基于UKKonen实现后缀树总结以及代码怎么写，很多新手对此不是很清楚，为了帮助大家解决这个难题，下面小编将为大家详细讲解，有这方面需求的人可以来学习下，希望你能有所收获。
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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。
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
#include
using namespace std;
class SuffixNode
{
public:
vector 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
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)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::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::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!"<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!"<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]:"<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 ; phasem_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;
}
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