学步园

  几年前曾实现过一个菜鸟版的SuffixTree。最近要用到后缀树处理些问题，认真实现了一个，主要是基于UKKonen的On-Line算法。稍微总结下。

  网上关于后缀树介绍的文章有几篇写的挺好的，我就不再费力去做重复工作了。这个只是我的个人总结帖，所以定位是给看了后缀树的简介，知道什么后缀树，然后看了UKKonen的加速文章，有点迷迷糊糊的同学的一个总结帖。

  首先国内后缀树介绍有几个博客写的蛮详细的：

  http://www.cnblogs.com/snowberg/archive/2011/10/21/2468588.html

  http://blog.csdn.net/v_july_v/article/details/6897097

    正宗的Paper应该是Ukkonen的下面这一篇paper。

  （1）      E. Ukkonen, On-Line Construction ofSuffix Trees, Algorithmica, 14 (1995), 249-260

    但是我看了，对我来说真心有点难懂啊，然后Gusfield后来写了不知道书还是Paper的下面一个文章，讲的就通俗易懂多了，想学习后缀树OnLine算法的话，强烈推荐看下面的Guesfield的文章。

  （2）      Gusfield, Dan (1999) [1997].Algorithms on Strings, Trees and Sequences: Computer Science and ComputationalBiology. USA: Cambridge University Press.

    上面两篇Paper都是英文，想看的同学Google下即可。

    大部分的同学一看后缀树都明白是什么回事了，但是一看到UKKonen的算法，三个加速大段大段的描述后，就晕掉了。

    我尝试忽略证明，简单并不严谨地总结下UKKonen算法中（没看过Guesfield或相关文章的同学，我只能表示对不住了），关键的三个加速：

（1）      SuffixLink ： 各种理论证明起来有点小复杂，但是道理用处说白了很简单。 因为当我们将s[i+1] 加到子串s[j-1…i]后，下一步我们就想将s[i+1]加到s[j….i]后面。正常来说我们就从根节点遍历s[j….i]呗，但是这个花时间啊，所以我们为什么不从s[j-1…..i]直接就跳到s[j….i]呢，而不要每次都从根节点遍历下来。所以所谓的SuffixLink，对s[j-1....i]来说，就是s[j…..i]的地址。

（2）      在Ukkonen算法中，叶节点总是叶节点（这个加速认真看下Gusfield的文章一看就懂，这里只是总结，就不深入去讲），所以每次遍历只需从最后一个叶节点开始。

（3）      但发现s[j…i+1]已经在后缀树中，那么s[j+1….i+1]这些后缀肯定也在后缀树中了，所以就不需要再遍历。

    Ukkoen的后缀树我觉得最难得还是代码实现。网上代码比较少，特来分享下。我这个肯定不是最快的，不过应该是后缀树注释最多之一的一份代码了，而且代码结构和Guesfield那文章的整体描述比较接近。然后为了方便入门，这个只实现了加速1，慢慢一个个的来。大家有兴趣的，稍微修改下加速2和加速3就来了。然后有错误，也麻烦大家指正，我做了不少测试了，结果都正确，但是暂时不敢100%包票。

    头文件：

#pragma once

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


class SuffixNode
{
public:
	vector<SuffixNode*> m_pSons;
	SuffixNode* m_pFarther;
	SuffixNode* m_pSuffixLink;
	int m_iPathPosition;
	int m_iEdgeStart;
	int m_iEdgeEnd;
};

class SuffixTree
{
public:
	//int m_iE;//The virtual end of all leaves.
	SuffixNode* m_pRoot;//The root of the tree.
	string m_czTreeStr;//the string that the tree represent.
};

//Means a sub string of the suffix tree (string[beging],string[end]). 
class TreePath
{
public:
	int m_iBegin;
	int m_iEnd;
};


//Represent the char in a node's incoming edge.
class TreePos
{
public:
	TreePos()
	{
		m_iEdgePos = 0;
		m_pNode = NULL;
	}
	TreePos(int edgePos,SuffixNode* pNode)
	{
		m_iEdgePos = edgePos;
		m_pNode = pNode;
	}
	int m_iEdgePos;//The ith char of the incoming edge.
	SuffixNode* m_pNode;//The node we are going to search.
};


//=====================================Class Declarations============================== 


void SingleCharExtesion(SuffixTree* pTree,TreePos* pPos ,TreePath extendStrPath,int* firstExtensionFlag);


/*
  Add s[0....i+1],s[1...i+1].... to the suffix tree
  Input:
  SuffixNode* pNode : When we only use trick 1,pNode is the pointer to the longest leaf,s[0........i].
  phase : Equals i+1 in the paper.
*/
void SinglePhaseExtend(SuffixTree* pTree,TreePos pPos,int phase);



SuffixNode* CreateTreeNode(SuffixNode* pFarther,int iedgeStart,int iedgeEnd);



/*
   FollowSuffixLink :
   Follows the suffix link of the source node according to Ukkonen's rules(jump from s[j-1...i] to s[j....i]). 

   Input : The tree, and node. The node is the last internal node we visited.
   Output: The destination node that represents the longest suffix of node's 
           path. Example: if node represents the path "abcde" then it returns 
           the node that represents "bcde".
*/
void FollowSuffixLink(SuffixTree* pTree,TreePos* pPos, TreePath strji);



int GetNodeLabelLength(SuffixTree* pTree, SuffixNode* pNode);



int GetNodeLabelEnd(SuffixTree* pTree,SuffixNode* pNode);



/*
  Find the son node which starts with the char,ch.
*/
SuffixNode* Find_Son(SuffixTree* pTree,SuffixNode* pFarNode, char ch);



bool IsTheLastCharInEdge(SuffixTree* pTree, SuffixNode* pNode, int edge_pos);



SuffixNode* ApplyExtensionRule2(SuffixNode* pNode,int edgeLabelBeg,int edgeLabelEnd,int edgePos,bool newLeafFlag);


/*
  Trace the sub string(TreePath str) from the node(SuffixNode* pNode).
  Input:
  int* edgePos : where the last char is found at that edge
  int* charsFound : how many chars of str have been found.
  bool skipFlag : Use skip trick or not.  
*/
SuffixNode* TraceString(SuffixTree* pTree,SuffixNode* pNode,TreePath str,int* edgePos,int* charsFound,bool skipFlag);


/*
  Trace the substring(TreePath strPath) in one single edge out of pNode.
*/
SuffixNode* TraceSingleEdge(SuffixTree* pTree,SuffixNode* pNode,TreePath strPath,int* charsFound,int* edgePos,bool* searchDone,bool skipFlag);


SuffixNode* CreateFirstCharacter(SuffixTree* pTree);//Add the first character to the suffix tree.


SuffixTree* CreateSuffixTree(string tStr);


/*
For Debug:
See if the sub string (from root to pPos) equals pTree->string[subPath.m_iBegin,subPath.m_iEnd]
*/
bool TestPosSubStringEqualPath(SuffixTree* pTree,TreePos *pPos, TreePath subPath);



bool FindSubString(SuffixTree* pTree,string subStr);
//=====================================================================================

  在看具体的实现前，先看看如何调用我这个后缀树的类吧，最简单的应用，查找某子串是否在母串中： 

	string str="MISSISSIPPI";
	string subStr="PP";
	SuffixTree* pTree = CreateSuffixTree(str);
	bool existFlag = FindSubString(pTree,subStr);

   最后来看具体的实现：

#pragma once

#include "SuffixTree.h"
#include <iostream>
using namespace std;


SuffixNode* pNodeNoSuffixLink=NULL;

//=====================================Class Definitions==============================


/*
  Trace the substring(TreePath strPath) in one single edge going out of pNode.
  Input:
  int* edgeCharsFound : how many characters we find matched in the outgoing edge of pNode.
*/
SuffixNode* TraceSingleEdge(SuffixTree* pTree,SuffixNode* pNode,TreePath strPath,int* edgeCharsFound,int* edgePos,bool* searchDone,bool skipFlag)
{
	//Find outgoing edge of pNode with our first character.
	SuffixNode* nextNode = Find_Son(pTree,pNode,pTree->m_czTreeStr[strPath.m_iBegin]);

	*searchDone = true;

	if(nextNode == NULL)
	{//There is no match in pNode's sons,so we can only return to pNode.
		*edgePos = GetNodeLabelLength(pTree,pNode); 
		*edgeCharsFound = 0;
		return pNode;
	}

	int edgeLen = GetNodeLabelLength(pTree,nextNode);
	int strLen = strPath.m_iEnd - strPath.m_iBegin + 1;

	if(skipFlag == true)//Use the trick1 : skip
	{
		if(edgeLen < strLen)
		{
			*searchDone = false;
			*edgeCharsFound = edgeLen;
			*edgePos = edgeLen - 1;
		}
		else if(edgeLen == strLen)
		{
			*edgeCharsFound = edgeLen;
			*edgePos = edgeLen - 1;
		}
		else
		{
			*edgeCharsFound = strLen;
			*edgePos = strLen - 1;
		}

		return nextNode;
	}


	else//No skip,match each char one after another
	{
		*edgePos = 0;
		*edgeCharsFound = 0;

		//Find out the min length
		if(strLen < edgeLen)
			edgeLen = strLen;

		for(*edgeCharsFound=1,*edgePos=1;(*edgePos)<edgeLen ;(*edgePos)++,(*edgeCharsFound)++)
		{
			if( pTree->m_czTreeStr[ nextNode->m_iEdgeStart + *edgePos ] != pTree->m_czTreeStr[strPath.m_iBegin + *edgePos ])
			{
				(*edgePos)--;
				return nextNode;
			}
		}
	}

	//When it comes here, (*edgePos) is one more;
	(*edgePos)--;

	if(*edgeCharsFound < strLen)
	{
		*searchDone = false;
	}
	return nextNode;
}


/*
  Trace the sub string(TreePath str) from the node(SuffixNode* pNode).
  Input:
  int* edgePos :For output , where the last char is found at that edge
  int* charsFound : How many chars of str have been found.
  bool skipFlag : Use skip trick or not.  
*/
SuffixNode* TraceString(SuffixTree* pTree,SuffixNode* pNode,TreePath str,int* edgePos,int* charsFound,bool skipFlag)
{
	bool searchDone=false;
	*charsFound = 0;
	*edgePos=0 ;
	int edgeCharsFound=0;

	while(searchDone==false)
	{
		edgeCharsFound = 0;
		*edgePos=0;

		pNode = TraceSingleEdge(pTree,pNode,str,&edgeCharsFound,edgePos,&searchDone,skipFlag);

		str.m_iBegin += edgeCharsFound;
		*charsFound += edgeCharsFound;
	}

	if(*charsFound == 0)
		return NULL;

	return pNode;
}



/*
  Input:
   (1) pNode : the node who is going to add a new son or whose edge is going to be split.
   (2) edgeLabelBeg :  when newleafFlag==true,it's the edge begin label of the new leaf. when when newleafFlag==false, it's the edge begin label of the new new leaf( the leaf of s[i+1], not s[i]).
   (3) like above : just the end
   (4 )int edgePos : where split is done to pNode if newLeafFlag==false (the 0th position or 1th position or...)
*/
SuffixNode* ApplyExtensionRule2(SuffixNode* pNode,int edgeLabelBeg,int edgeLabelEnd,int edgePos,bool newLeafFlag)
{
	if(newLeafFlag==true)
	{
		//Add an new leaf
		SuffixNode* newLeaf = CreateTreeNode(pNode,edgeLabelBeg,edgeLabelEnd);

		return newLeaf;
	}

	else
	{
		//Add an new internal node and an new leaf

		//First create the new internal node.
		SuffixNode* nInternalNode = CreateTreeNode(pNode->m_pFarther,pNode->m_iEdgeStart,pNode->m_iEdgeStart + edgePos);
		
		//Remove pNode from its farther's sons
		for(vector<SuffixNode*>::iterator pNodeIter=pNode->m_pFarther->m_pSons.begin();
			pNodeIter!=pNode->m_pFarther->m_pSons.end();pNodeIter++)
		{
			if( pNode == *pNodeIter )
			{
				pNode->m_pFarther->m_pSons.erase(pNodeIter);
				break;
			}
		}

		//Adjust pNode's information.
		pNode->m_iEdgeStart += (edgePos + 1);
		pNode->m_pFarther = nInternalNode;
		nInternalNode->m_pSons.push_back(pNode);

		//Create the new leaf for s[i+1]
		SuffixNode* nLeafNode = CreateTreeNode(nInternalNode,edgeLabelBeg,edgeLabelEnd);

		return nInternalNode;
	}
}


bool IsTheLastCharInEdge(SuffixTree* pTree, SuffixNode* pNode, int edge_pos)
{
	if( edge_pos == GetNodeLabelLength(pTree,pNode) - 1 )
		return true;
	return false;
}

int GetNodeLabelEnd(SuffixTree* pTree,SuffixNode* pNode)
{
	//if(pNode->m_pSons.size() == NULL)
	//{
	//	return pTree->m_iE;
	//}
	return pNode->m_iEdgeEnd;
}

int GetNodeLabelLength(SuffixTree* pTree, SuffixNode* pNode)
{
	int length = GetNodeLabelEnd(pTree,pNode) - pNode->m_iEdgeStart + 1;
	return length;
}

SuffixNode* CreateTreeNode(SuffixNode* pFarther,int iedgeStart,int iedgeEnd)
{
	SuffixNode* pNode=new SuffixNode();

	pNode->m_iEdgeStart = iedgeStart;
	pNode->m_iEdgeEnd = iedgeEnd;
	pNode->m_pFarther = pFarther;
	pNode->m_pSuffixLink = NULL;
	if(pFarther!=NULL)
	pFarther->m_pSons.push_back(pNode);

	return pNode;
}

//Find the son node which starts with the ch
SuffixNode* Find_Son(SuffixTree* pTree,SuffixNode* pFarNode, char ch)
{
	for(vector<SuffixNode*>::iterator nodeIter=pFarNode->m_pSons.begin();
		nodeIter!=pFarNode->m_pSons.end();nodeIter++)
	{
		if(pTree->m_czTreeStr[(*nodeIter) -> m_iEdgeStart] == ch )
		{
			return *nodeIter;
		}
	}
	return NULL;
}


/*
   FollowSuffixLink :
   Follows the suffix link of the source node according to Ukkonen's rules(jump from s[j-1...i] to s[j....i]). 

   Input : The tree, and node. The node is the last internal node we visited.
   Output: The destination node that represents the longest suffix of node's 
           path. Example: if node represents the path "abcde" then it returns 
           the node that represents "bcde".
*/
void FollowSuffixLink(SuffixTree* pTree,TreePos * pPos,TreePath strji)
{
	if(strji.m_iEnd < strji.m_iBegin)//Empty string,then we return to root.
	{
		pPos->m_iEdgePos=0;
		pPos->m_pNode = pTree->m_pRoot;
		return;
	}
	/*gama : the string(r in Gusfield's paper) between node and its father.
	If the node doesn't have suffix link , we need to go up to its farther*/
	TreePath gama;

	if(pPos->m_pNode == pTree->m_pRoot)
	{
		int charsFound=0;
		pPos->m_pNode = TraceString(pTree,pTree->m_pRoot,strji,&pPos->m_iEdgePos,&charsFound,false);
		if(pPos->m_pNode == NULL)
		{
			pPos->m_iEdgePos = 0;
			pPos->m_pNode =pTree->m_pRoot;
			if(strji.m_iBegin != strji.m_iEnd)
			{
				cout<<"There is s[j-1..i](not empty) doesn't exist!"<<endl;
				return;
			}
		}
		if(strji.m_iEnd != strji.m_iBegin && charsFound != strji.m_iEnd - strji.m_iBegin + 1)
		{
			cout<<"s[j...i] doesn't exit from root:["<<strji.m_iBegin<<","<<strji.m_iEnd<<"]"<<endl;
			return;
		}
		return;
	}

	// No suffix link,walk up at most one step(if it is not the root).
	if( pPos->m_pNode->m_pSuffixLink == NULL ) 
	{
		if(pPos->m_pNode->m_pFarther == pTree->m_pRoot)
		{//its farther is the root
			pPos->m_pNode = pTree->m_pRoot;

			int charsFound=0;
			pPos->m_pNode = TraceString(pTree,pTree->m_pRoot,strji,&pPos->m_iEdgePos,&charsFound,false);
			if(pPos->m_pNode == NULL)
			{
				pPos->m_iEdgePos = 0;
				pPos->m_pNode =pTree->m_pRoot;
				if(strji.m_iBegin != strji.m_iEnd)
				{
					cout<<"There is s[j-1..i](not empty) doesn't exist!"<<endl;
					return;
				}
			}
			if(strji.m_iEnd != strji.m_iBegin &&  charsFound != strji.m_iEnd - strji.m_iBegin + 1)
			{
				cout<<"s[j...i] doesn't exit from root:["<<strji.m_iBegin<<","<<strji.m_iEnd<<"]"<<endl;
				return;
			}
			return;
		}


		else
		{
			// Find the gamma (the substring between pPos's parent's and pPos's)
			gama.m_iBegin = pPos->m_pNode->m_iEdgeStart;
			gama.m_iEnd = pPos->m_pNode->m_iEdgeStart + pPos->m_iEdgePos;// the end of s[j..i] 

			//Follow farther's suffix link
			pPos->m_pNode = pPos->m_pNode->m_pFarther->m_pSuffixLink;

			//Down-walk gamma (until we found s[i],the character we add last extension)
			int charsFound=0;
			pPos->m_pNode = TraceString(pTree,pPos->m_pNode,gama,&pPos->m_iEdgePos,&charsFound,true);
			////////////////////////////////////////////////
		}
	}
	else
	{
		//A suffix link exists - just follow it.
		pPos->m_pNode = pPos->m_pNode->m_pSuffixLink;
		pPos->m_iEdgePos = GetNodeLabelLength(pTree,pPos->m_pNode) - 1; //The last char of pPos's suffix link represents s[i] (the character we add last extension).
	}
	return;
}


/*
For Debug:
See if the sub string (from root to pPos) equals pTree->string[subPath.m_iBegin,subPath.m_iEnd]
*/
bool TestPosSubStringEqualPath(SuffixTree* pTree,TreePos *pPos, TreePath subPath)
{
	if(pTree->m_pRoot == pPos->m_pNode && subPath.m_iBegin == subPath.m_iEnd)
	{
		return true;
	}
	int strRevIndex = subPath.m_iEnd;
	SuffixNode* tmpNode = pPos->m_pNode;
	int edgeRevIndex = tmpNode->m_iEdgeStart + pPos->m_iEdgePos;

	while(tmpNode != pTree->m_pRoot)
	{
		while( edgeRevIndex >= tmpNode->m_iEdgeStart && strRevIndex >= subPath.m_iBegin)
		{
			if( pTree->m_czTreeStr[edgeRevIndex] != pTree->m_czTreeStr[strRevIndex] )
			{
				return false;
			}

			edgeRevIndex--;
			strRevIndex--;
		}

		tmpNode = tmpNode->m_pFarther;
		edgeRevIndex = tmpNode->m_iEdgeEnd;
	}

	if(strRevIndex != subPath.m_iBegin-1)
		return false;

	return true;
}

/*
Input:
(1) SuffixTree* pTree : The suffix tree
(2) TreePos* pPos : The last internal node we visited , then we are going to jump to its suffix link in this extension.
(3) TreePath extendStrPath : The suffix (s[j...i+1]) we are goint to add to the tree.
*/
void SingleCharExtesion(SuffixTree* pTree,TreePos* pPos ,TreePath extendStrPath,int* firstExtend)
{
	TreePath sji;
	sji.m_iBegin = extendStrPath.m_iBegin;
	sji.m_iEnd = extendStrPath.m_iEnd - 1;

	if(*firstExtend != -1)
	{
		//Ready to jump from suffix link at or above s[j-1...i] that either has a suffix link (to s[j-1...i]) or is the root.
		FollowSuffixLink(pTree,pPos,sji);
	}
	*firstExtend = 1;

	//////////////////////////////////////////For Debug//////////////////////////////////////////////////
	if(sji.m_iEnd >= sji.m_iBegin)
	{
		if(TestPosSubStringEqualPath(pTree,pPos, sji) == false)
		{
			cout<<"FollowSuffixLink doesn't go to the right s[j..i]:"<<extendStrPath.m_iBegin<<":"<<extendStrPath.m_iEnd-1<<endl;
		}
	}
	///////////////////////////////////////////////////////////////////////////////////////////////////////

	int chars_found=0;

	//Now we are going to found out which rule to use for extension,rule1?rule2?rule3?
	//First test rule3.
	{
		/*
		We only need to extend the last character(s[i+1]) since 
		we use suffix link to jump from s[j-1..i] to s[j..i],
		and extendStrPath.m_iEnd is s[i+1].
		*/
		chars_found = 0;
		/*
		If the last character(s[i]) is the last of its edge,
		try to find s[i+1] in the next edge.
		*/
		if(IsTheLastCharInEdge(pTree,pPos->m_pNode,pPos->m_iEdgePos))
		{
			SuffixNode* pTmp = Find_Son(pTree,pPos->m_pNode,pTree->m_czTreeStr[extendStrPath.m_iEnd]);
			if(pTmp != 0)
			{  //s[i+1] exits already.
				chars_found = 1;
			}
		}

		//Else see if can find extendStrPath.m_iEnd in the current edge
		else
		{
			if( pTree->m_czTreeStr[ pPos->m_pNode->m_iEdgeStart + pPos->m_iEdgePos + 1]
			    == pTree->m_czTreeStr[extendStrPath.m_iEnd]
				)//Notice that " + 1 " means the next char of s[j...i] : yes, s[i+1]
				{//s[i+1] exits already.
					chars_found = 1;
				}
		}
	}

	//If s[i+1] was found - rule 3 applies
	if(chars_found == 1)
	{
		 /* If there is an internal node that has no suffix link yet (only one may 
         exist) - create a suffix link from it to the father - node of the 
         current position in the tree*/
		if(pNodeNoSuffixLink != NULL)
		{
			if(pPos->m_pNode->m_pSons.size() != 0)
			{
				pNodeNoSuffixLink->m_pSuffixLink = pPos->m_pNode;
				pNodeNoSuffixLink=NULL;
			}
		}
		//if(pPos->m_pNode->m_pSons.size()==0)
		//	*ruleApplied = 1;
		//else
		//	*ruleApplied = 3;
		return;
	}

	/*Since rule3 doesn't fit ( that s[j...i+1] is not in the tree),
	we are going to see rule2 and rule1.
	*/ 

	/* If last char s[j...i] found is the last char of an edge - create an new leaf
	,apply rule2(add a new leaf) or rule1 */
	if(IsTheLastCharInEdge(pTree,pPos->m_pNode,pPos->m_iEdgePos) || pPos->m_pNode==pTree->m_pRoot)
	{
		if(pPos->m_pNode->m_pSons.size() != 0)
		{
			//Internal node or root,apply rule2 that add a new leaf
			ApplyExtensionRule2(pPos->m_pNode, extendStrPath.m_iEnd, extendStrPath.m_iEnd, 0, true);

			//Suffix Link
			if(pNodeNoSuffixLink != NULL)
			{
				pNodeNoSuffixLink->m_pSuffixLink = pPos->m_pNode;
				pNodeNoSuffixLink = NULL;
			}
			/**ruleApplied = 2;*/
		}
		//else it's a leaf, We do nothing.
		else
		{
			pPos->m_pNode->m_iEdgeEnd++;
			/**ruleApplied = 1;*/
		}
	}

	//Else apply rule2 that adds an new intern node
	else
	{
		SuffixNode* nInternalNode = ApplyExtensionRule2(pPos->m_pNode,extendStrPath.m_iEnd,extendStrPath.m_iEnd,pPos->m_iEdgePos,false);

		if(pNodeNoSuffixLink != NULL)
		{
			pNodeNoSuffixLink->m_pSuffixLink = nInternalNode;
			pNodeNoSuffixLink = NULL;
		}

		//See the new internal node's suffix link.
		if( GetNodeLabelLength(pTree,nInternalNode)==1 && nInternalNode->m_pFarther == pTree->m_pRoot)
		{
			nInternalNode->m_pSuffixLink = pTree->m_pRoot;
			pNodeNoSuffixLink = NULL;
		}
		else
		{
			pNodeNoSuffixLink = nInternalNode;
		}

		//Adjust the node for the next extension
		pPos->m_pNode = nInternalNode;

		//*ruleApplied = 2;
	}
}


/*
  Add s[0....i+1],s[1...i+1].... to the suffix tree
  Input:
  SuffixNode* pNode: When we only use trick 1,pNode is the pointer to the longest leaf,s[0........i].
*/
void SinglePhaseExtend(SuffixTree* pTree,TreePos pPos,int phase)
{
	int iExtension=0;
	//pTree->m_iE = phase-1;
	int ruleApplied=-1;
	while(iExtension <= phase )
	{
		TreePath extendPath;
		extendPath.m_iBegin=iExtension;
		extendPath.m_iEnd=phase;

		SingleCharExtesion(pTree,&pPos,extendPath,&ruleApplied);

		iExtension++;
	}

	return;
}

SuffixNode* CreateFirstCharacter(SuffixTree* pTree)
{
	SuffixNode* firstLeaf = CreateTreeNode(pTree->m_pRoot,0,0);
	return firstLeaf;
}

SuffixTree* CreateSuffixTree(string tStr)
{
	SuffixTree* psTree=new SuffixTree();
	psTree->m_czTreeStr = tStr+"$";

	psTree->m_pRoot = CreateTreeNode(NULL,0,0);

	//Add the first char into it.
	SuffixNode* firstLeaf = CreateFirstCharacter(psTree);
	TreePos* firstLeafPos = new TreePos(0,firstLeaf);


	for(int phase = 1 ; phase<psTree->m_czTreeStr.length() ; phase++)
	{
		firstLeafPos->m_iEdgePos = firstLeafPos->m_pNode->m_iEdgeEnd - firstLeafPos->m_pNode->m_iEdgeStart; //start from s[j..i]
		SinglePhaseExtend(psTree,*firstLeafPos,phase);
	}

	return psTree;
}


bool FindSubString(SuffixTree* pTree,string subStr)
{
	SuffixNode* node = Find_Son(pTree,pTree->m_pRoot,subStr[0]);
	if(node == NULL)
	{
		return false;
	}

	int startIndex = node->m_iEdgeStart;

	int strIndex=0;
	int edgeIndex;

	while(node != NULL)
	{
		edgeIndex = node->m_iEdgeStart;
		int edgeLabelEnd = node->m_iEdgeEnd;//GetNodeLabelEnd(pTree,node);
		while(strIndex < subStr.length() && edgeIndex <= edgeLabelEnd && pTree->m_czTreeStr[edgeIndex] == subStr[strIndex])
		{
			strIndex++;
			edgeIndex++;
		}

		if(strIndex == subStr.length())
		{
			//we found it
			return true;
		}
		else if(edgeIndex > node->m_iEdgeEnd)
		{
			node = Find_Son(pTree,node,subStr[strIndex]);
		}
		else
		{
			return false;
		}
	}

	return false;
}