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A suffix tree is a data structure commonly used in string algorithms.

Given a string S of length n, its suffix tree is a tree T such that:

T has exactly n leaves numbered from 1 to n.
Except for the root, every internal node has at least two children.
Each edge of T is labelled with a non-empty substring of S.
No two edges starting out of a node can have string labels beginning with the same character.
The string obtained by concatenating all the string labels found on the path from the root to leaf i spells out suffix S[i..n], for i from 1 to n.

Such a tree does not exist for all strings. To ensure existence, a character that is not found in S must be appended at its end. The character '$' is traditionally used for this purpose.

For this task, build and display the suffix tree of the string "banana$". Displaying the tree can be done using the code from the visualize a tree task, but any other convenient method is accepted.

There are several ways to implement the tree data structure, for instance how edges should be labelled. Latitude is given in this matter, but notice that a simple way to do it is to label each node with the label of the edge leading to it.

The computation time for an efficient algorithm should be $O(n)$ , but such an algorithm might be difficult to implement. An easier, $O(n^{2})$ algorithm is accepted.

11l

Translation of: Python

T Node
   String sub
   [Int] ch
   F (sub, children)
      .sub = sub
      .ch = children

T SuffixTree
   nodes = [Node(‘’, [Int]())]
   F (str)
      L(i) 0 .< str.len
         .addSuffix(str[i..])

   F addSuffix(suf)
      V n = 0
      V i = 0
      L i < suf.len
         V b = suf[i]
         V x2 = 0
         Int n2
         L
            V children = .nodes[n].ch
            I x2 == children.len
               n2 = .nodes.len
               .nodes.append(Node(suf[i..], [Int]()))
               .nodes[n].ch.append(n2)
               R
            n2 = children[x2]
            I .nodes[n2].sub[0] == b
               L.break
            x2 = x2 + 1
         V sub2 = .nodes[n2].sub
         V j = 0
         L j < sub2.len
            I suf[i + j] != sub2[j]
               V n3 = n2
               n2 = .nodes.len
               .nodes.append(Node(sub2[0 .< j], [n3]))
               .nodes[n3].sub = sub2[j..]
               .nodes[n].ch[x2] = n2
               L.break
            j = j + 1
         i = i + j
         n = n2

   F visualize()
      I .nodes.empty
         print(‘<empty>’)
         R

      F f(Int n, String pre) -> N
         V children = @.nodes[n].ch
         I children.empty
            print(‘-- ’(@.nodes[n].sub))
            R
         print(‘+- ’(@.nodes[n].sub))
         L(c) children[0 .< (len)-1]
            print(pre‘ +-’, end' ‘ ’)
            @f(c, pre‘ | ’)
         print(pre‘ +-’, end' ‘ ’)
         @f(children.last, pre‘  ’)
      f(0, ‘’)

SuffixTree(‘banana$’).visualize()

Output:

+-
 +- -- banana$
 +- +- a
 |  +- +- na
 |  |  +- -- na$
 |  |  +- -- $
 |  +- -- $
 +- +- na
 |  +- -- na$
 |  +- -- $
 +- -- $

C#

Translation of: C++

using System;
using System.Collections.Generic;

namespace SuffixTree {
    class Node {
        public string sub;                     // a substring of the input string
        public List<int> ch = new List<int>(); // vector of child nodes

        public Node() {
            sub = "";
        }

        public Node(string sub, params int[] children) {
            this.sub = sub;
            ch.AddRange(children);
        }
    }

    class SuffixTree {
        readonly List<Node> nodes = new List<Node>();

        public SuffixTree(string str) {
            nodes.Add(new Node());
            for (int i = 0; i < str.Length; i++) {
                AddSuffix(str.Substring(i));
            }
        }

        public void Visualize() {
            if (nodes.Count == 0) {
                Console.WriteLine("<empty>");
                return;
            }

            void f(int n, string pre) {
                var children = nodes[n].ch;
                if (children.Count == 0) {
                    Console.WriteLine("- {0}", nodes[n].sub);
                    return;
                }
                Console.WriteLine("+ {0}", nodes[n].sub);

                var it = children.GetEnumerator();
                if (it.MoveNext()) {
                    do {
                        var cit = it;
                        if (!cit.MoveNext()) break;

                        Console.Write("{0}+-", pre);
                        f(it.Current, pre + "| ");
                    } while (it.MoveNext());
                }

                Console.Write("{0}+-", pre);
                f(children[children.Count-1], pre+"  ");
            }

            f(0, "");
        }

        private void AddSuffix(string suf) {
            int n = 0;
            int i = 0;
            while (i < suf.Length) {
                char b = suf[i];
                int x2 = 0;
                int n2;
                while (true) {
                    var children = nodes[n].ch;
                    if (x2 == children.Count) {
                        // no matching child, remainder of suf becomes new node
                        n2 = nodes.Count;
                        nodes.Add(new Node(suf.Substring(i)));
                        nodes[n].ch.Add(n2);
                        return;
                    }
                    n2 = children[x2];
                    if (nodes[n2].sub[0] == b) {
                        break;
                    }
                    x2++;
                }
                // find prefix of remaining suffix in common with child
                var sub2 = nodes[n2].sub;
                int j = 0;
                while (j < sub2.Length) {
                    if (suf[i + j] != sub2[j]) {
                        // split n2
                        var n3 = n2;
                        // new node for the part in common
                        n2 = nodes.Count;
                        nodes.Add(new Node(sub2.Substring(0, j), n3));
                        nodes[n3].sub = sub2.Substring(j); // old node loses the part in common
                        nodes[n].ch[x2] = n2;
                        break; // continue down the tree
                    }
                    j++;
                }
                i += j; // advance past part in common
                n = n2; // continue down the tree
            }
        }
    }

    class Program {
        static void Main() {
            new SuffixTree("banana$").Visualize();
        }
    }
}

Output:

+
+-- banana$
+-+ a
| +-+ na
| | +-- na$
| | +-- $
| +-- $
+-+ na
| +-- na$
| +-- $
+-- $

C++

Translation of: D

#include <functional>
#include <iostream>
#include <vector>

struct Node {
    std::string sub = "";   // a substring of the input string
    std::vector<int> ch;    // vector of child nodes

    Node() {
        // empty
    }

    Node(const std::string& sub, std::initializer_list<int> children) : sub(sub) {
        ch.insert(ch.end(), children);
    }
};

struct SuffixTree {
    std::vector<Node> nodes;

    SuffixTree(const std::string& str) {
        nodes.push_back(Node{});
        for (size_t i = 0; i < str.length(); i++) {
            addSuffix(str.substr(i));
        }
    }

    void visualize() {
        if (nodes.size() == 0) {
            std::cout << "<empty>\n";
            return;
        }

        std::function<void(int, const std::string&)> f;
        f = [&](int n, const std::string & pre) {
            auto children = nodes[n].ch;
            if (children.size() == 0) {
                std::cout << "- " << nodes[n].sub << '\n';
                return;
            }
            std::cout << "+ " << nodes[n].sub << '\n';

            auto it = std::begin(children);
            if (it != std::end(children)) do {
                if (std::next(it) == std::end(children)) break;
                std::cout << pre << "+-";
                f(*it, pre + "| ");
                it = std::next(it);
            } while (true);

            std::cout << pre << "+-";
            f(children[children.size() - 1], pre + "  ");
        };

        f(0, "");
    }

private:
    void addSuffix(const std::string & suf) {
        int n = 0;
        size_t i = 0;
        while (i < suf.length()) {
            char b = suf[i];
            int x2 = 0;
            int n2;
            while (true) {
                auto children = nodes[n].ch;
                if (x2 == children.size()) {
                    // no matching child, remainder of suf becomes new node
                    n2 = nodes.size();
                    nodes.push_back(Node(suf.substr(i), {}));
                    nodes[n].ch.push_back(n2);
                    return;
                }
                n2 = children[x2];
                if (nodes[n2].sub[0] == b) {
                    break;
                }
                x2++;
            }
            // find prefix of remaining suffix in common with child
            auto sub2 = nodes[n2].sub;
            size_t j = 0;
            while (j < sub2.size()) {
                if (suf[i + j] != sub2[j]) {
                    // split n2
                    auto n3 = n2;
                    // new node for the part in common
                    n2 = nodes.size();
                    nodes.push_back(Node(sub2.substr(0, j), { n3 }));
                    nodes[n3].sub = sub2.substr(j); // old node loses the part in common
                    nodes[n].ch[x2] = n2;
                    break; // continue down the tree
                }
                j++;
            }
            i += j; // advance past part in common
            n = n2; // continue down the tree
        }
    }
};

int main() {
    SuffixTree("banana$").visualize();
}

Output:

+
+-- banana$
+-+ a
| +-+ na
| | +-- na$
| | +-- $
| +-- $
+-+ na
| +-- na$
| +-- $
+-- $

D

Translation of: Kotlin

import std.stdio;

struct Node {
    string sub = ""; // a substring of the input string
    int[] ch;        // array of child nodes

    this(string sub, int[] children ...) {
        this.sub = sub;
        ch = children;
    }
}

struct SuffixTree {
    Node[] nodes;

    this(string str) {
        nodes ~= Node();
        for (int i=0; i<str.length; ++i) {
            addSuffix(str[i..$]);
        }
    }

    private void addSuffix(string suf) {
        int n = 0;
        int i = 0;
        while (i < suf.length) {
            char b  = suf[i];
            int x2 = 0;
            int n2;
            while (true) {
                auto children = nodes[n].ch;
                if (x2 == children.length) {
                    // no matching child, remainder of suf becomes new node.
                    n2 = nodes.length;
                    nodes ~= Node(suf[i..$]);
                    nodes[n].ch ~= n2;
                    return;
                }
                n2 = children[x2];
                if (nodes[n2].sub[0] == b) {
                    break;
                }
                x2++;
            }
            // find prefix of remaining suffix in common with child
            auto sub2 = nodes[n2].sub;
            int j = 0;
            while (j < sub2.length) {
                if (suf[i + j] != sub2[j]) {
                    // split n2
                    auto n3 = n2;
                    // new node for the part in common
                    n2 = nodes.length;
                    nodes ~= Node(sub2[0..j], n3);
                    nodes[n3].sub = sub2[j..$];  // old node loses the part in common
                    nodes[n].ch[x2] = n2;
                    break;  // continue down the tree
                }
                j++;
            }
            i += j;  // advance past part in common
            n = n2;  // continue down the tree
        }
    }

    void visualize() {
        if (nodes.length == 0) {
            writeln("<empty>");
            return;
        }

        void f(int n, string pre) {
            auto children = nodes[n].ch;
            if (children.length == 0) {
                writefln("╴ %s", nodes[n].sub);
                return;
            }
            writefln("┐ %s", nodes[n].sub);
            foreach (c; children[0..$-1]) {
                write(pre, "├─");
                f(c, pre ~ "│ ");
            }
            write(pre, "└─");
            f(children[$-1], pre ~ "  ");
        }

        f(0, "");
    }
}

void main() {
    SuffixTree("banana$").visualize();
}

Output:

┐ 
├─╴ banana$
├─┐ a
│ ├─┐ na
│ │ ├─╴ na$
│ │ └─╴ $
│ └─╴ $
├─┐ na
│ ├─╴ na$
│ └─╴ $
└─╴ $

Elixir

defmodule STree do
  defstruct branch: []
  
  defp suffixes([]), do: []
  defp suffixes(w), do: [w | suffixes tl(w)]
  
  defp lcp([], _, acc), do: acc
  defp lcp(_, [], acc), do: acc
  defp lcp([c | u], [a | w], acc) do 
    if c == a do 
      lcp(u, w, acc + 1) 
    else acc 
    end
  end
  
  defp g([], aw), do: [{{aw, length aw}, nil}]
  defp g(cusnes, aw) do
    [cusn | es] = cusnes
    {cus, node} = cusn
    {cu, culen} = cus
    cpl = case node do
      nil -> lcp cu, aw, 0
      _   -> lcp (Enum.take cu, culen), aw, 0
    end
    x = Enum.drop cu, cpl
    xlen = culen - cpl
    y = Enum.drop aw, cpl
    ex = {{x, xlen}, node}
    ey = {{y, length y}, nil}
    cond do
      hd(aw) > hd(cu)          -> [cusn | g(es, aw)]
      hd(aw) < hd(cu)          -> [{{aw, length aw}, nil} | cusnes]
      nil != node && xlen == 0 -> [{cus, insert_suffix(y, node)} | es]
      hd(x) < hd(y)            -> [{{cu, cpl}, %STree{branch: [ex, ey]}} | es] 
      true                     -> [{{cu, cpl}, %STree{branch: [ey, ex]}} | es] 
    end
  end

  defp insert_suffix(aw, node), do: %STree{branch: g(node.branch, aw)}
  
  def naive_insertion(t), do: List.foldl(suffixes(t), %STree{}, &insert_suffix/2)

  defp f(nil, _, label), do: IO.puts("╴ #{label}")
  defp f(%STree{branch: children}, pre, label) do
    IO.puts "┐ #{label}"
    children 
    |> Enum.take(length(children) - 1)
    |> Enum.each(fn c -> 
      IO.write(pre <> "├─")
      {ws, len} = elem(c, 0)
      f(elem(c, 1), pre <> "│ ", Enum.join(Enum.take ws, len))
    end)
    IO.write(pre <> "└─")
    c = List.last(children)
    {ws, len} = elem(c, 0)
    f(elem(c, 1), pre <> "  ", Enum.join(Enum.take ws, len))
  end

  def visualize(n), do: f(n, "", "")

  def main do
    "banana$"
    |> String.graphemes
    |> naive_insertion
    |> visualize
  end
end

Output:

┐
├─╴ $
├─┐ a
│ ├─╴ $
│ └─┐ na
│   ├─╴ $
│   └─╴ na$
├─╴ banana$
└─┐ na
  ├─╴ $
  └─╴ na$

Go

Vis function from Visualize_a_tree#Unicode.

package main

import "fmt"

func main() {
    vis(buildTree("banana$"))
}

type tree []node

type node struct {
    sub string // a substring of the input string
    ch  []int  // list of child nodes
}

func buildTree(s string) tree {
    t := tree{node{}} // root node
    for i := range s {
        t = t.addSuffix(s[i:])
    }
    return t
}

func (t tree) addSuffix(suf string) tree {
    n := 0
    for i := 0; i < len(suf); {
        b := suf[i]
        ch := t[n].ch
        var x2, n2 int
        for ; ; x2++ {
            if x2 == len(ch) {
                // no matching child, remainder of suf becomes new node.
                n2 = len(t)
                t = append(t, node{sub: suf[i:]})
                t[n].ch = append(t[n].ch, n2)
                return t
            }
            n2 = ch[x2]
            if t[n2].sub[0] == b {
                break
            }
        }
        // find prefix of remaining suffix in common with child
        sub2 := t[n2].sub
        j := 0
        for ; j < len(sub2); j++ {
            if suf[i+j] != sub2[j] {
                // split n2
                n3 := n2
                // new node for the part in common
                n2 = len(t)
                t = append(t, node{sub2[:j], []int{n3}})
                t[n3].sub = sub2[j:] // old node loses the part in common
                t[n].ch[x2] = n2
                break // continue down the tree
            }
        }
        i += j // advance past part in common
        n = n2 // continue down the tree
    }
    return t
}

func vis(t tree) {
    if len(t) == 0 {
        fmt.Println("<empty>")
        return
    }
    var f func(int, string)
    f = func(n int, pre string) {
        children := t[n].ch
        if len(children) == 0 {
            fmt.Println("╴", t[n].sub)
            return
        }
        fmt.Println("┐", t[n].sub)
        last := len(children) - 1
        for _, ch := range children[:last] {
            fmt.Print(pre, "├─")
            f(ch, pre+"│ ")
        }
        fmt.Print(pre, "└─")
        f(children[last], pre+"  ")
    }
    f(0, "")
}

Output:

┐ 
├─╴ banana$
├─┐ a
│ ├─┐ na
│ │ ├─╴ na$
│ │ └─╴ $
│ └─╴ $
├─┐ na
│ ├─╴ na$
│ └─╴ $
└─╴ $

J

Implementation:

classify=: {.@> </. ]

build_tree=:3 :0
  tree=. ,:_;_;''
  if. 0=#y do. tree return.end.
  if. 1=#y do. tree,(#;y);0;y return.end.
  for_box.classify y do.
    char=. {.>{.>box
    subtree=. }.build_tree }.each>box
    ndx=.I.0=1&{::"1 subtree
    n=.#tree
    if. 1=#ndx do.
      counts=. 1 + 0&{::"1 subtree
      parents=. (n-1) (+*]&*) 1&{::"1 subtree
      edges=. (ndx}~ <@(char,ndx&{::)) 2&{"1 subtree
      tree=. tree, counts;"0 1 parents;"0 edges
    else.
      tree=. tree,(__;0;,char),(1;n;0) + ::]&.>"1 subtree
    end.
  end.
)
 
suffix_tree=:3 :0
  assert. -.({:e.}:)y
  tree=. B=:|:build_tree <\. y
  ((1+#y)-each {.tree),}.tree
)

Task example:

   suffix_tree 'banana$'
┌──┬───────┬─┬──┬───┬─┬─┬──┬───┬─┬─┐
│__│1      │_│_ │2  │4│6│_ │3  │5│7│
├──┼───────┼─┼──┼───┼─┼─┼──┼───┼─┼─┤
│_ │0      │0│2 │3  │3│2│0 │7  │7│0│
├──┼───────┼─┼──┼───┼─┼─┼──┼───┼─┼─┤
│  │banana$│a│na│na$│$│$│na│na$│$│$│
└──┴───────┴─┴──┴───┴─┴─┴──┴───┴─┴─┘

The first row is the leaf number (_ for internal nodes).

The second row is parent index (_ for root node).

The third row is the edge's substring (empty for root node).

Visualizing, using showtree and prefixing the substring leading to each leaf with the leaf number (in brackets):

fmttree=: ;@(1&{) showtree~ {: (,~ }.`('[','] ',~":)@.(_>|))each {.

   fmttree suffix_tree 'banana$'
    ┌─ [1] banana$                    
    │                       ┌─ [2] na$
    │             ┌─ na ────┴─ [4] $  
────┼─ a ─────────┴─ [6] $            
    │             ┌─ [3] na$          
    ├─ na ────────┴─ [5] $            
    └─ [7] $

Java

Translation of: Kotlin

import java.util.ArrayList;
import java.util.List;

public class SuffixTreeProblem {
    private static class Node {
        String sub = "";                       // a substring of the input string
        List<Integer> ch = new ArrayList<>();  // list of child nodes
    }

    private static class SuffixTree {
        private List<Node> nodes = new ArrayList<>();

        public SuffixTree(String str) {
            nodes.add(new Node());
            for (int i = 0; i < str.length(); ++i) {
                addSuffix(str.substring(i));
            }
        }

        private void addSuffix(String suf) {
            int n = 0;
            int i = 0;
            while (i < suf.length()) {
                char b = suf.charAt(i);
                List<Integer> children = nodes.get(n).ch;
                int x2 = 0;
                int n2;
                while (true) {
                    if (x2 == children.size()) {
                        // no matching child, remainder of suf becomes new node.
                        n2 = nodes.size();
                        Node temp = new Node();
                        temp.sub = suf.substring(i);
                        nodes.add(temp);
                        children.add(n2);
                        return;
                    }
                    n2 = children.get(x2);
                    if (nodes.get(n2).sub.charAt(0) == b) break;
                    x2++;
                }
                // find prefix of remaining suffix in common with child
                String sub2 = nodes.get(n2).sub;
                int j = 0;
                while (j < sub2.length()) {
                    if (suf.charAt(i + j) != sub2.charAt(j)) {
                        // split n2
                        int n3 = n2;
                        // new node for the part in common
                        n2 = nodes.size();
                        Node temp = new Node();
                        temp.sub = sub2.substring(0, j);
                        temp.ch.add(n3);
                        nodes.add(temp);
                        nodes.get(n3).sub = sub2.substring(j);  // old node loses the part in common
                        nodes.get(n).ch.set(x2, n2);
                        break;  // continue down the tree
                    }
                    j++;
                }
                i += j;  // advance past part in common
                n = n2;  // continue down the tree
            }
        }

        public void visualize() {
            if (nodes.isEmpty()) {
                System.out.println("<empty>");
                return;
            }
            visualize_f(0, "");
        }

        private void visualize_f(int n, String pre) {
            List<Integer> children = nodes.get(n).ch;
            if (children.isEmpty()) {
                System.out.println("- " + nodes.get(n).sub);
                return;
            }
            System.out.println("┐ " + nodes.get(n).sub);
            for (int i = 0; i < children.size() - 1; i++) {
                Integer c = children.get(i);
                System.out.print(pre + "├─");
                visualize_f(c, pre + "│ ");
            }
            System.out.print(pre + "└─");
            visualize_f(children.get(children.size() - 1), pre + "  ");
        }
    }

    public static void main(String[] args) {
        new SuffixTree("banana$").visualize();
    }
}

Output:

┐ 
├─- banana$
├─┐ a
│ ├─┐ na
│ │ ├─- na$
│ │ └─- $
│ └─- $
├─┐ na
│ ├─- na$
│ └─- $
└─- $

JavaScript

Translation of: Java

class Node {
  sub = ''; // a substring of the input string
  children = []; // list of child nodes
}

class SuffixTree {
  nodes = [];

  constructor(str) {
    this.nodes.push(new Node());
    for (let i = 0; i < str.length; ++i) {
      this.addSuffix(str.slice(i));
    }
  }

  addSuffix(suf) {
    let n = 0;
    let i = 0;
    while (i < suf.length) {
      const b = suf.charAt(i);
      const children = this.nodes[n].children;
      let x2 = 0;
      let n2;
      while (true) {
        if (x2 === children.length) {
          // no matching child, remainder of suf becomes new node.
          n2 = this.nodes.length;
          const temp = new Node();
          temp.sub = suf.slice(i);
          this.nodes.push(temp);
          children.push(n2);
          return;
        }
        n2 = children[x2];
        if (this.nodes[n2].sub.charAt(0) === b) break;
        x2++;
      }
      // find prefix of remaining suffix in common with child
      const sub2 = this.nodes[n2].sub;
      let j = 0;
      while (j < sub2.length) {
        if (suf.charAt(i + j) !== sub2.charAt(j)) {
          // split n2
          const n3 = n2;
          // new node for the part in common
          n2 = this.nodes.length;
          const temp = new Node();
          temp.sub = sub2.slice(0, j);
          temp.children.push(n3);
          this.nodes.push(temp);
          this.nodes[n3].sub = sub2.slice(j);  // old node loses the part in common
          this.nodes[n].children[x2] = n2;
          break;  // continue down the tree
        }
        j++;
      }
      i += j;  // advance past part in common
      n = n2;  // continue down the tree
    }
  }

  toString() {
    if (this.nodes.length === 0) {
      return '<empty>';
    }
    return this.toString_f(0, '');
  }

  toString_f(n, pre) {
    const children = this.nodes[n].children;
    if (children.length === 0) {
      return '- ' + this.nodes[n].sub + '\n';
    }
    let s = '┐ ' + this.nodes[n].sub + '\n';
    for (let i = 0; i < children.length - 1; i++) {
      const c = children[i];
      s += pre + '├─';
      s += this.toString_f(c, pre + '│ ');
    }
    s += pre + '└─';
    s += this.toString_f(children[children.length - 1], pre + '  ');
    return s;
  }
}

const st = new SuffixTree('banana');
console.log(st.toString());

Output:

┐ 
├─- banana
├─┐ a
│ └─┐ na
│   └─- na
└─┐ na
  └─- na

Julia

Translation of: Go

import Base.print

mutable struct Node
    sub::String
    ch::Vector{Int}
    Node(str, v=Int[]) = new(str, v)
end

struct SuffixTree
    nodes::Vector{Node}
    function SuffixTree(s::String)
        nod = [Node("", Int[])]
        for i in 1:length(s)
            addSuffix!(nod, s[i:end])
        end
        return new(nod)
    end
end

function addSuffix!(tree::Vector{Node}, suf::String)
    n, i = 1, 1
    while i <= length(suf)
        x2, n2, b = 1, 1, suf[i]
        while true
            children = tree[n].ch
            if x2 > length(children)
                push!(tree, Node(suf[i:end]))
                push!(tree[n].ch, length(tree))
                return
            end
            n2 = children[x2]
            (tree[n2].sub[1] == b) && break
            x2 += 1
        end
        sub2, j = tree[n2].sub, 0
        while j < length(sub2)
            if suf[i + j] != sub2[j + 1]
                push!(tree, Node(sub2[1:j], [n2]))
                tree[n2].sub = sub2[j+1:end]
                n2 = length(tree)
                tree[n].ch[x2] = n2
                break
            end
            j += 1
        end
        i += j
        n = n2
    end
end

function Base.print(io::IO, suffixtree::SuffixTree)
    function treeprint(n::Int, pre::String)
        children = suffixtree.nodes[n].ch
        if isempty(children)
            println("╴ ", suffixtree.nodes[n].sub)
        else
            println("┐ ", suffixtree.nodes[n].sub)
            for c in children[1:end-1]
                print(pre, "├─")
                treeprint(c, pre * "│ ")
            end
            print(pre, "└─")
            treeprint(children[end], pre * "  ")
        end
    end
    if isempty(suffixtree.nodes)
        println("<empty>")
    else
        treeprint(1, "")
    end
end

println(SuffixTree("banana\$"))

Output:

┐
├─╴ banana$
├─┐ a
│ ├─┐ na
│ │ ├─╴ na$
│ │ └─╴ $
│ └─╴ $
├─┐ na
│ ├─╴ na$
│ └─╴ $
└─╴ $

Kotlin

Translation of: Go

// version 1.1.3

class Node {
    var sub = ""                    // a substring of the input string
    var ch  = mutableListOf<Int>()  // list of child nodes
}

class SuffixTree(val str: String) {
    val nodes = mutableListOf<Node>(Node())

    init {
        for (i in 0 until str.length) addSuffix(str.substring(i))
    }

    private fun addSuffix(suf: String) {
        var n = 0
        var i = 0
        while (i < suf.length) {
            val b  = suf[i]
            val children = nodes[n].ch
            var x2 = 0
            var n2: Int
            while (true) {
                if (x2 == children.size) {
                    // no matching child, remainder of suf becomes new node.
                    n2 = nodes.size
                    nodes.add(Node().apply { sub = suf.substring(i) } )
                    children.add(n2)
                    return
                }
                n2 = children[x2]
                if (nodes[n2].sub[0] == b) break
                x2++
            }
            // find prefix of remaining suffix in common with child
            val sub2 = nodes[n2].sub
            var j = 0
            while (j < sub2.length) {
                if (suf[i + j] != sub2[j]) {
                    // split n2
                    val n3 = n2
                    // new node for the part in common
                    n2 = nodes.size
                    nodes.add(Node().apply {
                        sub = sub2.substring(0, j)
                        ch.add(n3)
                    })
                    nodes[n3].sub = sub2.substring(j)  // old node loses the part in common
                    nodes[n].ch[x2] = n2
                    break  // continue down the tree
                }
                j++
            }
            i += j  // advance past part in common
            n = n2  // continue down the tree
        }
    }

    fun visualize() {
        if (nodes.isEmpty()) {
            println("<empty>")
            return
        }

        fun f(n: Int, pre: String) {
            val children = nodes[n].ch
            if (children.isEmpty()) {
                println("╴ ${nodes[n].sub}")
                return
            }
            println("┐ ${nodes[n].sub}")
            for (c in children.dropLast(1)) {
                print(pre + "├─")
                f(c, pre + "│ ")
            }
            print(pre + "└─")
            f(children.last(), pre + "  ")
        }

        f(0, "")
    }
}

fun main(args: Array<String>) {
    SuffixTree("banana$").visualize()
}

Output:

┐ 
├─╴ banana$
├─┐ a
│ ├─┐ na
│ │ ├─╴ na$
│ │ └─╴ $
│ └─╴ $
├─┐ na
│ ├─╴ na$
│ └─╴ $
└─╴ $

Nim

Translation of: Go

type

  Tree = seq[Node]

  Node = object
    sub: string   # a substring of the input string.
    ch: seq[int]  # list of child nodes.


proc addSuffix(t: var Tree; suf: string) =
  var n, i = 0
  while i < suf.len:
    let b = suf[i]
    let ch = t[n].ch
    var x2, n2: int
    while true:
      if x2 == ch.len:
        # No matching child, remainder of "suf" becomes new node.
        n2 = t.len
        t.add Node(sub: suf[i..^1])
        t[n].ch.add n2
        return
      n2 = ch[x2]
      if t[n2].sub[0] == b: break
      inc x2

    # Find prefix of remaining suffix in common with child.
    let sub2 = t[n2].sub
    var j = 0
    while j < sub2.len:
      if suf[i+j] != sub2[j]:
        # Split "sub2".
        let n3 = n2
        # New node for the part in common.
        n2 = t.len
        t.add Node(sub: sub2[0..<j], ch: @[n3])
        t[n3].sub = sub2[j..^1]   # Old node loses the part in common.
        t[n].ch[x2] = n2
        break   # Continue down the tree.
      inc j
    inc i, j  # Advance past part in common.
    n = n2    # Continue down the tree.


func newTree(s: string): Tree =
  result.add Node()     # root node.
  for i in 0..s.high:
    result.addSuffix s[i..^1]


proc vis(t: Tree) =
  if t.len == 0:
    echo "<empty>"
    return

  proc f(n: int; pre: string) =
    let children = t[n].ch
    if children.len == 0:
      echo "╴", t[n].sub
      return
    echo "┐", t[n].sub
    for i in 0..<children.high:
      stdout.write pre, "├─"
      f(children[i], pre & "│ ")
    stdout.write pre, "└─"
    f(children[^1], pre & "  ")

  f(0, "")


newTree("banana$").vis()

Output:

┐
├─╴banana$
├─┐a
│ ├─┐na
│ │ ├─╴na$
│ │ └─╴$
│ └─╴$
├─┐na
│ ├─╴na$
│ └─╴$
└─╴$

Perl

Translation of: Raku

use strict;
use warnings;
use Data::Dumper;
 
sub classify {
    my $h = {};
    for (@_) { push @{$h->{substr($_,0,1)}}, $_ }
    return $h;
}
sub suffixes {
    my $str = shift;
    map { substr $str, $_ } 0 .. length($str) - 1;
}
sub suffix_tree {
    return +{} if @_ == 0;
    return +{ $_[0] => +{} } if @_ == 1;
    my $h = {};
    my $classif = classify @_;
    for my $key (keys %$classif) {
        my $subtree = suffix_tree(
            map { substr $_, 1 } @{$classif->{$key}}
        );
        my @subkeys = keys %$subtree;
        if (@subkeys == 1) {
            my ($subkey) = @subkeys;
            $h->{"$key$subkey"} = $subtree->{$subkey};
        } else { $h->{$key} = $subtree }
    }
    return $h;
}
print +Dumper suffix_tree suffixes 'banana$';

Output:

$VAR1 = {
          '$' => {},
          'a' => {
                   '$' => {},
                   'na' => {
                             'na$' => {},
                             '$' => {}
                           }
                 },
          'banana$' => {},
          'na' => {
                    'na$' => {},
                    '$' => {}
                  }
        };

Phix

Translation of: D

with javascript_semantics
-- tree nodes are simply {string substr, sequence children_idx}
enum SUB=1, CHILDREN=2
 
function addSuffix(sequence t, string suffix)
    int n = 1, i = 1
    while i<=length(suffix) do
        integer ch = suffix[i], x2 = 1, n2
        while (true) do
            sequence children = t[n][CHILDREN]
            if x2>length(children) then
                -- no matching child, remainder of suffix becomes new node.
                t = append(t,{suffix[i..$],{}})
                t[n][CHILDREN] = deep_copy(children)&length(t)
                return t
            end if
            n2 = children[x2]
            if t[n2][SUB][1]==ch then exit end if
            x2 += 1
        end while
        -- find prefix of remaining suffix in common with child
        string prefix = t[n2][SUB]
        int j = 0
        while j<length(prefix) do
            if suffix[i+j]!=prefix[j+1] then
                -- split n2: new node for the part in common
                t = append(t,{prefix[1..j],{n2}})
                -- old node loses the part in common
                t[n2][SUB] = prefix[j+1..$]
                -- and child idx moves to newly created node
                n2 = length(t)
                sequence children = deep_copy(t[n][CHILDREN])
                children[x2] = n2
                t[n][CHILDREN] = children
                exit    -- continue down the tree
            end if
            j += 1
        end while
        i += j  -- advance past part in common
        n = n2  -- continue down the tree
    end while
    return t
end function
 
function SuffixTree(string s)
    sequence t = {{"",{}}}
    for i=1 to length(s) do
        t = addSuffix(t,s[i..$])
    end for
    return t
end function
 
procedure visualize(sequence t, integer n=1, string pre="")
    if length(t)=0 then
        printf(1,"<empty>\n");
        return;
    end if
    sequence children = t[n][CHILDREN]
    if length(children)=0 then
        printf(1,"- %s\n", {t[n][SUB]})
        return
    end if
    printf(1,"+ %s\n", {t[n][SUB]})
    integer l = length(children)
    for i=1 to l do
        puts(1,pre&"+-")
        visualize(t,children[i],pre&iff(i=l?"  ":"| "))
    end for
end procedure
 
sequence t = SuffixTree("banana$")
visualize(t)

Output:

+
+-- banana$
+-+ a
| +-+ na
| | +-- na$
| | +-- $
| +-- $
+-+ na
| +-- na$
| +-- $
+-- $

Python

Translation of: D

class Node:
    def __init__(self, sub="", children=None):
        self.sub = sub
        self.ch = children or []

class SuffixTree:
    def __init__(self, str):
        self.nodes = [Node()]
        for i in range(len(str)):
            self.addSuffix(str[i:])

    def addSuffix(self, suf):
        n = 0
        i = 0
        while i < len(suf):
            b = suf[i]
            x2 = 0
            while True:
                children = self.nodes[n].ch
                if x2 == len(children):
                    # no matching child, remainder of suf becomes new node
                    n2 = len(self.nodes)
                    self.nodes.append(Node(suf[i:], []))
                    self.nodes[n].ch.append(n2)
                    return
                n2 = children[x2]
                if self.nodes[n2].sub[0] == b:
                    break
                x2 = x2 + 1

            # find prefix of remaining suffix in common with child
            sub2 = self.nodes[n2].sub
            j = 0
            while j < len(sub2):
                if suf[i + j] != sub2[j]:
                    # split n2
                    n3 = n2
                    # new node for the part in common
                    n2 = len(self.nodes)
                    self.nodes.append(Node(sub2[:j], [n3]))
                    self.nodes[n3].sub = sub2[j:] # old node loses the part in common
                    self.nodes[n].ch[x2] = n2
                    break # continue down the tree
                j = j + 1
            i = i + j   # advance past part in common
            n = n2      # continue down the tree

    def visualize(self):
        if len(self.nodes) == 0:
            print "<empty>"
            return

        def f(n, pre):
            children = self.nodes[n].ch
            if len(children) == 0:
                print "--", self.nodes[n].sub
                return
            print "+-", self.nodes[n].sub
            for c in children[:-1]:
                print pre, "+-",
                f(c, pre + " | ")
            print pre, "+-",
            f(children[-1], pre + "  ")

        f(0, "")

SuffixTree("banana$").visualize()

Output:

+-
 +- -- banana$
 +- +- a
 |  +- +- na
 |  |  +- -- na$
 |  |  +- -- $
 |  +- -- $
 +- +- na
 |  +- -- na$
 |  +- -- $
 +- -- $

Racket

See Suffix trees with Ukkonen’s algorithm by Danny Yoo for more information on how to use suffix trees in Racket.

#lang racket
(require (planet dyoo/suffixtree))
(define tree (make-tree))
(tree-add! tree (string->label "banana$"))

(define (show-node nd dpth)
  (define children (node-children nd))
  (printf "~a~a ~a~%" (match dpth
                        [(regexp #px"(.*) $" (list _ d)) (string-append d "`")]
                        [else else]) (if (null? children) "--" "-+") (label->string (node-up-label nd)))
  (let l ((children children))
    (match children
      ((list) (void))
      ((list c) (show-node c (string-append dpth "  ")))
      ((list c ct ...) (show-node c (string-append dpth " |")) (l ct)))))

(show-node (tree-root tree) "")

Output:

-+ 
 |-- $
 |-+ a
 | |-- $
 | `-+ na
 |   |-- $
 |   `-- na$
 |-+ na
 | |-- $
 | `-- na$
 `-- banana$

Raku

(formerly Perl 6)

Works with: Rakudo version 2018.04

Here is quite a naive algorithm, probably $O(n^{2})$ .

The display code is a variant of the visualize a tree task code.

multi suffix-tree(Str $str) { suffix-tree flat map &flip, [\~] $str.flip.comb }
multi suffix-tree(@a) {
    hash
    @a == 0 ?? () !!
    @a == 1 ?? ( @a[0] => [] ) !!
    gather for @a.classify(*.substr(0, 1)) {
        my $subtree = suffix-tree(grep *.chars, map *.substr(1), .value[]);
        if $subtree == 1 {
            my $pair = $subtree.pick;
            take .key ~ $pair.key => $pair.value;
        } else {
            take .key => $subtree;
        }
    }
}

my $tree = root => suffix-tree 'banana$';

.say for visualize-tree $tree, *.key, *.value.List;

sub visualize-tree($tree, &label, &children,
                   :$indent = '',
                   :@mid = ('├─', '│ '),
                   :@end = ('└─', '  '),
) {
    sub visit($node, *@pre) {
        gather {
            take @pre[0] ~ $node.&label;
            my @children = sort $node.&children;
            my $end = @children.end;
            for @children.kv -> $_, $child {
                when $end { take visit($child, (@pre[1] X~ @end)) }
                default   { take visit($child, (@pre[1] X~ @mid)) }
            }
        }
    }
    flat visit($tree, $indent xx 2);
}

Output:

root
├─$
├─a
│ ├─$
│ └─na
│   ├─$
│   └─na$
├─banana$
└─na
  ├─$
  └─na$

Sidef

Translation of: Raku

func suffix_tree(Str t) {
    suffix_tree(^t.len -> map { t.substr(_) })
}

func suffix_tree(a {.len == 1}) {
    Hash(a[0] => nil) 
}

func suffix_tree(Arr a) {
    var h = Hash()
    for k,v in (a.group_by { .char(0) }) {
        var subtree = suffix_tree(v.map { .substr(1) })
        var subkeys = subtree.keys
        if (subkeys.len == 1) {
            var subk = subkeys[0]
            h{k + subk} = subtree{subk}
        }
        else {
            h{k} = subtree
        }
    }
    return h
}

say suffix_tree('banana$')

Output:

Hash(
    "$" => nil,
    "a" => Hash(
        "$" => nil,
        "na" => Hash(
            "$" => nil,
            "na$" => nil
        )
    ),
    "banana$" => nil,
    "na" => Hash(
        "$" => nil,
        "na$" => nil
    )
)

Wren

Translation of: Kotlin

class Node {
    construct new() {
        _sub = ""  // a substring of the input string
        _ch  = []  // list of child nodes
    }

    sub { _sub }
    ch  { _ch  }

    sub=(s) { _sub = s }
}

class SuffixTree {
    construct new(str) {
        _nodes = [Node.new()]
        for (i in 0...str.count) addSuffix_(str[i..-1])       
    }

    addSuffix_(suf) {
        var n = 0
        var i = 0
        while (i < suf.count) {
            var b  = suf[i]
            var children = _nodes[n].ch
            var x2 = 0
            var n2
            while (true) {
                if (x2 == children.count) {
                    // no matching child, remainder of suf becomes new node.
                    n2 = _nodes.count
                    var nd = Node.new()
                    nd.sub = suf[i..-1]
                    _nodes.add(nd)
                    children.add(n2)
                    return
                }
                n2 = children[x2]
                if (_nodes[n2].sub[0] == b) break
                x2 = x2 + 1
            }
            // find prefix of remaining suffix in common with child
            var sub2 = _nodes[n2].sub
            var j = 0
            while (j < sub2.count) {
                if (suf[i + j] != sub2[j]) {
                    // split n2
                    var n3 = n2
                    // new node for the part in common
                    n2 = _nodes.count
                    var nd = Node.new()
                    nd.sub = sub2[0...j]
                    nd.ch.add(n3)
                    _nodes.add(nd)
                    _nodes[n3].sub = sub2[j..-1]  // old node loses the part in common
                    _nodes[n].ch[x2] = n2
                    break  // continue down the tree
                }
                j = j + 1
            }
            i = i + j  // advance past part in common
            n = n2     // continue down the tree
        }
    }

    visualize() {
        if (_nodes.isEmpty) {
            System.print("<empty>")
            return
        }
 
        var f // recursive closure
        f = Fn.new { |n, pre|
            var children = _nodes[n].ch
            if (children.isEmpty) {
                System.print("╴ %(_nodes[n].sub)")
                return
            }
            System.print("┐ %(_nodes[n].sub)")
            for (c in children[0...-1]) {
                System.write(pre + "├─")
                f.call(c, pre + "│ ")
            }
            System.write(pre + "└─")
            f.call(children[-1], pre + "  ")
        }
 
        f.call(0, "")
    }
}

SuffixTree.new("banana$").visualize()

Output:

┐ 
├─╴ banana$
├─┐ a
│ ├─┐ na
│ │ ├─╴ na$
│ │ └─╴ $
│ └─╴ $
├─┐ na
│ ├─╴ na$
│ └─╴ $
└─╴ $