• Name
• Synopsis
• Description
• Multi-way Tree
  • root($tree)
  • leaf($tree)
  • find($root, $key)
  • leftMost($tree)
  • rightMost($tree)
  • height($tree)
  • depth($tree)
  • delete($root, $key)
  • insert($tree, $key, $data)
  • iterator($tree)
  • Tree::Multi::Iterator::next($iter)
  • reverseIterator($tree)
  • Tree::Multi::ReverseIterator::prev($iter)
  • flat($tree, @title)
  • print($tree, $i)
  • size($tree)
  • Tree::Multi Definition
    • Output fields
      • count
      • data
      • key
      • keys
      • less
      • more
      • node
      • number
      • pos
      • tree
      • up
• Private Methods
  • new()
  • minimumNumberOfKeys()
  • maximumNumberOfKeys()
  • maximumNumberOfNodes()
  • full($tree)
  • halfFull($tree)
  • separate(@k)
  • separateKeys($node)
  • separateData($node)
  • separateNode($node)
  • reUp($tree, @children)
  • splitFullNode($node)
  • findAndSplit($root, $key)
  • indexInParent($tree)
  • fillFromLeftOrRight($node, $dir)
  • mergeWithLeftOrRight($n, $dir)
  • merge($tree)
  • mergeOrFill($tree)
  • deleteLeafKey($tree, $i)
  • deleteKey($tree, $i)
  • T($tree, $expected)
  • disordered($n, $N)
  • disorderedCheck($t, $n, $N)
  • randomCheck($n, $N, $T)
• Index
• Installation
• Author
• Copyright

Name

Tree::Multi - Multi-way tree in Pure Perl with an even or odd number of keys per node.

Synopsis

Construct and query a multi-way tree in 100% Pure Perl with a choice of an odd or an even numbers of keys per node:

  local $Tree::Multi::numberOfKeysPerNode = 4;  # Number of keys per node - can be even

  my $t = Tree::Multi::new;                     # Construct tree
     $t->insert($_, 2 * $_) for reverse 1..32;  # Load tree in reverse

  is_deeply $t->print, <<END;
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END

  ok  $t->height     ==  3;                     # Height

  ok  $t->find  (16) == 32;                     # Find by key
      $t->delete(16);                           # Delete a key
  ok !$t->find  (16);                           # Key no longer present


  ok  $t->find  (17) == 34;                     # Find by key
  my @k;
  for(my $i = $t->iterator; $i->more; $i->next) # Iterator
   {push @k, $i->key unless $i->key == 17;
   }

  $t->delete($_) for @k;                        # Delete

  ok $t->find(17) == 34 && $t->size == 1;       # Size

Description

Multi-way tree in Pure Perl with an even or odd number of keys per node.

Version "20210605".

The following sections describe the methods in each functional area of this module. For an alphabetic listing of all methods by name see Index.

Multi-way Tree

Create and use a multi-way tree.

root($tree)

Return the root node of a tree.

     Parameter  Description
  1  $tree      Tree

Example:

    local $numberOfKeysPerNode = 3; my $N = 13; my $t = new;

    for my $n(1..$N)
     {$t->insert($n, $n);
     }

    is_deeply $t->leftMost ->keys, [1, 2];
    is_deeply $t->rightMost->keys, [13];
    ok $t->leftMost ->leaf;
    ok $t->rightMost->leaf;

    ok $t->root == $t;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    ok T($t, <<END);
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  END

leaf($tree)

Confirm that the tree is a leaf.

     Parameter  Description
  1  $tree      Tree

Example:

    local $numberOfKeysPerNode = 3; my $N = 13; my $t = new;

    for my $n(1..$N)
     {$t->insert($n, $n);
     }

    is_deeply $t->leftMost ->keys, [1, 2];
    is_deeply $t->rightMost->keys, [13];

    ok $t->leftMost ->leaf;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    ok $t->rightMost->leaf;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

    ok $t->root == $t;

    ok T($t, <<END);
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  END

find($root, $key)

Find a key in a tree returning its associated data or undef if the key does not exist.

     Parameter  Description
  1  $root      Root of tree
  2  $key       Key

Example:

    local $Tree::Multi::numberOfKeysPerNode = 4;                                  # Number of keys per node - can be even

    my $t = Tree::Multi::new;                                                     # Construct tree
       $t->insert($_, 2 * $_) for reverse 1..32;                                  # Load tree in reverse

    is_deeply $t->print, <<END;
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  END

    ok  $t->size       == 32;                                                     # Size
    ok  $t->height     ==  3;                                                     # Height
    ok  $t->delete(16) == 2 * 16;                                                 # Delete a key

    ok !$t->find  (16);                                                           # Key no longer present  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    ok  $t->find  (17) == 34;                                                     # Find by key  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    my @k;
    for(my $i = $t->iterator; $i->more; $i->next)                                 # Iterator
     {push @k, $i->key unless $i->key == 17;
     }

    ok $t->delete($_) == 2 * $_ for @k;                                           # Delete


    ok $t->find(17) == 34 && $t->size == 1;                                       # Size  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

leftMost($tree)

Return the left most node below the specified one.

     Parameter  Description
  1  $tree      Tree

Example:

    local $numberOfKeysPerNode = 3; my $N = 13; my $t = new;

    for my $n(1..$N)
     {$t->insert($n, $n);
     }


    is_deeply $t->leftMost ->keys, [1, 2];  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

    is_deeply $t->rightMost->keys, [13];

    ok $t->leftMost ->leaf;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

    ok $t->rightMost->leaf;
    ok $t->root == $t;

    ok T($t, <<END);
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  END

rightMost($tree)

Return the right most node below the specified one.

     Parameter  Description
  1  $tree      Tree

Example:

    local $numberOfKeysPerNode = 3; my $N = 13; my $t = new;

    for my $n(1..$N)
     {$t->insert($n, $n);
     }

    is_deeply $t->leftMost ->keys, [1, 2];

    is_deeply $t->rightMost->keys, [13];  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

    ok $t->leftMost ->leaf;

    ok $t->rightMost->leaf;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

    ok $t->root == $t;

    ok T($t, <<END);
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  END

height($tree)

Return the height of the tree.

     Parameter  Description
  1  $tree      Tree

Example:

    local $Tree::Multi::numberOfKeysPerNode = 3;

    my $t = new;      ok $t->height == 0; ok $t->leftMost->depth == 0; ok $t->size == 0;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(1, 1); ok $t->height == 1; ok $t->leftMost->depth == 1; ok $t->size == 1;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(2, 2); ok $t->height == 1; ok $t->leftMost->depth == 1; ok $t->size == 2;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(3, 3); ok $t->height == 1; ok $t->leftMost->depth == 1; ok $t->size == 3;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(4, 4); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 4;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(5, 5); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 5;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(6, 6); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 6;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(7, 7); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 7;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(8, 8); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 8;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    is_deeply $t->flat, <<END;  owf $logFile, $t->flat if $develop;

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  END

depth($tree)

Return the depth of a node within a tree.

     Parameter  Description
  1  $tree      Tree

Example:

    local $Tree::Multi::numberOfKeysPerNode = 3;

    my $t = new;      ok $t->height == 0; ok $t->leftMost->depth == 0; ok $t->size == 0;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(1, 1); ok $t->height == 1; ok $t->leftMost->depth == 1; ok $t->size == 1;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(2, 2); ok $t->height == 1; ok $t->leftMost->depth == 1; ok $t->size == 2;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(3, 3); ok $t->height == 1; ok $t->leftMost->depth == 1; ok $t->size == 3;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(4, 4); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 4;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(5, 5); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 5;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(6, 6); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 6;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(7, 7); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 7;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(8, 8); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 8;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    is_deeply $t->flat, <<END;  owf $logFile, $t->flat if $develop;

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  END

delete($root, $key)

Find a key in a tree, delete it and return any associated data.

     Parameter  Description
  1  $root      Tree root
  2  $key       Key

Example:

    local $Tree::Multi::numberOfKeysPerNode = 4;                                  # Number of keys per node - can be even

    my $t = Tree::Multi::new;                                                     # Construct tree
       $t->insert($_, 2 * $_) for reverse 1..32;                                  # Load tree in reverse

    is_deeply $t->print, <<END;
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  END

    ok  $t->size       == 32;                                                     # Size
    ok  $t->height     ==  3;                                                     # Height

    ok  $t->delete(16) == 2 * 16;                                                 # Delete a key  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

    ok !$t->find  (16);                                                           # Key no longer present
    ok  $t->find  (17) == 34;                                                     # Find by key

    my @k;
    for(my $i = $t->iterator; $i->more; $i->next)                                 # Iterator
     {push @k, $i->key unless $i->key == 17;
     }


    ok $t->delete($_) == 2 * $_ for @k;                                           # Delete  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    ok $t->find(17) == 34 && $t->size == 1;                                       # Size

insert($tree, $key, $data)

Insert the specified key and data into a tree.

     Parameter  Description
  1  $tree      Tree
  2  $key       Key
  3  $data      Data

Example:

    local $Tree::Multi::numberOfKeysPerNode = 4;                                  # Number of keys per node - can be even

    my $t = Tree::Multi::new;                                                     # Construct tree

       $t->insert($_, 2 * $_) for reverse 1..32;                                  # Load tree in reverse  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    is_deeply $t->print, <<END;
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  END

    ok  $t->size       == 32;                                                     # Size
    ok  $t->height     ==  3;                                                     # Height
    ok  $t->delete(16) == 2 * 16;                                                 # Delete a key
    ok !$t->find  (16);                                                           # Key no longer present
    ok  $t->find  (17) == 34;                                                     # Find by key

    my @k;
    for(my $i = $t->iterator; $i->more; $i->next)                                 # Iterator
     {push @k, $i->key unless $i->key == 17;
     }

    ok $t->delete($_) == 2 * $_ for @k;                                           # Delete

    ok $t->find(17) == 34 && $t->size == 1;                                       # Size

iterator($tree)

Make an iterator for a tree.

     Parameter  Description
  1  $tree      Tree

Example:

    local $numberOfKeysPerNode = 3; my $N = 256; my $e = 0;  my $t = new;

    for my $n(0..$N)
     {$t->insert($n, $n);

      my @n; for(my $i = $t->iterator; $i->more; $i->next) {push @n, $i->key}  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

      ++$e unless dump(\@n) eq dump [0..$n];
     }

    is_deeply $e, 0;

    local $Tree::Multi::numberOfKeysPerNode = 4;                                  # Number of keys per node - can be even

    my $t = Tree::Multi::new;                                                     # Construct tree
       $t->insert($_, 2 * $_) for reverse 1..32;                                  # Load tree in reverse

    is_deeply $t->print, <<END;
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  END

    ok  $t->size       == 32;                                                     # Size
    ok  $t->height     ==  3;                                                     # Height
    ok  $t->delete(16) == 2 * 16;                                                 # Delete a key
    ok !$t->find  (16);                                                           # Key no longer present
    ok  $t->find  (17) == 34;                                                     # Find by key

    my @k;

    for(my $i = $t->iterator; $i->more; $i->next)                                 # Iterator  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

     {push @k, $i->key unless $i->key == 17;
     }

    ok $t->delete($_) == 2 * $_ for @k;                                           # Delete

    ok $t->find(17) == 34 && $t->size == 1;                                       # Size

Tree::Multi::Iterator::next($iter)

Find the next key.

     Parameter  Description
  1  $iter      Iterator

Example:

    local $numberOfKeysPerNode = 3; my $N = 256; my $e = 0;  my $t = new;

    for my $n(0..$N)
     {$t->insert($n, $n);
      my @n; for(my $i = $t->iterator; $i->more; $i->next) {push @n, $i->key}
      ++$e unless dump(\@n) eq dump [0..$n];
     }

    is_deeply $e, 0;

reverseIterator($tree)

Create a reverse iterator for a tree.

     Parameter  Description
  1  $tree      Tree

Example:

    local $numberOfKeysPerNode = 3; my $N = 64;  my $e = 0;

    for my $n(0..$N)
     {my $t = new;
      for my $i(0..$n)
       {$t->insert($i, $i);
       }
      my @n;

      for(my $i = $t->reverseIterator; $i->less; $i->prev)  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

       {push @n, $i->key;
       }
      ++$e unless dump(\@n) eq dump [reverse 0..$n];
     }

    is_deeply $e, 0;

Tree::Multi::ReverseIterator::prev($iter)

Find the previous key.

     Parameter  Description
  1  $iter      Iterator

Example:

    local $numberOfKeysPerNode = 3; my $N = 64;  my $e = 0;

    for my $n(0..$N)
     {my $t = new;
      for my $i(0..$n)
       {$t->insert($i, $i);
       }
      my @n;
      for(my $i = $t->reverseIterator; $i->less; $i->prev)
       {push @n, $i->key;
       }
      ++$e unless dump(\@n) eq dump [reverse 0..$n];
     }

    is_deeply $e, 0;

flat($tree, @title)

Print the keys in a tree from left right to make it easier to visualize the structure of the tree.

     Parameter  Description
  1  $tree      Tree
  2  @title     Title

Example:

    local $Tree::Multi::numberOfKeysPerNode = 3;
    my $t = new;      ok $t->height == 0; ok $t->leftMost->depth == 0; ok $t->size == 0;
    $t->insert(1, 1); ok $t->height == 1; ok $t->leftMost->depth == 1; ok $t->size == 1;
    $t->insert(2, 2); ok $t->height == 1; ok $t->leftMost->depth == 1; ok $t->size == 2;
    $t->insert(3, 3); ok $t->height == 1; ok $t->leftMost->depth == 1; ok $t->size == 3;
    $t->insert(4, 4); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 4;
    $t->insert(5, 5); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 5;
    $t->insert(6, 6); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 6;
    $t->insert(7, 7); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 7;
    $t->insert(8, 8); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 8;


    is_deeply $t->flat, <<END;  owf $logFile, $t->flat if $develop;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


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  END

print($tree, $i)

Print the keys in a tree optionally marking the active key.

     Parameter  Description
  1  $tree      Tree
  2  $i         Optional index of active key

Example:

    local $Tree::Multi::numberOfKeysPerNode = 4;                                  # Number of keys per node - can be even

    my $t = Tree::Multi::new;                                                     # Construct tree
       $t->insert($_, 2 * $_) for reverse 1..32;                                  # Load tree in reverse


    is_deeply $t->print, <<END;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

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     18
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       31 32
  END

    ok  $t->size       == 32;                                                     # Size
    ok  $t->height     ==  3;                                                     # Height
    ok  $t->delete(16) == 2 * 16;                                                 # Delete a key
    ok !$t->find  (16);                                                           # Key no longer present
    ok  $t->find  (17) == 34;                                                     # Find by key

    my @k;
    for(my $i = $t->iterator; $i->more; $i->next)                                 # Iterator
     {push @k, $i->key unless $i->key == 17;
     }

    ok $t->delete($_) == 2 * $_ for @k;                                           # Delete

    ok $t->find(17) == 34 && $t->size == 1;                                       # Size

size($tree)

Count the number of keys in a tree.

     Parameter  Description
  1  $tree      Tree

Example:

    local $Tree::Multi::numberOfKeysPerNode = 3;

    my $t = new;      ok $t->height == 0; ok $t->leftMost->depth == 0; ok $t->size == 0;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(1, 1); ok $t->height == 1; ok $t->leftMost->depth == 1; ok $t->size == 1;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(2, 2); ok $t->height == 1; ok $t->leftMost->depth == 1; ok $t->size == 2;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(3, 3); ok $t->height == 1; ok $t->leftMost->depth == 1; ok $t->size == 3;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(4, 4); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 4;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(5, 5); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 5;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(6, 6); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 6;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(7, 7); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 7;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    $t->insert(8, 8); ok $t->height == 2; ok $t->leftMost->depth == 2; ok $t->size == 8;  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲


    is_deeply $t->flat, <<END;  owf $logFile, $t->flat if $develop;

             3           6
     1   2       4   5       7   8
  END

Tree::Multi Definition

Iterator

Output fields

count

Counter

data

Data at this position

key

Key at this position

keys

Array of key items for this node

less

Iteration not yet finished

more

Iteration not yet finished

node

Current node within tree

number

Number of the node for debugging purposes

pos

Current position within node

tree

Tree we are iterating over

up

Parent node

Private Methods

new()

Create a new multi-way tree node.

Example:

    local $Tree::Multi::numberOfKeysPerNode = 4;                                  # Number of keys per node - can be even


    my $t = Tree::Multi::new;                                                     # Construct tree  # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

       $t->insert($_, 2 * $_) for reverse 1..32;                                  # Load tree in reverse

    is_deeply $t->print, <<END;
   15 21 27
     3 6 9 12
       1 2
       4 5
       7 8
       10 11
       13 14
     18
       16 17
       19 20
     24
       22 23
       25 26
     30
       28 29
       31 32
  END

    ok  $t->size       == 32;                                                     # Size
    ok  $t->height     ==  3;                                                     # Height
    ok  $t->delete(16) == 2 * 16;                                                 # Delete a key
    ok !$t->find  (16);                                                           # Key no longer present
    ok  $t->find  (17) == 34;                                                     # Find by key

    my @k;
    for(my $i = $t->iterator; $i->more; $i->next)                                 # Iterator
     {push @k, $i->key unless $i->key == 17;
     }

    ok $t->delete($_) == 2 * $_ for @k;                                           # Delete

    ok $t->find(17) == 34 && $t->size == 1;                                       # Size

minimumNumberOfKeys()

Minimum number of keys per node.

maximumNumberOfKeys()

Maximum number of keys per node.

maximumNumberOfNodes()

Maximum number of children per parent.

full($tree)

Confirm that a node is full.

     Parameter  Description
  1  $tree      Tree

halfFull($tree)

Confirm that a node is half full.

     Parameter  Description
  1  $tree      Tree

separate(@k)

Return ([lower], center, [upper]) keys from an array.

     Parameter  Description
  1  @k         Array to split

separateKeys($node)

Return ([lower], center, [upper]) keys.

     Parameter  Description
  1  $node      Node to split

separateData($node)

Return ([lower], center, [upper]) data.

     Parameter  Description
  1  $node      Node to split

separateNode($node)

Return ([lower], [upper]) children.

     Parameter  Description
  1  $node      Node to split

reUp($tree, @children)

Reconnect the children to their new parent.

     Parameter  Description
  1  $tree      Tree
  2  @children  Children

splitFullNode($node)

Split a node, that is not a leaf, if it is full.

     Parameter  Description
  1  $node      Node to split

findAndSplit($root, $key)

Find a key in a tree splitting full nodes along the path to the key.

     Parameter  Description
  1  $root      Root of tree
  2  $key       Key

indexInParent($tree)

Get the index of a node in its parent.

     Parameter  Description
  1  $tree      Tree

fillFromLeftOrRight($node, $dir)

Fill a node from the specified sibling.

     Parameter  Description
  1  $node      Node to fill
  2  $dir       Node to fill from 0 for left or 1 for right

mergeWithLeftOrRight($n, $dir)

Merge two adjacent nodes.

     Parameter  Description
  1  $n         Node to merge into
  2  $dir       Node to merge is on right if 1 else left

merge($tree)

Merge the current node with its sibling.

     Parameter  Description
  1  $tree      Tree

mergeOrFill($tree)

Make a node larger than a half node.

     Parameter  Description
  1  $tree      Tree

deleteLeafKey($tree, $i)

Delete a key in a leaf.

     Parameter  Description
  1  $tree      Tree
  2  $i         Index to delete at

deleteKey($tree, $i)

Delete a key.

     Parameter  Description
  1  $tree      Tree
  2  $i         Index to delete at

T($tree, $expected)

Write a result to the log file

     Parameter  Description
  1  $tree      Tree
  2  $expected  Expected print

disordered($n, $N)

Disordered but stable insertions

     Parameter  Description
  1  $n         Keys per node
  2  $N         Nodes

disorderedCheck($t, $n, $N)

Check disordered insertions

     Parameter  Description
  1  $t         Tree to check
  2  $n         Keys per node
  3  $N         Nodes

randomCheck($n, $N, $T)

Random insertions

     Parameter  Description
  1  $n         Keys per node
  2  $N         Log 10 nodes
  3  $T         Log 10 number of tests

Index

1 delete - Find a key in a tree, delete it and return any associated data.

2 deleteKey - Delete a key.

3 deleteLeafKey - Delete a key in a leaf.

4 depth - Return the depth of a node within a tree.

5 disordered - Disordered but stable insertions

6 disorderedCheck - Check disordered insertions

7 fillFromLeftOrRight - Fill a node from the specified sibling.

8 find - Find a key in a tree returning its associated data or undef if the key does not exist.

9 findAndSplit - Find a key in a tree splitting full nodes along the path to the key.

10 flat - Print the keys in a tree from left right to make it easier to visualize the structure of the tree.

11 full - Confirm that a node is full.

12 halfFull - Confirm that a node is half full.

13 height - Return the height of the tree.

14 indexInParent - Get the index of a node in its parent.

15 insert - Insert the specified key and data into a tree.

16 iterator - Make an iterator for a tree.

17 leaf - Confirm that the tree is a leaf.

18 leftMost - Return the left most node below the specified one.

19 maximumNumberOfKeys - Maximum number of keys per node.

20 maximumNumberOfNodes - Maximum number of children per parent.

21 merge - Merge the current node with its sibling.

22 mergeOrFill - Make a node larger than a half node.

23 mergeWithLeftOrRight - Merge two adjacent nodes.

24 minimumNumberOfKeys - Minimum number of keys per node.

25 new - Create a new multi-way tree node.

26 print - Print the keys in a tree optionally marking the active key.

27 randomCheck - Random insertions

28 reUp - Reconnect the children to their new parent.

29 reverseIterator - Create a reverse iterator for a tree.

30 rightMost - Return the right most node below the specified one.

31 root - Return the root node of a tree.

32 separate - Return ([lower], center, [upper]) keys from an array.

33 separateData - Return ([lower], center, [upper]) data.

34 separateKeys - Return ([lower], center, [upper]) keys.

35 separateNode - Return ([lower], [upper]) children.

36 size - Count the number of keys in a tree.

37 splitFullNode - Split a node, that is not a leaf, if it is full.

38 T - Write a result to the log file

39 Tree::Multi::Iterator::next - Find the next key.

40 Tree::Multi::ReverseIterator::prev - Find the previous key.

Installation

This module is written in 100% Pure Perl and, thus, it is easy to read, comprehend, use, modify and install via cpan:

  sudo cpan install Tree::Multi

Author

philiprbrenan@gmail.com

http://www.appaapps.com

Copyright

Copyright (c) 2016-2021 Philip R Brenan.

This module is free software. It may be used, redistributed and/or modified under the same terms as Perl itself.