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Ukkonen’s Suffix Tree Construction – Part 6

Last Updated : 08 Mar, 2024
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This article is continuation of following five articles: 
Ukkonen’s Suffix Tree Construction – Part 1 
Ukkonen’s Suffix Tree Construction – Part 2 
Ukkonen’s Suffix Tree Construction – Part 3 
Ukkonen’s Suffix Tree Construction – Part 4 
Ukkonen’s Suffix Tree Construction – Part 5
Please go through Part 1, Part 2, Part 3, Part 4 and Part 5, before looking at current article, where we have seen few basics on suffix tree, high level ukkonen’s algorithm, suffix link and three implementation tricks and activePoints along with an example string “abcabxabcd” where we went through all phases of building suffix tree. 
Here, we will see the data structure used to represent suffix tree and the code implementation.
At that end of Part 5 article, we have discussed some of the operations we will be doing while building suffix tree and later when we use suffix tree in different applications. 
There could be different possible data structures we may think of to fulfill the requirements where some data structure may be slow on some operations and some fast. Here we will use following in our implementation:

We will have SuffixTreeNode structure to represent each node in tree. SuffixTreeNode structure will have following members: 

  • children – This will be an array of alphabet size. This will store all the children nodes of current node on different edges starting with different characters.
  • suffixLink – This will point to other node where current node should point via suffix link.
  • start, end – These two will store the edge label details from parent node to current node. (start, end) interval specifies the edge, by which the node is connected to its parent node. Each edge will connect two nodes, one parent and one child, and (start, end) interval of a given edge will be stored in the child node. Lets say there are two nods A (parent) and B (Child) connected by an edge with indices (5, 8) then this indices (5, 8) will be stored in node B.
  • suffixIndex – This will be non-negative for leaves and will give index of suffix for the path from root to this leaf. For non-leaf node, it will be -1 .

This data structure will answer to the required queries quickly as below:  

  • How to check if a node is root ? — Root is a special node, with no parent and so it’s start and end will be -1, for all other nodes, start and end indices will be non-negative.
  • How to check if a node is internal or leaf node ? — suffixIndex will help here. It will be -1 for internal node and non-negative for leaf nodes.
  • What is the length of path label on some edge? — Each edge will have start and end indices and length of path label will be end-start+1
  • What is the path label on some edge ? — If string is S, then path label will be substring of S from start index to end index inclusive, [start, end].
  • How to check if there is an outgoing edge for a given character c from a node A ? — If A->children is not NULL, there is a path, if NULL, no path.
  • What is the character value on an edge at some given distance d from a node A ? — Character at distance d from node A will be S[A->start + d], where S is the string.
  • Where an internal node is pointing via suffix link ? — Node A will point to A->suffixLink
  • What is the suffix index on a path from root to leaf ? — If leaf node is A on the path, then suffix index on that path will be A->suffixIndex

Following is C implementation of Ukkonen’s Suffix Tree Construction. The code may look a bit lengthy, probably because of a good amount of comments. 

C++




#include <iostream>
#include <cstring>
#include <cstdlib>
#define MAX_CHAR 256
  
struct SuffixTreeNode {
    SuffixTreeNode* children[MAX_CHAR];
    SuffixTreeNode* suffixLink;
    int start;
    int* end;
    int suffixIndex;
};
  
typedef SuffixTreeNode Node;
  
char text[100];
Node* root = nullptr;
Node* lastNewNode = nullptr;
Node* activeNode = nullptr;
int count = 0;
  
int activeEdge = -1;
int activeLength = 0;
  
int remainingSuffixCount = 0;
int leafEnd = -1;
int* rootEnd = nullptr;
int* splitEnd = nullptr;
int size = -1;
  
// Function to create a new node in the suffix tree
Node* newNode(int start, int* end) {
    count++;
    Node* node = new Node;
    for (int i = 0; i < MAX_CHAR; i++)
        node->children[i] = nullptr;
  
    node->suffixLink = root;
    node->start = start;
    node->end = end;
    node->suffixIndex = -1;
    return node;
}
  
// Function to calculate the length of an edge
int edgeLength(Node* n) {
    return *(n->end) - (n->start) + 1;
}
  
// Function to perform walk down in the tree
int walkDown(Node* currNode) {
    if (activeLength >= edgeLength(currNode)) {
        activeEdge = static_cast<int>(text[activeEdge + edgeLength(currNode)]) - static_cast<int>(' ');
        activeLength -= edgeLength(currNode);
        activeNode = currNode;
        return 1;
    }
    return 0;
}
  
// Function to extend the suffix tree
void extendSuffixTree(int pos) {
    leafEnd = pos;
    remainingSuffixCount++;
    lastNewNode = nullptr;
  
    while (remainingSuffixCount > 0) {
  
        if (activeLength == 0) {
            activeEdge = static_cast<int>(text[pos]) - static_cast<int>(' ');
        }
  
        if (activeNode->children[activeEdge] == nullptr) {
            activeNode->children[activeEdge] = newNode(pos, &leafEnd);
  
            if (lastNewNode != nullptr) {
                lastNewNode->suffixLink = activeNode;
                lastNewNode = nullptr;
            }
        }
        else {
            Node* next = activeNode->children[activeEdge];
            if (walkDown(next)) {
                continue;
            }
  
            if (text[next->start + activeLength] == text[pos]) {
                if (lastNewNode != nullptr && activeNode != root) {
                    lastNewNode->suffixLink = activeNode;
                    lastNewNode = nullptr;
                }
  
                activeLength++;
                break;
            }
  
            splitEnd = new int;
            *splitEnd = next->start + activeLength - 1;
  
            Node* split = newNode(next->start, splitEnd);
            activeNode->children[activeEdge] = split;
  
            split->children[static_cast<int>(text[pos]) - static_cast<int>(' ')] = newNode(pos, &leafEnd);
            next->start += activeLength;
            split->children[activeEdge] = next;
  
            if (lastNewNode != nullptr) {
                lastNewNode->suffixLink = split;
            }
  
            lastNewNode = split;
        }
  
        remainingSuffixCount--;
        if (activeNode == root && activeLength > 0) {
            activeLength--;
            activeEdge = static_cast<int>(text[pos - remainingSuffixCount + 1]) - static_cast<int>(' ');
        }
        else if (activeNode != root) {
            activeNode = activeNode->suffixLink;
        }
    }
}
  
// Function to print characters from index i to j
void print(int i, int j) {
    for (int k = i; k <= j; k++)
        std::cout << text[k];
}
  
// Function to set suffix index by DFS traversal
void setSuffixIndexByDFS(Node* n, int labelHeight) {
    if (n == nullptr) return;
  
    if (n->start != -1) {
        print(n->start, *(n->end));
    }
    int leaf = 1;
    for (int i = 0; i < MAX_CHAR; i++) {
        if (n->children[i] != nullptr) {
            if (leaf == 1 && n->start != -1)
                std::cout << " [" << n->suffixIndex << "]\n";
  
            leaf = 0;
            setSuffixIndexByDFS(n->children[i], labelHeight + edgeLength(n->children[i]));
        }
    }
    if (leaf == 1) {
        n->suffixIndex = size - labelHeight;
        std::cout << " [" << n->suffixIndex << "]\n";
    }
}
  
// Function to free memory in post-order traversal
void freeSuffixTreeByPostOrder(Node* n) {
    if (n == nullptr)
        return;
    for (int i = 0; i < MAX_CHAR; i++) {
        if (n->children[i] != nullptr) {
            freeSuffixTreeByPostOrder(n->children[i]);
        }
    }
    if (n->suffixIndex == -1)
        delete n->end;
    delete n;
}
  
// Function to build the suffix tree
void buildSuffixTree() {
    size = strlen(text);
    rootEnd = new int;
    *rootEnd = -1;
  
    root = newNode(-1, rootEnd);
  
    activeNode = root;
    for (int i = 0; i < size; i++)
        extendSuffixTree(i);
    int labelHeight = 0;
    setSuffixIndexByDFS(root, labelHeight);
  
    freeSuffixTreeByPostOrder(root);
}
  
// Main function
int main(int argc, char* argv[]) {
    strcpy(text, "abbc");
    buildSuffixTree();
    std::cout << "Number of nodes in suffix tree are " << count << std::endl;
    return 0;
}


C




// A C program to implement Ukkonen's Suffix Tree Construction 
#include <stdio.h> 
#include <string.h> 
#include <stdlib.h> 
#define MAX_CHAR 256 
  
struct SuffixTreeNode { 
    struct SuffixTreeNode *children[MAX_CHAR]; 
  
    //pointer to other node via suffix link 
    struct SuffixTreeNode *suffixLink; 
  
    /*(start, end) interval specifies the edge, by which the 
    node is connected to its parent node. Each edge will 
    connect two nodes, one parent and one child, and 
    (start, end) interval of a given edge will be stored 
    in the child node. Lets say there are two nods A and B 
    connected by an edge with indices (5, 8) then this 
    indices (5, 8) will be stored in node B. */
    int start; 
    int *end; 
  
    /*for leaf nodes, it stores the index of suffix for 
    the path from root to leaf*/
    int suffixIndex; 
}; 
  
typedef struct SuffixTreeNode Node; 
  
char text[100]; //Input string 
Node *root = NULL; //Pointer to root node 
  
/*lastNewNode will point to newly created internal node, 
waiting for it's suffix link to be set, which might get 
a new suffix link (other than root) in next extension of 
same phase. lastNewNode will be set to NULL when last 
newly created internal node (if there is any) got it's 
suffix link reset to new internal node created in next 
extension of same phase. */
Node *lastNewNode = NULL; 
Node *activeNode = NULL; 
int count=0;
  
/*activeEdge is represented as input string character 
index (not the character itself)*/
int activeEdge = -1; 
int activeLength = 0; 
  
// remainingSuffixCount tells how many suffixes yet to 
// be added in tree 
int remainingSuffixCount = 0; 
int leafEnd = -1; 
int *rootEnd = NULL; 
int *splitEnd = NULL; 
int size = -1; //Length of input string 
  
Node *newNode(int start, int *end) 
    count++;
    Node *node =(Node*) malloc(sizeof(Node)); 
    int i; 
    for (i = 0; i < MAX_CHAR; i++) 
        node->children[i] = NULL; 
  
    /*For root node, suffixLink will be set to NULL 
    For internal nodes, suffixLink will be set to root 
    by default in current extension and may change in 
    next extension*/
    node->suffixLink = root; 
    node->start = start; 
    node->end = end; 
  
    /*suffixIndex will be set to -1 by default and 
    actual suffix index will be set later for leaves 
    at the end of all phases*/
    node->suffixIndex = -1; 
    return node; 
  
int edgeLength(Node *n) { 
    return *(n->end) - (n->start) + 1; 
  
int walkDown(Node *currNode) 
    /*activePoint change for walk down (APCFWD) using 
    Skip/Count Trick (Trick 1). If activeLength is greater 
    than current edge length, set next internal node as 
    activeNode and adjust activeEdge and activeLength 
    accordingly to represent same activePoint*/
    if (activeLength >= edgeLength(currNode)) 
    
        activeEdge = 
         (int)text[activeEdge+edgeLength(currNode)]-(int)' '
        activeLength -= edgeLength(currNode); 
        activeNode = currNode; 
        return 1; 
    
    return 0; 
  
void extendSuffixTree(int pos) 
    /*Extension Rule 1, this takes care of extending all 
    leaves created so far in tree*/
    leafEnd = pos; 
  
    /*Increment remainingSuffixCount indicating that a 
    new suffix added to the list of suffixes yet to be 
    added in tree*/
    remainingSuffixCount++; 
  
    /*set lastNewNode to NULL while starting a new phase, 
    indicating there is no internal node waiting for 
    it's suffix link reset in current phase*/
    lastNewNode = NULL; 
  
    //Add all suffixes (yet to be added) one by one in tree 
    while(remainingSuffixCount > 0) { 
  
        if (activeLength == 0) {
            //APCFALZ 
            activeEdge = (int)text[pos]-(int)' '
        }
        // There is no outgoing edge starting with 
        // activeEdge from activeNode 
        if (activeNode->children[activeEdge] == NULL) 
        
            //Extension Rule 2 (A new leaf edge gets created) 
            activeNode->children[activeEdge] = 
                                  newNode(pos, &leafEnd); 
  
            /*A new leaf edge is created in above line starting 
            from an existing node (the current activeNode), and 
            if there is any internal node waiting for it's suffix 
            link get reset, point the suffix link from that last 
            internal node to current activeNode. Then set lastNewNode 
            to NULL indicating no more node waiting for suffix link 
            reset.*/
            if (lastNewNode != NULL) 
            
                lastNewNode->suffixLink = activeNode; 
                lastNewNode = NULL; 
            
        
        // There is an outgoing edge starting with activeEdge 
        // from activeNode 
        else
        
            // Get the next node at the end of edge starting 
            // with activeEdge 
            Node *next = activeNode->children[activeEdge];
            if (walkDown(next))//Do walkdown 
            
                //Start from next node (the new activeNode) 
                continue
            
            /*Extension Rule 3 (current character being processed 
            is already on the edge)*/
            if (text[next->start + activeLength] == text[pos]) 
            
                //If a newly created node waiting for it's 
                //suffix link to be set, then set suffix link 
                //of that waiting node to current active node 
                if(lastNewNode != NULL && activeNode != root) 
                
                    lastNewNode->suffixLink = activeNode; 
                    lastNewNode = NULL; 
                
  
                //APCFER3 
                activeLength++; 
                /*STOP all further processing in this phase 
                and move on to next phase*/
                break
            
  
            /*We will be here when activePoint is in middle of 
            the edge being traversed and current character 
            being processed is not on the edge (we fall off 
            the tree). In this case, we add a new internal node 
            and a new leaf edge going out of that new node. This 
            is Extension Rule 2, where a new leaf edge and a new 
            internal node get created*/
            splitEnd = (int*) malloc(sizeof(int)); 
            *splitEnd = next->start + activeLength - 1; 
  
            //New internal node 
            Node *split = newNode(next->start, splitEnd); 
            activeNode->children[activeEdge] = split; 
  
            //New leaf coming out of new internal node 
            split->children[(int)text[pos]-(int)' '] = 
                                      newNode(pos, &leafEnd); 
            next->start += activeLength; 
            split->children[activeEdge] = next; 
  
            /*We got a new internal node here. If there is any 
            internal node created in last extensions of same 
            phase which is still waiting for it's suffix link 
            reset, do it now.*/
            if (lastNewNode != NULL) 
            
            /*suffixLink of lastNewNode points to current newly 
            created internal node*/
                lastNewNode->suffixLink = split; 
            
  
            /*Make the current newly created internal node waiting 
            for it's suffix link reset (which is pointing to root 
            at present). If we come across any other internal node 
            (existing or newly created) in next extension of same 
            phase, when a new leaf edge gets added (i.e. when 
            Extension Rule 2 applies is any of the next extension 
            of same phase) at that point, suffixLink of this node 
            will point to that internal node.*/
            lastNewNode = split; 
        
  
        /* One suffix got added in tree, decrement the count of 
        suffixes yet to be added.*/
        remainingSuffixCount--; 
        if (activeNode == root && activeLength > 0) //APCFER2C1 
        
            activeLength--; 
            activeEdge = (int)text[pos - 
                            remainingSuffixCount + 1]-(int)' '
        
            
        //APCFER2C2 
        else if (activeNode != root) 
        
            activeNode = activeNode->suffixLink; 
        
    
  
void print(int i, int j) 
    int k; 
    for (k=i; k<=j; k++) 
        printf("%c", text[k]); 
  
//Print the suffix tree as well along with setting suffix index 
//So tree will be printed in DFS manner 
//Each edge along with it's suffix index will be printed 
void setSuffixIndexByDFS(Node *n, int labelHeight) 
    if (n == NULL) return
  
    if (n->start != -1) //A non-root node 
    
        //Print the label on edge from parent to current node 
        print(n->start, *(n->end)); 
    
    int leaf = 1; 
    int i; 
    for (i = 0; i < MAX_CHAR; i++) 
    
        if (n->children[i] != NULL) 
        
            if (leaf == 1 && n->start != -1) 
                printf(" [%d]\n", n->suffixIndex); 
  
            //Current node is not a leaf as it has outgoing 
            //edges from it. 
            leaf = 0; 
            setSuffixIndexByDFS(n->children[i], 
                  labelHeight + edgeLength(n->children[i])); 
        
    
    if (leaf == 1) 
    
        n->suffixIndex = size - labelHeight; 
        printf(" [%d]\n", n->suffixIndex); 
    
  
void freeSuffixTreeByPostOrder(Node *n) 
    if (n == NULL) 
        return
    int i; 
    for (i = 0; i < MAX_CHAR; i++) 
    
        if (n->children[i] != NULL) 
        
            freeSuffixTreeByPostOrder(n->children[i]); 
        
    
    if (n->suffixIndex == -1) 
        free(n->end); 
    free(n); 
  
/*Build the suffix tree and print the edge labels along with 
suffixIndex. suffixIndex for leaf edges will be >= 0 and 
for non-leaf edges will be -1*/
void buildSuffixTree() 
    size = strlen(text); 
    int i; 
    rootEnd = (int*) malloc(sizeof(int)); 
    *rootEnd = - 1; 
  
    /*Root is a special node with start and end indices as -1, 
    as it has no parent from where an edge comes to root*/
    root = newNode(-1, rootEnd); 
  
    activeNode = root; //First activeNode will be root 
    for (i=0; i<size; i++) 
        extendSuffixTree(i); 
    int labelHeight = 0; 
    setSuffixIndexByDFS(root, labelHeight); 
  
    //Free the dynamically allocated memory 
    freeSuffixTreeByPostOrder(root); 
  
// driver program to test above functions 
int main(int argc, char *argv[]) 
    strcpy(text, "abbc"); buildSuffixTree(); 
    printf("Number of nodes in suffix tree are %d\n",count);
    return 0; 


Java




class SuffixTreeNode {
    SuffixTreeNode[] children;
    SuffixTreeNode suffixLink;
    int start;
    int[] end;
    int suffixIndex;
  
    public SuffixTreeNode()
    {
        this.children
            = new SuffixTreeNode[256]; // Assuming ASCII
                                       // characters
        this.suffixLink = null;
        this.start = 0;
        this.end = new int[1];
        this.suffixIndex = -1;
    }
}
  
public class SuffixTree {
    static char[] text;
    static SuffixTreeNode root;
    static SuffixTreeNode lastNewNode;
    static SuffixTreeNode activeNode;
    static int count;
    static int activeEdge = -1;
    static int activeLength = 0;
    static int remainingSuffixCount = 0;
    static int leafEnd = -1;
    static int[] rootEnd;
    static int[] splitEnd;
    static int size = -1;
  
    public static SuffixTreeNode newNode(int start,
                                         int[] end)
    {
        count++;
        SuffixTreeNode node = new SuffixTreeNode();
        for (int i = 0; i < 256; i++) {
            node.children[i] = null;
        }
        node.suffixLink = root;
        node.start = start;
        node.end = end;
        node.suffixIndex = -1;
        return node;
    }
  
    public static int edgeLength(SuffixTreeNode n)
    {
        return n.end[0] - n.start + 1;
    }
  
    public static boolean walkDown(SuffixTreeNode currNode)
    {
        if (activeLength >= edgeLength(currNode)) {
            activeEdge
                = text[size - remainingSuffixCount + 1]
                  - ' ';
            activeLength -= edgeLength(currNode);
            activeNode = currNode;
            return true;
        }
        return false;
    }
  
    public static void extendSuffixTree(int pos)
    {
        leafEnd = pos;
        remainingSuffixCount++;
        lastNewNode = null;
  
        while (remainingSuffixCount > 0) {
  
            if (activeLength == 0) {
                activeEdge = text[pos] - ' ';
            }
  
            if (activeNode.children[activeEdge] == null) {
                activeNode.children[activeEdge]
                    = newNode(pos, new int[] { leafEnd });
  
                if (lastNewNode != null) {
                    lastNewNode.suffixLink = activeNode;
                    lastNewNode = null;
                }
            }
            else {
                SuffixTreeNode next
                    = activeNode.children[activeEdge];
                if (walkDown(next)) {
                    continue;
                }
  
                if (text[next.start + activeLength]
                    == text[pos]) {
                    if (lastNewNode != null
                        && activeNode != root) {
                        lastNewNode.suffixLink = activeNode;
                        lastNewNode = null;
                    }
  
                    activeLength++;
                    break;
                }
  
                splitEnd = new int[] { next.start
                                       + activeLength - 1 };
                SuffixTreeNode split
                    = newNode(next.start, splitEnd);
                activeNode.children[activeEdge] = split;
  
                split.children - ' ']
                    = newNode(pos, new int[] { leafEnd });
                next.start += activeLength;
                split.children[activeEdge] = next;
  
                if (lastNewNode != null) {
                    lastNewNode.suffixLink = split;
                }
  
                lastNewNode = split;
            }
  
            remainingSuffixCount--;
            if (activeNode == root && activeLength > 0) {
                activeLength--;
                activeEdge
                    = text[pos - remainingSuffixCount + 1]
                      - ' ';
            }
            else if (activeNode != root) {
                activeNode = activeNode.suffixLink;
            }
        }
    }
  
    public static void print(int i, int j)
    {
        for (int k = i; k <= j; k++) {
            System.out.print(text[k]);
        }
    }
  
    public static void setSuffixIndexByDFS(SuffixTreeNode n,
                                           int labelHeight)
    {
        if (n == null)
            return;
  
        if (n.start != -1) {
            print(n.start, n.end[0]);
        }
        int leaf = 1;
        for (int i = 0; i < 256; i++) {
            if (n.children[i] != null) {
                if (leaf == 1 && n.start != -1) {
                    System.out.println(" [" + n.suffixIndex
                                       + "]");
                }
  
                leaf = 0;
                setSuffixIndexByDFS(
                    n.children[i],
                    labelHeight
                        + edgeLength(n.children[i]));
            }
        }
        if (leaf == 1) {
            n.suffixIndex = size - labelHeight;
            System.out.println(" [" + n.suffixIndex + "]");
        }
    }
  
    public static void
    freeSuffixTreeByPostOrder(SuffixTreeNode n)
    {
        if (n == null)
            return;
  
        for (int i = 0; i < 256; i++) {
            if (n.children[i] != null) {
                freeSuffixTreeByPostOrder(n.children[i]);
            }
        }
        if (n.suffixIndex == -1) {
            n.end = null;
        }
    }
  
    public static void buildSuffixTree()
    {
        size = text.length;
        rootEnd = new int[1];
        rootEnd[0] = -1;
  
        root = newNode(-1, rootEnd);
  
        activeNode = root;
        for (int i = 0; i < size; i++) {
            extendSuffixTree(i);
        }
        int labelHeight = 0;
        setSuffixIndexByDFS(root, labelHeight);
  
        freeSuffixTreeByPostOrder(root);
    }
  
    public static void main(String[] args)
    {
        text = "abbc".toCharArray();
        buildSuffixTree();
        System.out.println(
            "Number of nodes in suffix tree are " + count);
    }
}


Python3




class SuffixTreeNode:
    def __init__(self):
        # Initialize children list to store child nodes for each ASCII character
        self.children = [None] * 256  # Assuming ASCII characters
        # Suffix link for suffix tree construction
        self.suffix_link = None
        # Start index of the substring represented by the edge leading to this node
        self.start = 0
        # End index (as a list to facilitate updates) of the substring represented by the edge leading to this node
        self.end = [0]
        # Index of the suffix represented by the path from root to this node
        self.suffix_index = -1
  
# Function to create a new suffix tree node
def new_node(start, end):
    global count
    count += 1
    node = SuffixTreeNode()
    # Set suffix link to root initially
    node.suffix_link = root
    node.start = start
    node.end = end
    node.suffix_index = -1
    return node
  
# Function to calculate the length of an edge represented by a node
def edge_length(n):
    return n.end[0] - n.start + 1
  
# Function to handle the walk down in suffix tree construction
def walk_down(curr_node):
    global active_length, active_edge, remaining_suffix_count
    if active_length >= edge_length(curr_node):
        # Update active edge and active length to walk down the tree
        active_edge = ord(text[size - remaining_suffix_count + 1]) - ord(' ')
        active_length -= edge_length(curr_node)
        active_node = curr_node
        return True
    return False
  
# Function to extend the suffix tree for a given position in the text
def extend_suffix_tree(pos):
    global leaf_end, remaining_suffix_count, last_new_node, active_node, active_length, active_edge
    leaf_end = pos
    remaining_suffix_count += 1
    last_new_node = None
  
    while remaining_suffix_count > 0:
        if active_length == 0:
            # If active length is zero, set active edge for the current position
            active_edge = ord(text[pos]) - ord(' ')
  
        if not active_node.children[active_edge]:
            # If active edge has no child, create a new node
            active_node.children[active_edge] = new_node(pos, [leaf_end])
  
            if last_new_node:
                # If there was a previously created node, update its suffix link
                last_new_node.suffix_link = active_node
                last_new_node = None
        else:
            next_node = active_node.children[active_edge]
            if walk_down(next_node):
                continue
  
            if text[next_node.start + active_length] == text[pos]:
                if last_new_node and active_node != root:
                    last_new_node.suffix_link = active_node
                    last_new_node = None
                active_length += 1
                break
  
            split_end = [next_node.start + active_length - 1]
            split_node = new_node(next_node.start, split_end)
            active_node.children[active_edge] = split_node
            split_node.children[ord(text[pos]) - ord(' ')] = new_node(pos, [leaf_end])
            next_node.start += active_length
            split_node.children[active_edge] = next_node
  
            if last_new_node:
                last_new_node.suffix_link = split_node
  
            last_new_node = split_node
  
        remaining_suffix_count -= 1
        if active_node == root and active_length > 0:
            active_length -= 1
            active_edge = ord(text[pos - remaining_suffix_count + 1]) - ord(' ')
        elif active_node != root:
            active_node = active_node.suffix_link
  
# Function to print the substring of the text given its start and end indices
def print_string(i, j):
    output = ""
    for k in range(i, j + 1):
        output += text[k]
    print(output)
  
# Function to set suffix indices using depth-first search (DFS)
def set_suffix_index_by_dfs(n, label_height):
    if not n:
        return
  
    if n.start != -1:
        # Print the substring represented by the edge leading to this node
        print_string(n.start, n.end[0])
  
    leaf = 1
    for i in range(256):
        if n.children[i]:
            if leaf == 1 and n.start != -1:
                # If this node has children and it's not a leaf node, print its suffix index
                print(" [" + str(n.suffix_index) + "]")
  
            leaf = 0
            set_suffix_index_by_dfs(
                n.children[i],
                label_height + edge_length(n.children[i]))
  
    if leaf == 1:
        # If this is a leaf node, set its suffix index
        n.suffix_index = size - label_height
        print(" [" + str(n.suffix_index) + "]")
  
# Function to free the memory allocated for the suffix tree using post-order traversal
def free_suffix_tree_by_post_order(n):
    if not n:
        return
  
    for i in range(256):
        if n.children[i]:
            free_suffix_tree_by_post_order(n.children[i])
  
    if n.suffix_index == -1:
        # If this node doesn't represent any suffix, free its memory
        n.end = None
  
# Function to build the suffix tree for the given text
def build_suffix_tree():
    global size, root_end, root, active_node, remaining_suffix_count, active_length, active_edge
    size = len(text)
    root_end = [None]
    root_end[0] = -1
  
    root = new_node(-1, root_end)
  
    active_node = root
    remaining_suffix_count = 0
    active_length = 0
    active_edge = -1
  
    for i in range(size):
        # Extend the suffix tree for each position in the text
        extend_suffix_tree(i)
    label_height = 0
    # Set suffix indices using depth-first search (DFS)
    set_suffix_index_by_dfs(root, label_height)
  
    # Free the memory allocated for the suffix tree using post-order traversal
    free_suffix_tree_by_post_order(root)
  
if __name__ == "__main__":
    text = list("abbc")
    root = None
    last_new_node = None
    active_node = None
    count = 0
    active_edge = -1
    active_length = 0
    remaining_suffix_count = 0
    leaf_end = -1
    root_end = None
    split_end = None
    size = -1
    build_suffix_tree()
    print("Number of nodes in suffix tree are", count)


C#




using System;
  
public class SuffixTreeNode
{
    public SuffixTreeNode[] Children { get; } = new SuffixTreeNode[256];
  // Assuming ASCII characters
    public SuffixTreeNode SuffixLink { get; set; }
    public int Start { get; set; }
    public int[] End { get; set; }
    public int SuffixIndex { get; set; }
  
    public SuffixTreeNode()
    {
        for (int i = 0; i < 256; i++)
        {
            Children[i] = null;
        }
  
        SuffixLink = null;
        Start = 0;
        End = new int[1];
        SuffixIndex = -1;
    }
}
  
public class SuffixTree
{
    private static char[] text;
    private static SuffixTreeNode root;
    private static SuffixTreeNode lastNewNode;
    private static SuffixTreeNode activeNode;
    private static int count;
    private static int activeEdge = -1;
    private static int activeLength = 0;
    private static int remainingSuffixCount = 0;
    private static int leafEnd = -1;
    private static int[] rootEnd;
    private static int[] splitEnd;
    private static int size = -1;
  
    public static SuffixTreeNode NewNode(int start, int[] end)
    {
        count++;
        var node = new SuffixTreeNode
        {
            SuffixLink = root,
            Start = start,
            End = end,
            SuffixIndex = -1
        };
        return node;
    }
  
    public static int EdgeLength(SuffixTreeNode n)
    {
        return n.End[0] - n.Start + 1;
    }
  
    public static bool WalkDown(SuffixTreeNode currNode)
    {
        if (activeLength >= EdgeLength(currNode))
        {
            activeEdge = text[size - remainingSuffixCount + 1] - ' ';
            activeLength -= EdgeLength(currNode);
            activeNode = currNode;
            return true;
        }
        return false;
    }
  
    public static void ExtendSuffixTree(int pos)
    {
        leafEnd = pos;
        remainingSuffixCount++;
        lastNewNode = null;
  
        while (remainingSuffixCount > 0)
        {
            if (activeLength == 0)
            {
                activeEdge = text[pos] - ' ';
            }
  
            if (activeNode.Children[activeEdge] == null)
            {
                activeNode.Children[activeEdge] = NewNode(pos, new int[] { leafEnd });
  
                if (lastNewNode != null)
                {
                    lastNewNode.SuffixLink = activeNode;
                    lastNewNode = null;
                }
            }
            else
            {
                var next = activeNode.Children[activeEdge];
                if (WalkDown(next))
                {
                    continue;
                }
  
                if (text[next.Start + activeLength] == text[pos])
                {
                    if (lastNewNode != null && activeNode != root)
                    {
                        lastNewNode.SuffixLink = activeNode;
                        lastNewNode = null;
                    }
  
                    activeLength++;
                    break;
                }
  
                splitEnd = new int[] { next.Start + activeLength - 1 };
                var split = NewNode(next.Start, splitEnd);
                activeNode.Children[activeEdge] = split;
  
                split.Children - ' '] = NewNode(pos, new int[] { leafEnd });
                next.Start += activeLength;
                split.Children[activeEdge] = next;
  
                if (lastNewNode != null)
                {
                    lastNewNode.SuffixLink = split;
                }
  
                lastNewNode = split;
            }
  
            remainingSuffixCount--;
            if (activeNode == root && activeLength > 0)
            {
                activeLength--;
                activeEdge = text[pos - remainingSuffixCount + 1] - ' ';
            }
            else if (activeNode != root)
            {
                activeNode = activeNode.SuffixLink;
            }
        }
    }
  
    public static void Print(int i, int j)
    {
        for (int k = i; k <= j; k++)
        {
            Console.Write(text[k]);
        }
    }
  
    public static void SetSuffixIndexByDFS(SuffixTreeNode n, int labelHeight)
    {
        if (n == null)
            return;
  
        if (n.Start != -1)
        {
            Print(n.Start, n.End[0]);
        }
  
        int leaf = 1;
        for (int i = 0; i < 256; i++)
        {
            if (n.Children[i] != null)
            {
                if (leaf == 1 && n.Start != -1)
                {
                    Console.WriteLine(" [" + n.SuffixIndex + "]");
                }
  
                leaf = 0;
                SetSuffixIndexByDFS(n.Children[i], labelHeight + EdgeLength(n.Children[i]));
            }
        }
        if (leaf == 1)
        {
            n.SuffixIndex = size - labelHeight;
            Console.WriteLine(" [" + n.SuffixIndex + "]");
        }
    }
  
    public static void FreeSuffixTreeByPostOrder(SuffixTreeNode n)
    {
        if (n == null)
            return;
  
        for (int i = 0; i < 256; i++)
        {
            if (n.Children[i] != null)
            {
                FreeSuffixTreeByPostOrder(n.Children[i]);
            }
        }
  
        if (n.SuffixIndex == -1)
        {
            n.End = null;
        }
    }
  
    public static void BuildSuffixTree()
    {
        size = text.Length;
        rootEnd = new int[1];
        rootEnd[0] = -1;
  
        root = NewNode(-1, rootEnd);
  
        activeNode = root;
        for (int i = 0; i < size; i++)
        {
            ExtendSuffixTree(i);
        }
        int labelHeight = 0;
        SetSuffixIndexByDFS(root, labelHeight);
  
        FreeSuffixTreeByPostOrder(root);
    }
  
    public static void Main(string[] args)
    {
        text = "abbc".ToCharArray();
        BuildSuffixTree();
        Console.WriteLine("Number of nodes in suffix tree are " + count);
    }
}


Javascript




const MAX_CHAR = 256;
  
class SuffixTreeNode {
    constructor() {
        this.children = new Array(MAX_CHAR).fill(null);
        this.suffixLink = null;
        this.start = 0;
        this.end = null;
        this.suffixIndex = -1;
    }
}
  
let text = "";
let root = null;
let lastNewNode = null;
let activeNode = null;
let count = 0;
  
let activeEdge = -1;
let activeLength = 0;
  
let remainingSuffixCount = 0;
let leafEnd = -1;
let rootEnd = null;
let splitEnd = null;
let size = -1;
  
// Function to create a new node in the suffix tree
const newNode = (start, end) => {
    count++;
    const node = new SuffixTreeNode();
    for (let i = 0; i < MAX_CHAR; i++)
        node.children[i] = null;
  
    node.suffixLink = root;
    node.start = start;
    node.end = end;
    node.suffixIndex = -1;
    return node;
};
  
// Function to calculate the length of an edge
const edgeLength = (n) => {
    return n.end - n.start + 1;
};
  
// Function to perform walk down in the tree
const walkDown = (currNode) => {
    if (activeLength >= edgeLength(currNode)) {
        activeEdge = text.charCodeAt(activeEdge + edgeLength(currNode)) - ' '.charCodeAt();
        activeLength -= edgeLength(currNode);
        activeNode = currNode;
        return true;
    }
    return false;
};
  
// Function to extend the suffix tree
const extendSuffixTree = (pos) => {
    leafEnd = pos;
    remainingSuffixCount++;
    lastNewNode = null;
  
    while (remainingSuffixCount > 0) {
  
        if (activeLength === 0) {
            activeEdge = text.charCodeAt(pos) - ' '.charCodeAt();
        }
  
        if (activeNode.children[activeEdge] === null) {
            activeNode.children[activeEdge] = newNode(pos, leafEnd);
  
            if (lastNewNode !== null) {
                lastNewNode.suffixLink = activeNode;
                lastNewNode = null;
            }
        } else {
            const next = activeNode.children[activeEdge];
            if (walkDown(next)) {
                continue;
            }
  
            if (text[next.start + activeLength] === text[pos]) {
                if (lastNewNode !== null && activeNode !== root) {
                    lastNewNode.suffixLink = activeNode;
                    lastNewNode = null;
                }
  
                activeLength++;
                break;
            }
  
            splitEnd = next.start + activeLength - 1;
            const split = newNode(next.start, splitEnd);
            activeNode.children[activeEdge] = split;
  
            split.children = newNode(pos, leafEnd);
            next.start += activeLength;
            split.children[activeEdge] = next;
  
            if (lastNewNode !== null) {
                lastNewNode.suffixLink = split;
            }
  
            lastNewNode = split;
        }
  
        remainingSuffixCount--;
        if (activeNode === root && activeLength > 0) {
            activeLength--;
            activeEdge = text.charCodeAt(pos - remainingSuffixCount + 1) - ' '.charCodeAt();
        } else if (activeNode !== root) {
            activeNode = activeNode.suffixLink;
        }
    }
};
  
// Function to print characters from index i to j
const print = (i, j) => {
    for (let k = i; k <= j; k++) {
        process.stdout.write(text[k]);
    }
};
  
// Function to set suffix index by DFS traversal
const setSuffixIndexByDFS = (n, labelHeight) => {
    if (n === null) return;
  
    if (n.start !== -1) {
        print(n.start, n.end);
    }
    let leaf = 1;
    for (let i = 0; i < MAX_CHAR; i++) {
        if (n.children[i] !== null) {
            if (leaf === 1 && n.start !== -1) {
                console.log(` [${n.suffixIndex}]`);
            }
  
            leaf = 0;
            setSuffixIndexByDFS(n.children[i], labelHeight + edgeLength(n.children[i]));
        }
    }
    if (leaf === 1) {
        n.suffixIndex = size - labelHeight;
        console.log(` [${n.suffixIndex}]`);
    }
};
  
// Function to free memory in post-order traversal
const freeSuffixTreeByPostOrder = (n) => {
    if (n === null) return;
  
    for (let i = 0; i < MAX_CHAR; i++) {
        if (n.children[i] !== null) {
            freeSuffixTreeByPostOrder(n.children[i]);
        }
    }
    if (n.suffixIndex === -1) {
        delete n.end;
    }
    delete n;
};
  
// Function to build the suffix tree
const buildSuffixTree = () => {
    size = text.length;
    rootEnd = -1;
  
    root = newNode(-1, rootEnd);
  
    activeNode = root;
    for (let i = 0; i < size; i++) {
        extendSuffixTree(i);
    }
    let labelHeight = 0;
    setSuffixIndexByDFS(root, labelHeight);
  
    freeSuffixTreeByPostOrder(root);
};
  
// Main function
const main = () => {
    text = "abbc";
    buildSuffixTree();
    console.log(`Number of nodes in suffix tree are ${count}`);
};
  
main();


Output (Each edge of Tree, along with suffix index of child node on edge, is printed in DFS order. To understand the output better, match it with the last figure no 43 in previous Part 5 article):

abbc [0]
b [-1]
bc [1]
c [2]
c [3]
Number of nodes in suffix tee are 6

Now we are able to build suffix tree in linear time, we can solve many string problem in efficient way: 

  • Check if a given pattern P is substring of text T (Useful when text is fixed and pattern changes, KMP otherwise
  • Find all occurrences of a given pattern P present in text T
  • Find longest repeated substring
  • Linear Time Suffix Array Creation

The above basic problems can be solved by DFS traversal on suffix tree. 
We will soon post articles on above problems and others like below:  

And More.
Test you understanding? 

  1. Draw suffix tree (with proper suffix link, suffix indices) for string “AABAACAADAABAAABAA$” on paper and see if that matches with code output.
  2. Every extension must follow one of the three rules: Rule 1, Rule 2 and Rule 3. 
    Following are the rules applied on five consecutive extensions in some Phase i (i > 5), which ones are valid: 
    A) Rule 1, Rule 2, Rule 2, Rule 3, Rule 3 
    B) Rule 1, Rule 2, Rule 2, Rule 3, Rule 2 
    C) Rule 2, Rule 1, Rule 1, Rule 3, Rule 3 
    D) Rule 1, Rule 1, Rule 1, Rule 1, Rule 1 
    E) Rule 2, Rule 2, Rule 2, Rule 2, Rule 2 
    F) Rule 3, Rule 3, Rule 3, Rule 3, Rule 3 
     
  3. What are the valid sequences in above for Phase 5
  4. Every internal node MUST have it’s suffix link set to another node (internal or root). Can a newly created node point to already existing internal node or not ? Can it happen that a new node created in extension j, may not get it’s right suffix link in next extension j+1 and get the right one in later extensions like j+2, j+3 etc ?
  5. Try solving the basic problems discussed above.

We have published following articles on suffix tree applications:  



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