基于UKKonen实现后缀树总结以及代码怎么写

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。

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 chSuffixNode* 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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