap;
		map<pair<int,int>,int> result;
		for(int i =0 ; i< query.size(); i++)
		{
			int u = query[i].first;
			int v = query[i].second;
			set<int> temp;
			if(queryMap.count(u) == 0)
				queryMap[u] = temp;
			if(queryMap.count(v) == 0)
				queryMap[v] = temp;
			queryMap[u].insert(v);
			queryMap[v].insert(u);
		}
		tarjan(0,queryMap,result);
		return result;
	}

	void tarjan(int u,map<int,set<int> > & queryMap, map<pair<int,int>,int> & result)
	{
		fatSet.father[u] = u;
		hasVisit[u] = true;
		cout << u << endl;
		for(set<int>::iterator it = queryMap[u].begin(); it != queryMap[u].end();it++)
		{
			int v = *it;
			if(hasVisit[*it])
			{
				pair<int,int> temp(v,u);
				result[temp] = fatSet.find(v);
			}
		}
		for(int i = 0; i < tree[u].chlidren.size(); i++)
		{
			int v = tree[u].chlidren[i];
			if(false == hasVisit[tree[u].chlidren[i]])
			{
				tarjan(v,queryMap,result);
				fatSet.unionSet(u,v);
			}

		}
	}

private:
	int capacity;
	bool * hasVisit;
	UnSet fatSet;
	Node * tree;

};


int main()
{
	Node testTree[5]={1,2,3,4,5};
	testTree[0].chlidren.push_back(1);	
	testTree[0].chlidren.push_back(2);	
	testTree[1].chlidren.push_back(3);	
	testTree[1].chlidren.push_back(4);	
	vector<pair<int,int> > query;
	pair<int,int> a(2,3),b(3,4),c(4,1);
	query.push_back(a);
	query.push_back(b);
	query.push_back(c);
	LCA l(testTree,5);
	map<pair<int,int>,int> ret = l.calLCA(query);
	for(map<pair<int,int>,int>::iterator it = ret.begin(); it != ret.end(); it++)
	{
		cout << it->first.first << "," << it->first.second << "->" << it->second << "\t";	
	}
	return 0;
}