Given a text string and a pattern string, find all occurrences of the pattern in string. Few pattern searching algorithms (KMP, Rabin-Karp, Naive Algorithm, Finite Automata) are already discussed, which can be used for this check. Here we will discuss the suffix tree based algorithm. In the 1st Suffix Tree Application (Substring Check), we saw how to check whether a given pattern is substring of a text or not. It is advised to go through Substring Check 1st.
In this article, we will go a bit further on same problem. If a pattern is substring of a text, then we will find all the positions on pattern in the text. As a prerequisite, we must know how to build a suffix tree in one or the other way.
Here we will build suffix tree using Ukkonen’s Algorithm, discussed already as below:
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
Ukkonen’s Suffix Tree Construction – Part 6
Lets look at following figure:
- Substring “b” is at indices 1, 4 and 7
- Substring “bc” is at indices 1 and 7
With above explanation, we should be able to see following:
- Substring “ab” is at indices 0, 3 and 6
- Substring “abc” is at indices 0 and 6
- Substring “c” is at indices 2 and 8
- Substring “xab” is at index 5
- Substring “d” is at index 9
- Substring “cd” is at index 8
Can you see how to find all the occurrences of a pattern in a string ?
- 1st of all, check if the given pattern really exists in string or not (As we did in Substring Check). For this, traverse the suffix tree against the pattern.
- If you find pattern in suffix tree (don’t fall off the tree), then traverse the subtree below that point and find all suffix indices on leaf nodes. All those suffix indices will be pattern indices in string
// A C program to implement Ukkonen's Suffix Tree Construction // And find all locations of a pattern in string #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. Let's 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 the 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; /*activeEdge is represented as an 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)
{ 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) {
if (n == root)
return 0;
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 += edgeLength(currNode);
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)
activeEdge = pos; //APCFALZ
// There is no outgoing edge starting with
// activeEdge from activeNode
if (activeNode->children] == NULL)
{
//Extension Rule 2 (A new leaf edge gets created)
activeNode->children] =
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 its 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];
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] = split;
//New leaf coming out of new internal node
split->children] = newNode(pos, &leafEnd);
next->start += activeLength;
split->children] = 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 = pos - remainingSuffixCount + 1;
}
else if (activeNode != root) //APCFER2C2
{
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
//Uncomment below line to print suffix tree
// print(n->start, *(n->end));
}
int leaf = 1;
int i;
for (i = 0; i < MAX_CHAR; i++)
{
if (n->children[i] != NULL)
{
//Uncomment below two lines to print suffix index
// 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;
//Uncomment below line to print suffix index
//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);
} int traverseEdge( char *str, int idx, int start, int end)
{ int k = 0;
//Traverse the edge with character by character matching
for (k=start; k<=end && str[idx] != '\0' ; k++, idx++)
{
if (text[k] != str[idx])
return -1; // mo match
}
if (str[idx] == '\0' )
return 1; // match
return 0; // more characters yet to match
} int doTraversalToCountLeaf(Node *n)
{ if (n == NULL)
return 0;
if (n->suffixIndex > -1)
{
printf ("\nFound at position: %d", n->suffixIndex);
return 1;
}
int count = 0;
int i = 0;
for (i = 0; i < MAX_CHAR; i++)
{
if (n->children[i] != NULL)
{
count += doTraversalToCountLeaf(n->children[i]);
}
}
return count;
} int countLeaf(Node *n)
{ if (n == NULL)
return 0;
return doTraversalToCountLeaf(n);
} int doTraversal(Node *n, char * str, int idx)
{ if (n == NULL)
{
return -1; // no match
}
int res = -1;
//If node n is not root node, then traverse edge
//from node n's parent to node n.
if (n->start != -1)
{
res = traverseEdge(str, idx, n->start, *(n->end));
if (res == -1) //no match
return -1;
if (res == 1) //match
{
if (n->suffixIndex > -1)
printf ("\nsubstring count: 1 and position: %d",
n->suffixIndex);
else
printf ("\nsubstring count: %d", countLeaf(n));
return 1;
}
}
//Get the character index to search
idx = idx + edgeLength(n);
//If there is an edge from node n going out
//with current character str[idx], traverse that edge
if (n->children[str[idx]] != NULL)
return doTraversal(n->children[str[idx]], str, idx);
else
return -1; // no match
} void checkForSubString( char * str)
{ int res = doTraversal(root, str, 0);
if (res == 1)
printf ("\nPattern <%s> is a Substring\n", str);
else
printf ("\nPattern <%s> is NOT a Substring\n", str);
} // driver program to test above functions int main( int argc, char *argv[])
{ strcpy (text, "GEEKSFORGEEKS$");
buildSuffixTree();
printf ("Text: GEEKSFORGEEKS, Pattern to search: GEEKS");
checkForSubString("GEEKS");
printf ("\n\nText: GEEKSFORGEEKS, Pattern to search: GEEK1");
checkForSubString("GEEK1");
printf ("\n\nText: GEEKSFORGEEKS, Pattern to search: FOR");
checkForSubString("FOR");
//Free the dynamically allocated memory
freeSuffixTreeByPostOrder(root);
strcpy (text, "AABAACAADAABAAABAA$");
buildSuffixTree();
printf ("\n\nText: AABAACAADAABAAABAA, Pattern to search: AABA");
checkForSubString("AABA");
printf ("\n\nText: AABAACAADAABAAABAA, Pattern to search: AA");
checkForSubString("AA");
printf ("\n\nText: AABAACAADAABAAABAA, Pattern to search: AAE");
checkForSubString("AAE");
//Free the dynamically allocated memory
freeSuffixTreeByPostOrder(root);
strcpy (text, "AAAAAAAAA$");
buildSuffixTree();
printf ("\n\nText: AAAAAAAAA, Pattern to search: AAAA");
checkForSubString("AAAA");
printf ("\n\nText: AAAAAAAAA, Pattern to search: AA");
checkForSubString("AA");
printf ("\n\nText: AAAAAAAAA, Pattern to search: A");
checkForSubString("A");
printf ("\n\nText: AAAAAAAAA, Pattern to search: AB");
checkForSubString("AB");
//Free the dynamically allocated memory
freeSuffixTreeByPostOrder(root);
return 0;
} |
// A CPP program to implement Ukkonen's Suffix Tree // Construction And find all locations of a pattern in // string #include <bits/stdc++.h> using namespace std;
#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. Let's 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 the 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; /*activeEdge is represented as an 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)
{ Node* node = (Node*) malloc ( sizeof (Node));
int i;
for (i = 0; i & lt; 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)
{ if (n == root)
return 0;
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& gt; = edgeLength(currNode)) {
activeEdge += edgeLength(currNode);
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 & gt; 0) {
if (activeLength == 0)
activeEdge = pos; // APCFALZ
// There is no outgoing edge starting with
// activeEdge from activeNode
if (activeNode - >
children] == NULL) {
// Extension Rule 2 (A new leaf edge gets
// created)
activeNode - >
children]
= 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 its 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];
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 & amp; &
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] = split;
// New leaf coming out of new internal node
split - >
children]
= newNode(pos, & leafEnd);
next - >
start += activeLength;
split - >
children] = 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 & amp; &
activeLength & gt; 0) // APCFER2C1
{
activeLength--;
activeEdge = pos - remainingSuffixCount + 1;
}
else if (activeNode != root) // APCFER2C2
{
activeNode = activeNode - >
suffixLink;
}
}
} void print( int i, int j)
{ int k;
for (k = i; k& lt; = j; k++)
printf (" % c & quot;, 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 Uncomment below line to print suffix tree
// print(n->start, *(n->end));
}
int leaf = 1;
int i;
for (i = 0; i & lt; MAX_CHAR; i++) {
if (n - > children[i] != NULL) {
// Uncomment below two lines to print suffix
// index
// 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;
// Uncomment below line to print suffix index
// printf(" [%d]\n", n->suffixIndex);
}
} void freeSuffixTreeByPostOrder(Node* n)
{ if (n == NULL)
return ;
int i;
for (i = 0; i & lt; 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 & lt; size; i++)
extendSuffixTree(i);
int labelHeight = 0;
setSuffixIndexByDFS(root, labelHeight);
} int traverseEdge( char * str, int idx, int start, int end)
{ int k = 0;
// Traverse the edge with character by character
// matching
for (k = start; k& lt; = end & amp; &
str[idx] != '\0' ; k++, idx++) {
if (text[k] != str[idx])
return -1; // mo match
}
if (str[idx] == '\0' )
return 1; // match
return 0; // more characters yet to match
} int doTraversalToCountLeaf(Node* n)
{ if (n == NULL)
return 0;
if (n - > suffixIndex & gt; - 1) {
printf ("\nFound at position
:
% d & quot;, n - > suffixIndex);
return 1;
}
int count = 0;
int i = 0;
for (i = 0; i & lt; MAX_CHAR; i++) {
if (n - > children[i] != NULL) {
count += doTraversalToCountLeaf(n - >
children[i]);
}
}
return count;
} int countLeaf(Node* n)
{ if (n == NULL)
return 0;
return doTraversalToCountLeaf(n);
} int doTraversal(Node* n, char * str, int idx)
{ if (n == NULL) {
return -1; // no match
}
int res = -1;
// If node n is not root node, then traverse edge
// from node n's parent to node n.
if (n - > start != -1) {
res = traverseEdge(str, idx, n - >
start, *(n - > end));
if (res == -1) // no match
return -1;
if (res == 1) // match
{
if (n - > suffixIndex & gt; - 1)
printf ("\nsubstring count : 1
and position
:
% d & quot;, n - > suffixIndex);
else
printf ("\nsubstring count
:
% d & quot;, countLeaf(n));
return 1;
}
}
// Get the character index to search
idx = idx + edgeLength(n);
// If there is an edge from node n going out
// with current character str[idx], traverse that edge
if (n - > children[str[idx]] != NULL)
return doTraversal(n - >
children[str[idx]], str, idx);
else
return -1; // no match
} void checkForSubString( char * str)
{ int res = doTraversal(root, str, 0);
if (res == 1)
printf ("\nPattern & lt; % s & gt;
is a Substring\n & quot;, str);
else
printf ("\nPattern & lt; % s & gt;
is NOT a Substring\n & quot;, str);
} // driver program to test above functions int main( int argc, char * argv[])
{ strcpy (text, " GEEKSFORGEEKS$ & quot;);
buildSuffixTree();
printf (" Text
: GEEKSFORGEEKS, Pattern to search
: GEEKS & quot;);
checkForSubString(" GEEKS & quot;);
printf ("\n\nText
: GEEKSFORGEEKS, Pattern to search
: GEEK1 & quot;);
checkForSubString(" GEEK1 & quot;);
printf ("\n\nText
: GEEKSFORGEEKS, Pattern to search
: FOR & quot;);
checkForSubString(" FOR & quot;);
// Free the dynamically allocated memory
freeSuffixTreeByPostOrder(root);
strcpy (text, " AABAACAADAABAAABAA$ & quot;);
buildSuffixTree();
printf ("\n\nText
: AABAACAADAABAAABAA, Pattern to search
: AABA & quot;);
checkForSubString(" AABA & quot;);
printf ("\n\nText
: AABAACAADAABAAABAA, Pattern to search
: AA & quot;);
checkForSubString(" AA & quot;);
printf ("\n\nText
: AABAACAADAABAAABAA, Pattern to search
: AAE & quot;);
checkForSubString(" AAE & quot;);
// Free the dynamically allocated memory
freeSuffixTreeByPostOrder(root);
strcpy (text, " AAAAAAAAA$ & quot;);
buildSuffixTree();
printf ("\n\nText
: AAAAAAAAA, Pattern to search
: AAAA & quot;);
checkForSubString(" AAAA & quot;);
printf ("\n\nText
: AAAAAAAAA, Pattern to search
: AA & quot;);
checkForSubString(" AA & quot;);
printf ("\n\nText
: AAAAAAAAA, Pattern to search
: A & quot;);
checkForSubString(" A & quot;);
printf ("\n\nText
: AAAAAAAAA, Pattern to search
: AB & quot;);
checkForSubString(" AB & quot;);
// Free the dynamically allocated memory
freeSuffixTreeByPostOrder(root);
return 0;
} |
Output:
Text: GEEKSFORGEEKS, Pattern to search: GEEKS Found at position: 8 Found at position: 0 substring count: 2 Pattern <GEEKS> is a Substring Text: GEEKSFORGEEKS, Pattern to search: GEEK1 Pattern <GEEK1> is NOT a Substring Text: GEEKSFORGEEKS, Pattern to search: FOR substring count: 1 and position: 5 Pattern <FOR> is a Substring Text: AABAACAADAABAAABAA, Pattern to search: AABA Found at position: 13 Found at position: 9 Found at position: 0 substring count: 3 Pattern <AABA> is a Substring Text: AABAACAADAABAAABAA, Pattern to search: AA Found at position: 16 Found at position: 12 Found at position: 13 Found at position: 9 Found at position: 0 Found at position: 3 Found at position: 6 substring count: 7 Pattern <AA> is a Substring Text: AABAACAADAABAAABAA, Pattern to search: AAE Pattern <AAE> is NOT a Substring Text: AAAAAAAAA, Pattern to search: AAAA Found at position: 5 Found at position: 4 Found at position: 3 Found at position: 2 Found at position: 1 Found at position: 0 substring count: 6 Pattern <AAAA> is a Substring Text: AAAAAAAAA, Pattern to search: AA Found at position: 7 Found at position: 6 Found at position: 5 Found at position: 4 Found at position: 3 Found at position: 2 Found at position: 1 Found at position: 0 substring count: 8 Pattern <AA> is a Substring Text: AAAAAAAAA, Pattern to search: A Found at position: 8 Found at position: 7 Found at position: 6 Found at position: 5 Found at position: 4 Found at position: 3 Found at position: 2 Found at position: 1 Found at position: 0 substring count: 9 Pattern <A> is a Substring Text: AAAAAAAAA, Pattern to search: AB Pattern <AB> is NOT a Substring
Ukkonen’s Suffix Tree Construction takes O(N) time and space to build suffix tree for a string of length N and after that, traversal for substring check takes O(M) for a pattern of length M and then if there are Z occurrences of the pattern, it will take O(Z) to find indices of all those Z occurrences. Overall pattern complexity is linear: O(M + Z).
A bit more detailed analysis
How many internal nodes will there in a suffix tree of string of length N ??
Answer: N-1 (Why ??)
There will be N suffixes in a string of length N. Each suffix will have one leaf. So a suffix tree of string of length N will have N leaves. As each internal node has at least 2 children, an N-leaf suffix tree has at most N-1 internal nodes. If a pattern occurs Z times in string, means it will be part of Z suffixes, so there will be Z leaves below in point (internal node and in between edge) where pattern match ends in tree and so subtree with Z leaves below that point will have Z-1 internal nodes. A tree with Z leaves can be traversed in O(Z) time. Overall pattern complexity is linear: O(M + Z). For a given pattern, Z (the number of occurrences) can be atmost N. So worst case complexity can be: O(M + N) if Z is close/equal to N (A tree traversal with N nodes take O(N) time).
Followup questions:
- Check if a pattern is prefix of a text?
- Check if a pattern is suffix of a text?
We have published following more articles on suffix tree applications:
- Suffix Tree Application 1 – Substring Check
- Suffix Tree Application 3 – Longest Repeated Substring
- Suffix Tree Application 4 – Build Linear Time Suffix Array
- Generalized Suffix Tree 1
- Suffix Tree Application 5 – Longest Common Substring
- Suffix Tree Application 6 – Longest Palindromic Substring