# Ukkonen’s suffix tree construction

Ukkonen’s suffix tree construction
You are encouraged to solve this task according to the task description, using any language you may know.

Suffix Trees are very useful in numerous string processing and computational biology problems.

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. ## 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.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 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 finish = 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> iterator = substrings.get(substring).iterator(); iterator.hasNext(); ) {
System.out.print(iterator.next());
if ( iterator.hasNext() ) {
System.out.print(" and ");
}
}
System.out.println();
}

System.out.println("Time taken: " + ( finish - 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 * aWord.length() + 2];
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);
Map<String, Set<Integer>> result = new HashMap<String, Set<Integer>>();

if ( indexes.get(0) > 0 ) {
for ( int i = 1; i < indexes.size(); i++ ) {
String substring = word.substring(indexes.get(i), indexes.get(i) + indexes.get(0));
}
}

return result;
}

// PRIVATE //

private void extendSuffixTree(char aCharacter) {
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);
} else {
final int next = nodes[activeNode].children.get(text[activeEdge]);
if ( walkDown(next) ) {
continue;
}

if ( text[nodes[next].start + activeLength] == aCharacter ) {
activeLength++;
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);
}

remainder--;

if ( activeNode == root && activeLength > 0 ) {
activeLength--;
activeEdge = textIndex - remainder + 1;
} else {
}
}

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;
}

if ( needParentLink != UNDEFINED ) {
}

}

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>();

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();
} else if ( aIndexes.get(0) == aHeight - aNode.edgeLength() ) {
}

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:
'82534' starting at index 87 and 902
'33446' starting at index 214 and 830
'60943' starting at index 396 and 550
'23846' starting at index 15 and 578
'93751' starting at index 44 and 940
'99999' starting at index 761 and 762
'42019' starting at index 700 and 993
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: 8 milliseconds.

First 100000 digits of pi has longest repeated characters:
'041021944' starting at index 21760 and 75869
'201890888' starting at index 30626 and 33843
'134926158' starting at index 69596 and 86281
Time taken: 100 milliseconds.

The timings show that the implementation has approximately linear performance.


## Julia

Translation of: Go

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
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
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

end
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.remainder += 1
while st.remainder > 0
st.activelength == 0 && (st.activeedge = st.position)
nodenum = newnode(st, st.position, oo)
st.nodes[st.activenode].children[activeedge(st)] = nodenum
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]
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
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
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

Translation of: Julia
Library: Nim-Integers
import std/[sequtils, strformat, strutils, tables]

const ∞ = int.high

type

# Suffix-tree node.
Node = ref object
children: Table[char, int]
first: int
last: int
suffixIndex: int

# Ukkonen suffix-tree.
SuffixTree = object
nodes: seq[Node]
text: string
root: int
position: int
currentNode: 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 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
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
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]:
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

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:

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):

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

Translation of: Go
-- demo/rosetta/Ukkonens_Suffix_Tree.exw
with javascript_semantics
integer maxChar = 'z'

sequence children = {},
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))
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
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
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
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
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

Translation of: Go
Library: Wren-big
Library: Wren-dynamic
Library: Wren-trait

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 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 = 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 = 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
lastNewNode = split
}
remainingSuffixCount = remainingSuffixCount - 1
if (activeNode == root && activeLength > 0) {
activeLength = activeLength - 1
activeEdge = pos - remainingSuffixCount + 1
} else if (activeNode != root) {
}
}
}

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
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)