Ukkonen's Suffix Tree Construction Part 6 (original) (raw)

Last Updated : 23 Jul, 2025

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:

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

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 #include #include #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(text[activeEdge + edgeLength(currNode)]) - static_cast(' '); 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[text[pos] - ' ']
                = 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);
}

}

Python

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[text[pos] - ' ']
                = NewNode(pos, new int[] { leafEnd });
            next.Start += activeLength;
            split.Children[text[next.Start] - ' ']
                = 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[text.charCodeAt(pos) - ' '.charCodeAt()] = 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

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

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):

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

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: