Ukkonen’s suffix tree construction
Suffix Trees are very useful in numerous string processing and computational biology problems.
You are encouraged to solve this task according to the task description, using any language you may know.
The task is to create a function which implements Ukkonen’s algorithm to create a useful Suffix Tree as described:
Part 1 Part 2 Part 3 Part 4 Part 5 Part 6
Using Arithmetic-geometric mean/Calculate Pi generate the first 1000, 10000, and 100000 decimal places of pi. Using your implementation with an alphabet of 0 through 9 (plus $ say to make the tree explicit) find the longest repeated string in each list. Time your results and demonstrate that your implementation is linear (i.e. that 10000 takes approx. 10 times as long as 1000). You may vary the size of the lists of decimal places of pi to give reasonable answers.
C++
#include <algorithm>
#include <chrono>
#include <cstdint>
#include <fstream>
#include <iostream>
#include <limits>
#include <map>
#include <set>
#include <string>
#include <vector>
class Node {
public:
Node(const int32_t& start, const int32_t& end) : start(start), end(end) {}
int32_t edge_length(const int32_t& text_index) {
return std::min(end, text_index + 1) - start;
}
int32_t start, end, parent_link = 0, leaf_index = 0;
std::map<char, int32_t> children{ };
};
class SuffixTree {
public:
SuffixTree(const std::string& word) {
text = word + '\u0004'; // Terminal character
nodes.reserve(2 * text.length());
root = newNode(UNDEFINED, UNDEFINED);
active_node = root;
for ( const char& character : text ) {
extend_suffix_tree(character);
}
}
std::map<std::string, std::set<int32_t>> get_longest_repeated_substrings() {
std::vector<int32_t> indexes = doTraversal();
std::string word = text.substr(0, text.length() - 1);
std::map<std::string, std::set<int32_t>> result{ };
if ( indexes.front() > 0 ) {
for ( uint32_t i = 1; i < indexes.size(); ++i ) {
std::string substring = word.substr(indexes[i], indexes.front());
result[substring].insert(indexes[i]);
}
}
return result;
}
private:
void extend_suffix_tree(const char& character) {
need_parent_link = UNDEFINED;
remainder++;
while ( remainder > 0 ) {
if ( active_length == 0 ) {
active_edge = text_index;
}
if ( ! nodes[active_node].children.contains(text[active_edge]) ) {
const int32_t leaf = newNode(text_index, LEAF_NODE);
nodes[active_node].children[text[active_edge]] = leaf;
add_suffix_link(active_node);
} else {
const int32_t next = nodes[active_node].children[text[active_edge]];
if ( walk_down(next) ) {
continue;
}
if ( text[nodes[next].start + active_length] == character ) {
active_length++;
add_suffix_link(active_node);
break;
}
const uint32_t split = newNode(nodes[next].start, nodes[next].start + active_length);
nodes[active_node].children[text[active_edge]] = split;
const int32_t leaf = newNode(text_index, LEAF_NODE);
nodes[split].children[character] = leaf;
nodes[next].start += active_length;
nodes[split].children[text[nodes[next].start]] = next;
add_suffix_link(split);
}
remainder--;
if ( active_node == root && active_length > 0 ) {
active_length--;
active_edge = text_index - remainder + 1;
} else {
active_node = ( nodes[active_node].parent_link > 0 ) ? nodes[active_node].parent_link : root;
}
}
text_index++;
}
bool walk_down(const int32_t& node) {
if ( active_length >= nodes[node].edge_length(text_index) ) {
active_edge += nodes[node].edge_length(text_index);
active_length -= nodes[node].edge_length(text_index);
active_node = node;
return true;
}
return false;
}
void add_suffix_link(const int32_t& node) {
if ( need_parent_link != UNDEFINED ) {
nodes[need_parent_link].parent_link = node;
}
need_parent_link = node;
}
uint32_t newNode(const int32_t& start, const int32_t& end) {
Node node(start, end);
node.leaf_index = ( end == LEAF_NODE ) ? leaf_index_generator++ : UNDEFINED;
nodes[current_node] = node;
return current_node++;
}
std::vector<int32_t> doTraversal() {
std::vector<int32_t> indexes{ };
indexes.emplace_back(UNDEFINED);
return traversal(indexes, nodes[root], 0);
}
std::vector<int32_t> traversal(std::vector<int32_t>& indexes, Node node, const int32_t& height) {
if ( node.leaf_index == UNDEFINED ) {
for ( std::pair<char, int32_t> entry : node.children ) {
Node child = nodes[entry.second];
traversal(indexes, child, height + child.edge_length(text_index));
}
} else if ( indexes.front() < height - node.edge_length(text_index) ) {
indexes.clear();
indexes.emplace_back(height - node.edge_length(text_index));
indexes.emplace_back(node.leaf_index);
} else if ( indexes.front() == height - node.edge_length(text_index) ) {
indexes.emplace_back(node.leaf_index);
}
return indexes;
}
std::vector<Node> nodes;
std::string text;
int32_t root;
int32_t active_node, active_length = 0, active_edge = 0;
int32_t text_index = 0, current_node = 0, need_parent_link = 0, remainder = 0, leaf_index_generator = 0;
const int32_t UNDEFINED = -1;
const int32_t LEAF_NODE = INT32_MAX;
};
int main() {
std::vector<int32_t> limits = { 1'000, 10'000, 100'000 };
for ( const int32_t& limit : limits ) {
std::ifstream stream("../piDigits.txt");
std::string contents( ( std::istreambuf_iterator<char>(stream) ),
( std::istreambuf_iterator<char>() ) );
std::string pi_digits = contents.substr(0, limit);
auto begin = std::chrono::high_resolution_clock::now();
SuffixTree tree(pi_digits);
std::map<std::string, std::set<int32_t>> substrings = tree.get_longest_repeated_substrings();
auto end = std::chrono::high_resolution_clock::now();
auto elapsed = std::chrono::duration_cast<std::chrono::milliseconds>( end - begin );
std::cout << "First " << limit << " digits of pi has longest repeated characters:" << std::endl;
for ( std::pair<std::string, std::set<int32_t>> entry : substrings ) {
std::cout << " '" << entry.first << "' starting at index ";
for ( int32_t index : entry.second ) {
std::cout << index << " ";
}
std::cout << std::endl;
}
std::cout << "Time taken: " << elapsed << " milliseconds." << std::endl << std::endl;
}
std::cout << "The timings show that the implementation has approximately linear performance."
<< std::endl;
}
- Output:
First 1000 digits of pi has longest repeated characters: '23846' starting at index 15 578 '33446' starting at index 214 830 '42019' starting at index 700 993 '60943' starting at index 396 550 '82534' starting at index 87 902 '93751' starting at index 44 940 '99999' starting at index 761 762 Time taken: 1ms milliseconds. First 10000 digits of pi has longest repeated characters: '7111369' starting at index 3501 6114 '8530614' starting at index 4166 4600 Time taken: 12ms milliseconds. First 100000 digits of pi has longest repeated characters: '041021944' starting at index 21760 75869 '134926158' starting at index 69596 86281 '201890888' starting at index 30626 33843 Time taken: 155ms milliseconds. The timings show that the implementation has approximately linear performance.
Go
This is a translation of the C code here which is an extended form of the code in Part 6 of the task description for finding the longest repeated substring of a given string. In the interests of brevity, the extensive comments in the C version have been largely omitted. The C code doesn't compile as it stands but I have added a fix in the Talk Page.
For convenience I have included the code from the Arithmetic-geometric_mean/Calculate_Pi#Go task in the same package.
It takes around 25 seconds on my machine (Celeron @1.6GHz) to calculate the first 100,000 (or so) decimal places of Pi. Having done that, the timings for extracting the longest repeated sequence of digits are quick and fairly linear as expected.
As the task doesn't say whether overlapping sequences are to be counted, I've assumed that they are as this is what the algorithm naturally produces.
package main
import (
"fmt"
"math/big"
"time"
)
var maxChar = 128
type Node struct {
children []*Node
suffixLink *Node
start int
end *int
suffixIndex int
}
var (
text string
root *Node
lastNewNode *Node
activeNode *Node
activeEdge = -1
activeLength = 0
remainingSuffixCount = 0
leafEnd = -1
rootEnd *int
splitEnd *int
size = -1
)
func newNode(start int, end *int) *Node {
node := new(Node)
node.children = make([]*Node, maxChar)
node.suffixLink = root
node.start = start
node.end = end
node.suffixIndex = -1
return node
}
func edgeLength(n *Node) int {
if n == root {
return 0
}
return *(n.end) - n.start + 1
}
func walkDown(currNode *Node) bool {
if activeLength >= edgeLength(currNode) {
activeEdge += edgeLength(currNode)
activeLength -= edgeLength(currNode)
activeNode = currNode
return true
}
return false
}
func extendSuffixTree(pos int) {
leafEnd = pos
remainingSuffixCount++
lastNewNode = nil
for remainingSuffixCount > 0 {
if activeLength == 0 {
activeEdge = pos
}
if activeNode.children[text[activeEdge]] == nil {
activeNode.children[text[activeEdge]] = newNode(pos, &leafEnd)
if lastNewNode != nil {
lastNewNode.suffixLink = activeNode
lastNewNode = nil
}
} else {
next := activeNode.children[text[activeEdge]]
if walkDown(next) {
continue
}
if text[next.start+activeLength] == text[pos] {
if lastNewNode != nil && activeNode != root {
lastNewNode.suffixLink = activeNode
lastNewNode = nil
}
activeLength++
break
}
temp := next.start + activeLength - 1
splitEnd = &temp
split := newNode(next.start, splitEnd)
activeNode.children[text[activeEdge]] = split
split.children[text[pos]] = newNode(pos, &leafEnd)
next.start += activeLength
split.children[text[next.start]] = next
if lastNewNode != nil {
lastNewNode.suffixLink = split
}
lastNewNode = split
}
remainingSuffixCount--
if activeNode == root && activeLength > 0 {
activeLength--
activeEdge = pos - remainingSuffixCount + 1
} else if activeNode != root {
activeNode = activeNode.suffixLink
}
}
}
func setSuffixIndexByDFS(n *Node, labelHeight int) {
if n == nil {
return
}
if n.start != -1 {
// Uncomment line below to print suffix tree
// fmt.Print(text[n.start: *(n.end) +1])
}
leaf := 1
for i := 0; i < maxChar; i++ {
if n.children[i] != nil {
// Uncomment the 3 lines below to print suffix index
//if leaf == 1 && n.start != -1 {
// fmt.Printf(" [%d]\n", n.suffixIndex)
//}
leaf = 0
setSuffixIndexByDFS(n.children[i], labelHeight+edgeLength(n.children[i]))
}
}
if leaf == 1 {
n.suffixIndex = size - labelHeight
// Uncomment line below to print suffix index
//fmt.Printf(" [%d]\n", n.suffixIndex)
}
}
func buildSuffixTree() {
size = len(text)
temp := -1
rootEnd = &temp
root = newNode(-1, rootEnd)
activeNode = root
for i := 0; i < size; i++ {
extendSuffixTree(i)
}
labelHeight := 0
setSuffixIndexByDFS(root, labelHeight)
}
func doTraversal(n *Node, labelHeight int, maxHeight, substringStartIndex *int) {
if n == nil {
return
}
if n.suffixIndex == -1 {
for i := 0; i < maxChar; i++ {
if n.children[i] != nil {
doTraversal(n.children[i], labelHeight+edgeLength(n.children[i]),
maxHeight, substringStartIndex)
}
}
} else if n.suffixIndex > -1 && (*maxHeight < labelHeight-edgeLength(n)) {
*maxHeight = labelHeight - edgeLength(n)
*substringStartIndex = n.suffixIndex
}
}
func getLongestRepeatedSubstring(s string) {
maxHeight := 0
substringStartIndex := 0
doTraversal(root, 0, &maxHeight, &substringStartIndex)
// Uncomment line below to print maxHeight and substringStartIndex
// fmt.Printf("maxHeight %d, substringStartIndex %d\n", maxHeight, substringStartIndex)
if s == "" {
fmt.Printf(" %s is: ", text)
} else {
fmt.Printf(" %s is: ", s)
}
k := 0
for ; k < maxHeight; k++ {
fmt.Printf("%c", text[k+substringStartIndex])
}
if k == 0 {
fmt.Print("No repeated substring")
}
fmt.Println()
}
func calculatePi() *big.Float {
one := big.NewFloat(1)
two := big.NewFloat(2)
four := big.NewFloat(4)
prec := uint(325 * 1024) // enough to calculate Pi to 100,182 decimal digits
a := big.NewFloat(1).SetPrec(prec)
g := new(big.Float).SetPrec(prec)
// temporary variables
t := new(big.Float).SetPrec(prec)
u := new(big.Float).SetPrec(prec)
g.Quo(a, t.Sqrt(two))
sum := new(big.Float)
pow := big.NewFloat(2)
for a.Cmp(g) != 0 {
t.Add(a, g)
t.Quo(t, two)
g.Sqrt(u.Mul(a, g))
a.Set(t)
pow.Mul(pow, two)
t.Sub(t.Mul(a, a), u.Mul(g, g))
sum.Add(sum, t.Mul(t, pow))
}
t.Mul(a, a)
t.Mul(t, four)
pi := t.Quo(t, u.Sub(one, sum))
return pi
}
func main() {
tests := []string{
"GEEKSFORGEEKS$",
"AAAAAAAAAA$",
"ABCDEFG$",
"ABABABA$",
"ATCGATCGA$",
"banana$",
"abcpqrabpqpq$",
"pqrpqpqabab$",
}
fmt.Println("Longest Repeated Substring in:\n")
for _, test := range tests {
text = test
buildSuffixTree()
getLongestRepeatedSubstring("")
}
fmt.Println()
pi := calculatePi()
piStr := fmt.Sprintf("%v", pi)
piStr = piStr[2:] // remove initial 3.
numbers := []int{1e3, 1e4, 1e5}
maxChar = 58
for _, number := range numbers {
start := time.Now()
text = piStr[0:number] + "$"
buildSuffixTree()
getLongestRepeatedSubstring(fmt.Sprintf("first %d d.p. of Pi", number))
elapsed := time.Now().Sub(start)
fmt.Printf(" (this took %s)\n\n", elapsed)
}
}
- Output:
Sample run:
Longest Repeated Substring in: GEEKSFORGEEKS$ is: GEEKS AAAAAAAAAA$ is: AAAAAAAAA ABCDEFG$ is: No repeated substring ABABABA$ is: ABABA ATCGATCGA$ is: ATCGA banana$ is: ana abcpqrabpqpq$ is: ab pqrpqpqabab$ is: ab first 1000 d.p. of Pi is: 23846 (this took 7.728858ms) first 10000 d.p. of Pi is: 7111369 (this took 57.524478ms) first 100000 d.p. of Pi is: 041021944 (this took 599.770281ms)
Java
import java.io.IOException;
import java.nio.file.Files;
import java.nio.file.Path;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Set;
import java.util.SortedMap;
import java.util.TreeMap;
import java.util.TreeSet;
public final class UkkonenSuffixTree {
public static void main(String[] aArgs) throws IOException {
List<Integer> limits = List.of( 1_000, 10_000, 100_000 );
for ( int limit : limits ) {
String contents = Files.readString(Path.of("piDigits.txt"));
String piDigits = contents.substring(0, limit + 1);
final long start = System.currentTimeMillis();
SuffixTree tree = new SuffixTree(piDigits);
Map<String, Set<Integer>> substrings = tree.getLongestRepeatedSubstrings();
final long end = System.currentTimeMillis();
System.out.println("First " + limit + " digits of pi has longest repeated characters:");
for ( String substring : substrings.keySet() ) {
System.out.print(" '" + substring + "' starting at index ");
for ( Iterator<Integer> iter = substrings.get(substring).iterator(); iter.hasNext(); ) {
System.out.print(iter.next());
if ( iter.hasNext() ) {
System.out.print(" and ");
}
}
System.out.println();
}
System.out.println("Time taken: " + ( end - start ) + " milliseconds." + System.lineSeparator());
}
System.out.println("The timings show that the implementation has approximately linear performance.");
}
private final static class SuffixTree {
public SuffixTree(String aWord) {
text = Arrays.copyOfRange(aWord.toCharArray(), 0, aWord.length() + 1);
text[aWord.length()] = '\uF123'; // Terminal character
nodes = new Node[2 * text.length];
root = newNode(UNDEFINED, UNDEFINED);
activeNode = root;
for ( char character : text ) {
extendSuffixTree(character);
}
}
public Map<String, Set<Integer>> getLongestRepeatedSubstrings() {
List<Integer> indexes = doTraversal();
String word = String.valueOf(text).substring(0, text.length - 1);
SortedMap<String, Set<Integer>> result = new TreeMap<String, Set<Integer>>();
if ( indexes.getFirst() > 0 ) {
for ( int i = 1; i < indexes.size(); i++ ) {
String substring = word.substring(indexes.get(i), indexes.get(i) + indexes.get(0));
result.computeIfAbsent(substring, k -> new TreeSet<Integer>()).add(indexes.get(i));
}
}
return result;
}
// PRIVATE //
private void extendSuffixTree(char aCharacter) {
needParentLink = UNDEFINED;
remainder++;
while ( remainder > 0 ) {
if ( activeLength == 0 ) {
activeEdge = textIndex;
}
if ( ! nodes[activeNode].children.containsKey(text[activeEdge]) ) {
final int leaf = newNode(textIndex, LEAF_NODE);
nodes[activeNode].children.put(text[activeEdge], leaf);
addSuffixLink(activeNode);
} else {
final int next = nodes[activeNode].children.get(text[activeEdge]);
if ( walkDown(next) ) {
continue;
}
if ( text[nodes[next].start + activeLength] == aCharacter ) {
activeLength++;
addSuffixLink(activeNode);
break;
}
final int split = newNode(nodes[next].start, nodes[next].start + activeLength);
nodes[activeNode].children.put(text[activeEdge], split);
final int leaf = newNode(textIndex, LEAF_NODE);
nodes[split].children.put(aCharacter, leaf);
nodes[next].start += activeLength;
nodes[split].children.put(text[nodes[next].start], next);
addSuffixLink(split);
}
remainder--;
if ( activeNode == root && activeLength > 0 ) {
activeLength--;
activeEdge = textIndex - remainder + 1;
} else {
activeNode = ( nodes[activeNode].parentLink > 0 ) ? nodes[activeNode].parentLink : root;
}
}
textIndex++;
}
private boolean walkDown(int aNode) {
if ( activeLength >= nodes[aNode].edgeLength() ) {
activeEdge += nodes[aNode].edgeLength();
activeLength -= nodes[aNode].edgeLength();
activeNode = aNode;
return true;
}
return false;
}
private void addSuffixLink(int aNode) {
if ( needParentLink != UNDEFINED ) {
nodes[needParentLink].parentLink = aNode;
}
needParentLink = aNode;
}
private int newNode(int aStart, int aEnd) {
Node node = new Node(aStart, aEnd);
node.leafIndex = ( aEnd == LEAF_NODE ) ? leafIndexGenerator++ : UNDEFINED;
nodes[currentNode] = node;
return currentNode++;
}
private List<Integer> doTraversal() {
List<Integer> indexes = new ArrayList<Integer>();
indexes.add(UNDEFINED);
return traversal(indexes, nodes[root], 0);
}
private List<Integer> traversal(List<Integer> aIndexes, Node aNode, int aHeight) {
if ( aNode.leafIndex == UNDEFINED ) {
for ( int index : aNode.children.values() ) {
Node child = nodes[index];
traversal(aIndexes, child, aHeight + child.edgeLength());
}
} else if ( aIndexes.get(0) < aHeight - aNode.edgeLength() ) {
aIndexes.clear();
aIndexes.add(aHeight - aNode.edgeLength());
aIndexes.add(aNode.leafIndex);
} else if ( aIndexes.get(0) == aHeight - aNode.edgeLength() ) {
aIndexes.add(aNode.leafIndex);
}
return aIndexes;
}
private final class Node {
public Node(int aStart, int aEnd) {
start = aStart;
end = aEnd;
}
public int edgeLength() {
return Math.min(end, textIndex + 1) - start;
}
private int start, end, parentLink, leafIndex;
private Map<Character, Integer> children = new HashMap<Character, Integer>();
}
private Node[] nodes;
private char[] text;
private int activeNode, activeLength, activeEdge;
private int root, textIndex, currentNode, needParentLink, remainder, leafIndexGenerator;
private static final int UNDEFINED = -1;
private static final int LEAF_NODE = Integer.MAX_VALUE;
}
}
- Output:
First 1000 digits of pi has longest repeated characters: '23846' starting at index 15 and 578 '33446' starting at index 214 and 830 '42019' starting at index 700 and 993 '60943' starting at index 396 and 550 '82534' starting at index 87 and 902 '93751' starting at index 44 and 940 '99999' starting at index 761 and 762 Time taken: 13 milliseconds. First 10000 digits of pi has longest repeated characters: '7111369' starting at index 3501 and 6114 '8530614' starting at index 4166 and 4600 Time taken: 6 milliseconds. First 100000 digits of pi has longest repeated characters: '041021944' starting at index 21760 and 75869 '134926158' starting at index 69596 and 86281 '201890888' starting at index 30626 and 33843 Time taken: 77 milliseconds. The timings show that the implementation has approximately linear performance.
Julia
Uses array indices instead of the Go version's node pointers.
const oo = typemax(Int)
"""The suffix-tree's node."""
mutable struct Node
children::Dict{Char, Int}
start::Int
ending::Int
suffixlink::Int
suffixindex::Int
end
Node() = Node(Dict(), 0, oo, 0, -1)
Node(start, ending) = Node(Dict(), start, ending, 0, -1)
""" Ukkonen Suffix-Tree """
mutable struct SuffixTree
nodes::Vector{Node}
text::Vector{Char}
root::Int
position::Int
currentnode::Int
needsuffixlink::Int
remainder::Int
activenode::Int
activelength::Int
activeedge::Int
end
edgelength(st, n::Node) = min(n.ending, st.position + 1) - n.start
function newnode(st, start, ending)
st.currentnode += 1
st.nodes[st.currentnode] = Node(start, ending)
return st.currentnode
end
function SuffixTree(str::String)
nodes = [Node() for _ in 1:length(str) * 2]
st = SuffixTree(nodes, [c for c in str], 1, 0, 0, 0, 0, 1, 1, 1)
st.root = newnode(st, 0, 0)
st.activenode = st.root
for i in 1:length(st.text)
extendsuffixtree(st, i)
end
setsuffixindexbyDFS(st, st.nodes[st.root], 0)
return st
end
function addsuffixlink(st, nodenum::Int)
if st.needsuffixlink > 0
st.nodes[st.needsuffixlink].suffixlink = nodenum
end
st.needsuffixlink = nodenum
end
activeedge(st) = st.text[st.activeedge]
function walkdown!(st, currnode::Int)
len = edgelength(st, st.nodes[currnode])
st.activelength < len && return false
st.activeedge += len
st.activelength -= len
st.activenode = currnode
return true
end
function extendsuffixtree(st, pos)
st.position = pos
st.needsuffixlink = 0
st.remainder += 1
while st.remainder > 0
st.activelength == 0 && (st.activeedge = st.position)
if !haskey(st.nodes[st.activenode].children, activeedge(st))
nodenum = newnode(st, st.position, oo)
st.nodes[st.activenode].children[activeedge(st)] = nodenum
addsuffixlink(st, st.activenode)
else
next = st.nodes[st.activenode].children[activeedge(st)]
walkdown!(st, next) && continue
if st.text[st.nodes[next].start + st.activelength] == st.text[pos]
addsuffixlink(st, st.activenode)
st.activelength += 1
break
end
splt = newnode(st, st.nodes[next].start, st.nodes[next].start + st.activelength)
st.nodes[st.activenode].children[activeedge(st)] = splt
nodenum = newnode(st, st.position, oo)
st.nodes[splt].children[st.text[pos]] = nodenum
st.nodes[next].start += st.activelength
st.nodes[splt].children[st.text[st.nodes[next].start]] = next
addsuffixlink(st, splt)
end
st.remainder -= 1
if st.activenode == st.root && st.activelength > 0
st.activelength -= 1
st.activeedge = st.position - st.remainder + 1
elseif st.activenode != st.root
st.activenode = st.nodes[st.activenode].suffixlink
end
end
end
function setsuffixindexbyDFS(st, node, labelheight, verbose=false)
verbose && node.start > 0 && print(st.text[node.start:min(node.ending, length(st.text))])
isleaf = true
for child in map(v -> st.nodes[v], collect(values(node.children)))
verbose && isleaf && node.start > 0 && println(" [", node.suffixindex, "]")
isleaf = false
setsuffixindexbyDFS(st, child, labelheight + edgelength(st, child))
end
if isleaf
idx = length(st.text) - labelheight
node.suffixindex = idx
verbose && println(" [$idx]")
end
end
function dotraversal(st)
maxheight, substringstartindices = 0, [0]
function traversal(node::Node, labelheight)
if node.suffixindex == -1
for child in map(v -> st.nodes[v], collect(values(node.children)))
traversal(child, labelheight + edgelength(st, child))
end
elseif maxheight < labelheight - edgelength(st, node)
maxheight = labelheight - edgelength(st, node)
substringstartindices = [node.suffixindex + 1]
elseif maxheight == labelheight - edgelength(st, node)
push!(substringstartindices, node.suffixindex + 1)
end
end
traversal(st.nodes[st.root], 0)
return maxheight, substringstartindices
end
function getlongestrepeatedsubstring(st::SuffixTree, label="", printresult=true)
len, starts = dotraversal(st)
substring = len == 0 ? "" :
join(unique(map(x -> String(st.text[x:x+len-1]), starts)), " (or) ")
if printresult
print(" ", label == "" ? String(st.text) : label, ": ")
println(len == 0 ? "No repeated substring." : substring)
end
return substring
end
function testsuffixtree()
tests = [
"CAAAABAAAABD\$",
"GEEKSFORGEEKS\$",
"AAAAAAAAAA\$",
"ABCDEFG\$",
"ABABABA\$",
"ATCGATCGA\$",
"banana\$",
"abcpqrabpqpq\$",
"pqrpqpqabab\$",
]
println("Longest Repeated Substring in:\n")
for test in tests
st = SuffixTree(test)
getlongestrepeatedsubstring(st)
end
println()
sπ = ""
setprecision(4000000) do
sπ = string(BigFloat(π))[3:end]
end
for number in [1000, 10000, 100000, 1000000]
text = sπ[1:number] * "\$"
@time begin
st = SuffixTree(text)
getlongestrepeatedsubstring(st, "first $number d.p. of π")
end
end
end
testsuffixtree()
- Output:
Longest Repeated Substring in: CAAAABAAAABD: AAAAB GEEKSFORGEEKS: GEEKS AAAAAAAAAA: AAAAAAAAA ABCDEFG: No repeated substring. ABABABA: ABABA ATCGATCGA: ATCGA banana: ana abcpqrabpqpq: ab (or) pq pqrpqpqabab: ab (or) pq first 1000 d.p. of π: 60943 (or) 42019 (or) 82534 (or) 99999 (or) 93751 (or) 23846 (or) 33446 0.003336 seconds (34.86 k allocations: 4.252 MiB) first 10000 d.p. of π: 7111369 (or) 8530614 0.038749 seconds (351.60 k allocations: 42.460 MiB, 16.54% gc time) first 100000 d.p. of π: 134926158 (or) 041021944 (or) 201890888 0.533892 seconds (3.52 M allocations: 425.035 MiB, 22.42% gc time) first 1000000 d.p. of π: 756130190263 6.008879 seconds (35.25 M allocations: 4.152 GiB, 23.20% gc time)
Nim
import std/[sequtils, strformat, strutils, tables]
const ∞ = int.high
type
# Suffix-tree node.
Node = ref object
children: Table[char, int]
first: int
last: int
suffixLink: int
suffixIndex: int
# Ukkonen suffix-tree.
SuffixTree = object
nodes: seq[Node]
text: string
root: int
position: int
currentNode: int
needSuffixLink: int
remainder: int
activeNode: int
activeLength: int
activeEdge: int
func newNode(): Node =
Node(first: -1, last: ∞, suffixLink: -1, suffixIndex: -1)
func newNode(first, last: int): Node =
Node(first: first, last: last, suffixLink: 0, suffixIndex: -1)
func newNode(st: var SuffixTree; first, last: int): int =
inc st.currentNode
st.nodes[st.currentNode] = newNode(first, last)
result = st.currentNode
func activeEdgeChar(st: SuffixTree): char {.inline.} = st.text[st.activeedge]
func edgeLength(st: SuffixTree; n: Node): int =
min(n.last, st.position + 1) - n.first
func addSuffixLink(st: var SuffixTree; nodenum: int) =
if st.needSuffixLink >= 0:
st.nodes[st.needSuffixLink].suffixLink = nodenum
st.needSuffixLink = nodenum
func walkdown(st: var SuffixTree; currNode: int): bool =
let length = st.edgeLength(st.nodes[currNode])
if st.activeLength < length: return false
inc st.activeEdge, length
dec st.activeLength, length
st.activeNode = currnode
result = true
func extendSuffixTree(st: var SuffixTree; pos: int) =
st.position = pos
st.needSuffixLink = -1
inc st.remainder
while st.remainder > 0:
if st.activeLength == 0: st.activeEdge = st.position
if st.activeEdgeChar() notin st.nodes[st.activeNode].children:
let nodeNum = st.newNode(st.position, ∞)
st.nodes[st.activeNode].children[st.activeEdgeChar()] = nodeNum
st.addSuffixLink(st.activeNode)
else:
let next = st.nodes[st.activeNode].children[st.activeEdgeChar()]
if st.walkdown(next): continue
if st.text[st.nodes[next].first + st.activeLength] == st.text[pos]:
st.addSuffixLink(st.activeNode)
inc st.activeLength
break
let split = st.newNode(st.nodes[next].first, st.nodes[next].first + st.activeLength)
st.nodes[st.activeNode].children[st.activeEdgeChar()] = split
let nodeNum = st.newNode(st.position, ∞)
st.nodes[split].children[st.text[pos]] = nodeNum
st.nodes[next].first += st.activelength
st.nodes[split].children[st.text[st.nodes[next].first]] = next
st.addSuffixLink(split)
dec st.remainder
if st.activeNode == st.root and st.activeLength > 0:
dec st.activelength
st.activeEdge = st.position - st.remainder + 1
elif st.activeNode != st.root:
st.activeNode = st.nodes[st.activeNode].suffixLink
proc setSuffixIndexByDFS(st: var SuffixTree; node: Node; labelHeight: Natural; verbose = false) =
if verbose and node.first >= 0:
echo st.text[node.first..<min(node.last, st.text.len)]
var isLeaf = true
for ichild in node.children.values:
let child = st.nodes[ichild]
if verbose and isLeaf and node.first >= 0:
echo &" [{node.suffixindex}]"
isLeaf = false
st.setSuffixIndexbyDFS(child, labelHeight + st.edgeLength(child))
if isleaf:
node.suffixindex = st.text.len - labelHeight
if verbose: echo &" [{node.suffixindex}]"
proc initSuffixTree(str: string): SuffixTree =
var nodes = newSeqWith(str.len * 2, newNode())
result = SuffixTree(nodes: nodes, text: str, position: -1, currentNode: -1,
needSuffixLink: -1, remainder: 0, activeLength: 1, activeEdge: 0)
result.root = result.newNode(0, 0)
result.activeNode = result.root
for i in 0..result.text.high:
result.extendSuffixTree(i)
result.setSuffixIndexByDFS(result.nodes[result.root], 0)
func doTraversal(st: SuffixTree): (int, seq[int]) =
var maxHeight = 0
var substringStartIndices = @[-1]
func traversal(node: Node; labelHeight: int) =
if node.suffixIndex == -1:
for ichild in node.children.values:
let child = st.nodes[ichild]
traversal(child, labelHeight + st.edgeLength(child))
elif maxHeight < labelHeight - st.edgeLength(node):
maxHeight = labelHeight - st.edgeLength(node)
substringStartIndices = @[node.suffixIndex]
elif maxHeight == labelHeight - st.edgelength(node):
substringStartIndices.add node.suffixIndex
traversal(st.nodes[st.root], 0)
result = (maxHeight, move(substringStartIndices))
proc getLongestRepeatedSubstring(st: SuffixTree; label = ""; printResult = true): string =
let (length, starts) = st.dotraversal()
result = if length == 0: ""
else: starts.mapIt(st.text[it..it+length-1]).deduplicate().join(" (or) ")
if printResult:
stdout.write " ", if label.len == 0: join(st.text) else: label, ": "
echo if length == 0: "No repeated substring." else: result
const Tests = ["CAAAABAAAABD$",
"GEEKSFORGEEKS$",
"AAAAAAAAAA$",
"ABCDEFG$",
"ABABABA$",
"ATCGATCGA$",
"banana$",
"abcpqrabpqpq$",
"pqrpqpqabab$"]
echo "Longest Repeated Substring in:\n"
for test in Tests:
var st = initSuffixTree(test)
discard st.getLongestRepeatedSubstring()
echo()
#############################################################################
# Pi calculation.
import std/[monotimes, times]
import integers
func isr(term, guess: Integer): Integer =
var term = term
result = guess
let value = term * result
while true:
if abs(term - result) <= 1:
break
result = (result + term) shr 1
term = value div result
func calcAgm(lam, gm: Integer; z: var Integer; ep: Integer): Integer =
var am: Integer
var lam = lam
var gm = gm
var n = 1
while true:
am = (lam + gm) shr 1
gm = isr(lam, gm)
let v = am - lam
let zi = v * v * n
if zi < ep:
break
z -= zi
inc n, n
lam = am
result = am
func bip(exp: int; man = 1): Integer {.inline.} = man * 10^exp
func calculatePi(): string =
const Digits = 4_000_000
let am = bip(Digits)
let gm = isqrt(bip(Digits + Digits - 1, 5))
var z = bip(Digits + Digits - 2, 25)
let agm = calcAGM(am, gm, z, bip(Digits + 1))
let pi = agm * agm * bip(Digits - 2) div z
result = $pi
let sπ = calculatePi()
for number in [1000, 10000, 100000, 1000000]:
let text = sπ[2..<number] & '$'
let start = getMonoTime()
var st = initSuffixTree(text)
discard st.getlongestrepeatedsubstring(&"first {number} d.p. of π")
echo &" → Temps: {(getMonoTime() - start).inMicroseconds} µs"
- Output:
Longest Repeated Substring in: CAAAABAAAABD$: AAAAB GEEKSFORGEEKS$: GEEKS AAAAAAAAAA$: AAAAAAAAA ABCDEFG$: No repeated substring. ABABABA$: ABABA ATCGATCGA$: ATCGA banana$: ana abcpqrabpqpq$: ab (or) pq pqrpqpqabab$: ab (or) pq first 1000 d.p. of π: 60943 (or) 42019 (or) 82534 (or) 33446 (or) 93751 (or) 99999 (or) 23846 → Temps: 780 µs first 10000 d.p. of π: 7111369 (or) 8530614 → Temps: 14726 µs first 100000 d.p. of π: 134926158 (or) 041021944 (or) 201890888 → Temps: 178656 µs first 1000000 d.p. of π: 756130190263 → Temps: 1919290 µs
Phix
-- demo/rosetta/Ukkonens_Suffix_Tree.exw with javascript_semantics integer maxChar = 'z' sequence children = {}, suffixLinks = {}, starts = {}, endIndices = {}, suffixIndices = {}, leaves = {} function new_leaf(integer v=0) leaves = append(leaves,v) return length(leaves) end function string text integer splitEndIdx, rootEndIdx, leafEndIdx = new_leaf(), root = NULL, lastNewNode, activeNode, activeEdge = -1, activeLength = 0, remainingSuffixCount = 0, size = -1 function newNode(integer start, finishIdx, bool bKids=false) children = append(children,iff(bKids?repeat(NULL,maxChar):0)) suffixLinks = append(suffixLinks,root) starts = append(starts,start) endIndices = append(endIndices,finishIdx) suffixIndices = append(suffixIndices,-1) return length(children) end function function edgeLength(integer n) return iff(n==root?0:leaves[endIndices[n]] - starts[n] + 1) end function function walkDown(integer currNode) integer l = edgeLength(currNode) if activeLength >= l then activeEdge += l activeLength -= l activeNode = currNode return true end if return false end function procedure extendSuffixTree(integer pos) leaves[leafEndIdx] = pos remainingSuffixCount += 1 lastNewNode = NULL while remainingSuffixCount > 0 do if activeLength == 0 then activeEdge = pos end if integer ta = text[activeEdge] bool ca0 = children[activeNode]=0 integer next = iff(ca0?NULL:children[activeNode][ta]) if next==null then if ca0 then children[activeNode] = repeat(NULL,maxChar) end if children[activeNode][ta] = newNode(pos, leafEndIdx) if lastNewNode!=NULL then suffixLinks[lastNewNode] = activeNode lastNewNode = NULL end if else if walkDown(next) then continue end if integer tp = text[pos] if text[starts[next]+activeLength] == tp then if lastNewNode!=NULL and activeNode!=root then suffixLinks[lastNewNode] = activeNode lastNewNode = NULL end if activeLength += 1 exit end if integer temp = starts[next] + activeLength - 1 splitEndIdx = new_leaf(temp) integer splitnode = newNode(starts[next], splitEndIdx, true) ta = text[activeEdge] children[activeNode][ta] = splitnode children[splitnode][tp] = newNode(pos, leafEndIdx) starts[next] += activeLength children[splitnode][text[starts[next]]] = next if lastNewNode!=NULL then suffixLinks[lastNewNode] = splitnode end if lastNewNode = splitnode end if remainingSuffixCount -= 1 if activeNode==root and activeLength>0 then activeLength -= 1 activeEdge = pos - remainingSuffixCount + 1 elsif activeNode!=root then activeNode = suffixLinks[activeNode] end if end while end procedure procedure setSuffixIndexByDFS(integer n, labelHeight) if n!=NULL then if children[n]=0 then suffixIndices[n] = size - labelHeight else bool leaf = true for i=1 to maxChar do integer nci = children[n][i] if nci!=NULL then leaf = false setSuffixIndexByDFS(nci, labelHeight+edgeLength(nci)) end if end for if leaf then ?9/0 end if -- (sanity check) end if end if end procedure procedure buildSuffixTree() size = length(text) rootEndIdx = new_leaf(-1) root = newNode(-1, rootEndIdx) activeNode = root for i=1 to size do extendSuffixTree(i) end for integer labelHeight = 0 setSuffixIndexByDFS(root, labelHeight) end procedure procedure doTraversal(integer n, labelHeight, maxHeightIdx, substringStartIndex) if n!=NULL then integer nsi = suffixIndices[n], newHeight if nsi == -1 then for i=1 to maxChar do integer nci = children[n][i] if nci!=NULL then newHeight = labelHeight+edgeLength(nci) doTraversal(nci, newHeight, maxHeightIdx, substringStartIndex) end if end for elsif nsi > -1 then newHeight = labelHeight-edgeLength(n) if leaves[maxHeightIdx]<newHeight then leaves[maxHeightIdx] = newHeight leaves[substringStartIndex] = nsi end if end if end if end procedure function getLongestRepeatedSubstring() integer maxHeightIdx = new_leaf(), substringStartIndex = new_leaf() doTraversal(root, 0, maxHeightIdx, substringStartIndex) integer maxHeight = leaves[maxHeightIdx], start = leaves[substringStartIndex] string t = iff(maxHeight=0?"No repeated substring" :text[start+1..start+maxHeight]) return t end function constant tests = {"CAAAABAAAABD$", "GEEKSFORGEEKS$", "AAAAAAAAAA$", "ABCDEFG$", "ABABABA$", "ATCGATCGA$", "banana$", "abcpqrabpqpq$", "pqrpqpqabab$"} printf(1,"Longest Repeated Substring in:\n") for i=1 to length(tests) do text = tests[i] buildSuffixTree() printf(1," %s is: %s\n", {text,getLongestRepeatedSubstring()}) end for printf(1,"\n") include mpfr.e string piStr if platform()=JS then mpfr pi = mpfr_init(0,-1001) -- (set precision to 1,000 dp, plus the "3.") mpfr_const_pi(pi) piStr = mpfr_get_fixed(pi,1000) -- (all we can really manage under pwa/p2js) else -- gmp crashes when I try 100,000 dp, so just get from file piStr = get_text(`E:\downloads\misc\arm\pi-10million.txt`) end if piStr = piStr[3..$] -- discard leading "3." maxChar = '9' for i=3 to iff(platform()=JS?3:6) do atom t0 = time() integer n = power(10,i) text = piStr[1..n] & "$" buildSuffixTree() string r = getLongestRepeatedSubstring(), e = elapsed(time()-t0) printf(1," first %,d d.p. of Pi is: %s (%s)\n", {n,r,e}) end for
- Output:
Longest Repeated Substring in: CAAAABAAAABD$ is: AAAAB GEEKSFORGEEKS$ is: GEEKS AAAAAAAAAA$ is: AAAAAAAAA ABCDEFG$ is: No repeated substring ABABABA$ is: ABABA ATCGATCGA$ is: ATCGA banana$ is: ana abcpqrabpqpq$ is: ab pqrpqpqabab$ is: ab first 1,000 d.p. of Pi is: 23846 (0s) first 10,000 d.p. of Pi is: 7111369 (0.0s) first 100,000 d.p. of Pi is: 041021944 (0.3s) first 1,000,000 d.p. of Pi is: 756130190263 (3.2s)
Note that mpfr_const_pi() struggles to generate more than 1,000 digits of pi under pwa/p2js [and will continue to do so unless someone graciously donates a decent/fast Chudnovsky method in pure Phix or JavaScript...]
Wren
As it would take a very long time to calculate the first 100,000 digits of Pi using the code from the Arithmetic-geometric_mean/Calculate_Pi#Wren task, I have instead saved the digits produced by the Go entry to a file (which only takes a few seconds) and then loaded that into the Wren script.
Having done that, the timings for extracting the longest repeated sequence of digits are reasonably quick and fairly linear as expected.
import "./big" for BigRat
import "./dynamic" for Struct
import "./trait" for ByRef
import "io" for File
var maxChar = 128
var Node = Struct.create("Node", ["children", "suffixLink", "start", "pEnd", "suffixIndex"])
var text = ""
var root = null
var lastNewNode = null
var activeNode = null
var activeEdge = -1
var activeLength = 0
var remainingSuffixCount = 0
var pLeafEnd = ByRef.new(-1)
var pRootEnd = null
var pSplitEnd = null
var size = -1
var newNode = Fn.new { |start, pEnd|
var children = List.filled(maxChar, null)
var suffixLink = root
var suffixIndex = -1
return Node.new(children, suffixLink, start, pEnd, suffixIndex)
}
var edgeLength = Fn.new { |n|
if (n == root) return 0
return n.pEnd.value - n.start + 1
}
var walkDown = Fn.new { |currNode|
var el = edgeLength.call(currNode)
if (activeLength >= el) {
activeEdge = activeEdge + el
activeLength = activeLength - el
activeNode = currNode
return true
}
return false
}
var extendSuffixTree = Fn.new { |pos|
pLeafEnd.value = pos
remainingSuffixCount = remainingSuffixCount + 1
lastNewNode = null
while (remainingSuffixCount > 0) {
if (activeLength == 0) activeEdge = pos
if (!activeNode.children[text[activeEdge].bytes[0]]) {
activeNode.children[text[activeEdge].bytes[0]] = newNode.call(pos, pLeafEnd)
if (lastNewNode) {
lastNewNode.suffixLink = activeNode
lastNewNode = null
}
} else {
var next = activeNode.children[text[activeEdge].bytes[0]]
if (walkDown.call(next)) continue
if (text[next.start + activeLength] == text[pos]) {
if (lastNewNode && activeNode != root) {
lastNewNode.suffixLink = activeNode
lastNewNode = null
}
activeLength = activeLength + 1
break
}
var temp = next.start + activeLength - 1
pSplitEnd = ByRef.new(temp)
var split = newNode.call(next.start, pSplitEnd)
activeNode.children[text[activeEdge].bytes[0]] = split
split.children[text[pos].bytes[0]] = newNode.call(pos, pLeafEnd)
next.start = next.start + activeLength
split.children[text[next.start].bytes[0]] = next
if (lastNewNode) lastNewNode.suffixLink = split
lastNewNode = split
}
remainingSuffixCount = remainingSuffixCount - 1
if (activeNode == root && activeLength > 0) {
activeLength = activeLength - 1
activeEdge = pos - remainingSuffixCount + 1
} else if (activeNode != root) {
activeNode = activeNode.suffixLink
}
}
}
var setSuffixIndexByDFS // recursive
setSuffixIndexByDFS = Fn.new { |n, labelHeight|
if (!n) return
if (n.start != -1) {
// Uncomment line below to print suffix tree
// System.write(text[n.start..n.pEnd.value])
}
var leaf = 1
for (i in 0...maxChar) {
if (n.children[i]) {
// Uncomment the 3 lines below to print suffix index
// if (leaf == 1 && n.start != -1) {
// System.print(" [%(n.suffixIndex)]")
// }
leaf = 0
setSuffixIndexByDFS.call(n.children[i], labelHeight + edgeLength.call(n.children[i]))
}
}
if (leaf == 1) {
n.suffixIndex = size - labelHeight
// Uncomment line below to print suffix index
// System.print(" [%(n.suffixIndex)]")
}
}
var buildSuffixTree = Fn.new {
size = text.count
var temp = -1
pRootEnd = ByRef.new(temp)
root = newNode.call(-1, pRootEnd)
activeNode = root
for (i in 0...size) extendSuffixTree.call(i)
var labelHeight = 0
setSuffixIndexByDFS.call(root, labelHeight)
}
var doTraversal // recursive
doTraversal = Fn.new { |n, labelHeight, pMaxHeight, pSubstringStartIndex|
if (!n) return
if (n.suffixIndex == -1) {
for (i in 0...maxChar) {
if (n.children[i]) {
doTraversal.call(n.children[i], labelHeight + edgeLength.call(n.children[i]),
pMaxHeight, pSubstringStartIndex)
}
}
} else if (n.suffixIndex > -1 && (pMaxHeight.value < labelHeight - edgeLength.call(n))) {
pMaxHeight.value = labelHeight - edgeLength.call(n)
pSubstringStartIndex.value = n.suffixIndex
}
}
var getLongestRepeatedSubstring = Fn.new { |s|
var maxHeight = 0
var substringStartIndex = 0
var pMaxHeight = ByRef.new(maxHeight)
var pSubstringStartIndex = ByRef.new(substringStartIndex)
doTraversal.call(root, 0, pMaxHeight, pSubstringStartIndex)
maxHeight = pMaxHeight.value
substringStartIndex = pSubstringStartIndex.value
// Uncomment line below to print maxHeight and substringStartIndex
// System.print("maxHeight %(maxHeight), substringStartIndex %(substringStartIndex)")
if (s == "") {
System.write(" %(text) is: ")
} else {
System.write(" %(s) is: ")
}
var k = 0
while (k < maxHeight) {
System.write(text[k + substringStartIndex])
k = k + 1
}
if (k == 0) {
System.write("No repeated substring")
}
System.print()
}
var tests = [
"GEEKSFORGEEKS$",
"AAAAAAAAAA$",
"ABCDEFG$",
"ABABABA$",
"ATCGATCGA$",
"banana$",
"abcpqrabpqpq$",
"pqrpqpqabab$",
]
System.print("Longest Repeated Substring in:\n")
for (test in tests) {
text = test
buildSuffixTree.call()
getLongestRepeatedSubstring.call("")
}
System.print()
// load pi to 100,182 digits
var piStr = File.read("pi_100000.txt")
piStr = piStr[2..-1] // remove initial 3.
var numbers = [1e3, 1e4, 1e5]
maxChar = 58
for (number in numbers) {
var start = System.clock
text = piStr[0...number] + "$"
buildSuffixTree.call()
getLongestRepeatedSubstring.call("first %(number) d.p. of Pi")
var elapsed = (System.clock - start) * 1000
System.print(" (this took %(elapsed) ms)\n")
}
- Output:
Longest Repeated Substring in: GEEKSFORGEEKS$ is: GEEKS AAAAAAAAAA$ is: AAAAAAAAA ABCDEFG$ is: No repeated substring ABABABA$ is: ABABA ATCGATCGA$ is: ATCGA banana$ is: ana abcpqrabpqpq$ is: ab pqrpqpqabab$ is: ab first 1000 d.p. of Pi is: 23846 (this took 9.987 ms) first 10000 d.p. of Pi is: 7111369 (this took 89.12 ms) first 100000 d.p. of Pi is: 041021944 (this took 1031.072 ms)