Struct outils::tree::bst::aaforest::AaForest

pub struct AaForest<V> where
    V: ValueType,  { /* fields omitted */ }

AaForest<V> is a data structure for holding balanced binary trees. Its tree nodes are held in a memory arena and are addressed through their associated NodeIndex.

AaForest is parameterized over:

• Associated values of type V, where V must implement the trait ValueType

The balancing method for maintaining a tree height of log(n) where n is the number nodes in the tree is described here: AA tree.

Forest trees can be joined and split as required by the provided operations, which will also take care of the re-balancing of the trees. The in-order of the forest trees implies an ordered sequence of values - this order does not depend on the order traits of the type V (i.e. std::cmp::Ord) but solely on the in-order of the nodes which is under the control of the user (see the documentation of split and append).

use outils::prelude::*;
use outils::tree::traversal::BinaryInOrderValues;
let mut aaforest = AaForest::new(10);

// Insert values into the forest - each value will be a single-node tree in the forest.
let n1 = aaforest.insert(1);
let n2 = aaforest.insert(2);
let n3 = aaforest.insert(3);

// Link the single-node trees, constructing the in-order sequence 1,2,3.
aaforest.append(n1, n2);
aaforest.append(n2, n3);

let seq: Vec<&usize> = BinaryInOrderValues::new(&aaforest, n1).collect();
assert_eq!(seq, vec![&1, &2, &3]);

Implementations

impl<V> AaForest<V> where
    V: ValueType, 

pub fn new(size: usize) -> Self

Construct a new empty AaForest with an initial capacity of size.

Trait Implementations

impl<V> BalancedBinaryForest<V, usize> for AaForest<V> where
    V: ValueType, 

fn insert(&mut self, value: V) -> NodeIndex

Inserts value into the forest as a new singleton (i.e. sole leaf) node.

fn remove(&mut self, node: NodeIndex) -> Option<V>

Removes the tree node indexed by node from the tree if present, in this case returning the associated value.

use outils::prelude::*;                             // The resulting tree is shown below:
use outils::tree::traversal::BinaryInOrderValues;   //
                                                    //       -- (3) --
let mut aaforest = AaForest::new(10);               //      /         \
                                                    //    (1)         (5)
let mut indices = Vec::new();                       //   /   \       /   \
indices.push(aaforest.insert(0));                   // (0)   (2)    (4)   (6)

for i in 1..7 {
    indices.push(aaforest.insert(i));
    aaforest.append(indices[i-1], indices[i]);
}

assert_eq!(aaforest.remove(indices[5]), Some(5));
let seq: Vec<&usize> = BinaryInOrderValues::new(&aaforest, indices[0]).collect();
assert_eq!(seq, vec![&0, &1, &2, &3, &4, &6]);

fn split(
    &mut self,
    node: NodeIndex,
    dir: BstDirection
) -> (Option<NodeIndex>, Option<NodeIndex>)

Splits the sequence of tree nodes represented by the forest tree containing the tree node indexed by node.

If dir == BstDirection::Left, node will index the last tree node of the left sequence, while if dir == BstDirection::Right, node will index the first tree node of the right sequence (both with respect to in-order). The roots of the resulting sequences will be returned as a tuple.

use outils::prelude::*;                             // The resulting trees are shown below:
use outils::tree::traversal::BinaryInOrderValues;   //
                                                    //       -- (3) --
let mut aaforest1 = AaForest::new(10);              //      /         \
let mut aaforest2 = AaForest::new(10);              //    (1)         (5)
                                                    //   /   \       /   \
let mut indices1 = Vec::new();                      // (0)   (2)    (4)   (6)
indices1.push(aaforest1.insert(0));
let mut indices2 = Vec::new();
indices2.push(aaforest2.insert(0));

for i in 1..7 {
    indices1.push(aaforest1.insert(i));
    aaforest1.append(indices1[i-1], indices1[i]);
    indices2.push(aaforest2.insert(i));
    aaforest2.append(indices2[i-1], indices2[i]);
}

// Split the tree at 3 and keep 3 as part of the left (i.e. _smaller_) tree.
let result1 = aaforest1.split(indices1[3], BstDirection::Left);
match(result1) {
    (Some(left), Some(right)) => {
        let seq_left: Vec<&usize> = BinaryInOrderValues::new(&aaforest1, left).collect();
        assert_eq!(seq_left, vec![&0, &1, &2, &3]);
        let seq_right: Vec<&usize> = BinaryInOrderValues::new(&aaforest1, right).collect();
        assert_eq!(seq_right, vec![&4, &5, &6]);
    }
    _ => {
        panic!("3 was neither first nor last, so the returned tuple should be (Some, Some)")
    }
}

// Split the tree at 3 and keep 3 as part of the right (i.e. _bigger_) tree.
let result2 = aaforest2.split(indices2[3], BstDirection::Right);
match(result2) {
    (Some(left), Some(right)) => {
        let seq_left: Vec<&usize> = BinaryInOrderValues::new(&aaforest2, left).collect();
        assert_eq!(seq_left, vec![&0, &1, &2]);
        let seq_right: Vec<&usize> = BinaryInOrderValues::new(&aaforest2, right).collect();
        assert_eq!(seq_right, vec![&3, &4, &5, &6]);
    }
    _ => {
        panic!("3 was neither first nor last, so the returned tuple should be (Some, Some)");
    }
}

fn split_all(
    &mut self,
    node: NodeIndex,
    size_hint: Option<usize>
) -> Vec<NodeIndex>

Splits the whole sequence of tree nodes represented by the forest tree containing the tree node indexed by node into singleton (i.e. sole leaf) nodes.

If the tree nodes to be split is known beforehand, it can be specified optionally as the size_hint of the returned Vec containing the split tree nodes.

Generally, this operation will be much faster than calling split on each node of the sequence separately, the reason being that no re-balancing is necessary when it is known beforehand that every tree node will be split.

use outils::prelude::*;                // The resulting tree is shown below:
                                       //
let mut aaforest = AaForest::new(10);  //       -- (3) --
                                       //      /         \
let mut indices = Vec::new();          //    (1)         (5)
indices.push(aaforest.insert(0));      //   /   \       /   \
                                       // (0)   (2)    (4)   (6)
for i in 1..7 {
    indices.push(aaforest.insert(i));
    aaforest.append(indices[i-1], indices[i]);
}

let split_nodes = aaforest.split_all(indices[0], Some(7));
assert_eq!(split_nodes.len(), indices.len());

// After splitting the forest tree, every one of its former nodes should be a singleton:
for i in 0..7 {
    assert!(split_nodes.contains(&indices[i]));
    assert_eq!(aaforest.parent(indices[i]), None);
    assert_eq!(aaforest.child(indices[i], 0), None);
    assert_eq!(aaforest.child(indices[i], 1), None);
}

fn append(&mut self, node_u: NodeIndex, node_v: NodeIndex) -> Option<NodeIndex>

Concatenate the sequences of tree nodes represented by the forest trees containing the tree nodes indexed by node_u and node_v, respectively.

With respect to in-order, the former sequence will represent the smaller part of the new sequence, the latter sequence the bigger part. The root of the resulting sequence will be returned.

use outils::prelude::*;
use outils::tree::traversal::BinaryInOrderValues;
let mut aaforest = AaForest::new(10);

// Insert values into the forest - each value will be a single-node tree in the forest.
let mut indices = Vec::new();
for i in 0..7 {
    indices.push(aaforest.insert(i));
}

// Construct the _smaller_ tree, containing the in-order sequence 0,1,2,3
let mut left = indices[0];
left = aaforest.append(left, indices[1]).expect("Result should not be None");
left = aaforest.append(left, indices[2]).expect("Result should not be None");
left = aaforest.append(left, indices[3]).expect("Result should not be None");

{ // Restrict scope of the borrow of `aaforest`.
    let seq: Vec<&usize> = BinaryInOrderValues::new(&aaforest, left).collect();
    assert_eq!(seq, vec![&0, &1, &2, &3]);
}

// Construct the _bigger_ tree, containing the in-order sequence 4,5,6
let mut right = indices[4];
right = aaforest.append(right, indices[5]).expect("Result should not be None");
right = aaforest.append(right, indices[6]).expect("Result should not be None");

{ // Restrict scope of the borrow of `aaforest`.
    let seq: Vec<&usize> = BinaryInOrderValues::new(&aaforest, right).collect();
    assert_eq!(seq, vec![&4, &5, &6]);
}

// Link left and right, constructing the in-order sequence 0,1,2,3,4,5,6.
let root = aaforest.append(left, right).expect("Result should not be None");
let seq: Vec<&usize> = BinaryInOrderValues::new(&aaforest, root).collect();
assert_eq!(seq, vec![&0, &1, &2, &3, &4, &5, &6]);

impl<V: Clone> Clone for AaForest<V> where
    V: ValueType, 

fn clone(&self) -> AaForest<V>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<V: Debug> Debug for AaForest<V> where
    V: ValueType, 

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<V> Index<NodeIndex<usize>> for AaForest<V> where
    V: ValueType, 

type Output = V

The returned type after indexing.

fn index(&self, index: NodeIndex) -> &V

Performs the indexing (container[index]) operation.

impl<V> IndexMut<NodeIndex<usize>> for AaForest<V> where
    V: ValueType, 

fn index_mut(&mut self, index: NodeIndex) -> &mut V

Performs the mutable indexing (container[index]) operation.

impl<V> OrderedTree<usize> for AaForest<V> where
    V: ValueType, 

fn sub_predecessor(&self, node: NodeIndex) -> Option<NodeIndex>

Returns the biggest node of the left subtree of the tree node indexed by node.

use outils::prelude::*;                // The resulting tree is shown below:
                                       //
let mut aaforest = AaForest::new(10);  //       -- (3) --
                                       //      /         \
let mut indices = Vec::new();          //    (1)         (5)
indices.push(aaforest.insert(0));      //   /   \       /   \
                                       // (0)   (2)    (4)   (6)
for i in 1..7 {
    indices.push(aaforest.insert(i));
    aaforest.append(indices[i-1], indices[i]);
}

// 2 is biggest key in left subtree of 3.
assert_eq!(aaforest.sub_predecessor(indices[3]), Some(indices[2]));
// 4 is a leaf and thus has no subtrees.
assert_eq!(aaforest.sub_predecessor(indices[4]), None);

fn sub_successor(&self, node: NodeIndex) -> Option<NodeIndex>

Returns the smallest node of the right subtree of the tree node indexed by node.

Usage is analogous to sub_predecessor

fn predecessor(&self, node: NodeIndex) -> Option<NodeIndex>

Returns the biggest node of the whole tree which is smaller than the tree node indexed by node.

use outils::prelude::*;                // The resulting tree is shown below:
                                       //
let mut aaforest = AaForest::new(10);  //       -- (3) --
                                       //      /         \
let mut indices = Vec::new();          //    (1)         (5)
indices.push(aaforest.insert(0));      //   /   \       /   \
                                       // (0)   (2)    (4)   (6)
for i in 1..7 {
    indices.push(aaforest.insert(i));
    aaforest.append(indices[i-1], indices[i]);
}

// 3 is the biggest key of the whole tree smaller than 4.
assert_eq!(aaforest.predecessor(indices[4]), Some(indices[3]));
// 0 is globally the smallest key of the whole tree and thus has no predecessor.
assert_eq!(aaforest.predecessor(indices[0]), None);

fn successor(&self, node: NodeIndex) -> Option<NodeIndex>

Returns the smallest node of the whole tree which is bigger than the tree node indexed by node.

Usage is analogous to predecessor

fn first(&self, node: NodeIndex) -> Option<NodeIndex>

Returns the smallest node of the left subtree of the tree node indexed by node.

use outils::prelude::*;                // The resulting tree is shown below:
                                       //
let mut aaforest = AaForest::new(10);  //       -- (3) --
                                       //      /         \
let mut indices = Vec::new();          //    (1)         (5)
indices.push(aaforest.insert(0));      //   /   \       /   \
                                       // (0)   (2)    (4)   (6)
for i in 1..7 {
    indices.push(aaforest.insert(i));
    aaforest.append(indices[i-1], indices[i]);
}

// 0 is the smallest key of the left subtree of 3
assert_eq!(aaforest.first(indices[3]), Some(indices[0]));
// 0 is the smallest key of the left subtree of 1
assert_eq!(aaforest.first(indices[1]), Some(indices[0]));

fn last(&self, node: NodeIndex) -> Option<NodeIndex>

Returns the biggest node of the right subtree of the tree node indexed by node.

Usage is analogous to first

fn is_smaller(&self, node_u: NodeIndex, node_v: NodeIndex) -> bool

Returns true if the tree node indexed by node_u is smaller than the tree node indexed by node_v. Otherwise, and in particular if one of the specified indices is invalid, or if the nodes do not belong to the same forest tree, false is returned.

Panics if the path to the root from either of the tree nodes to be compared contains more than 64 nodes. This is because the directions (i.e. left or right) on the path are encoded in a bitmap of type u64. In practice it is next to impossible for this method to panic because the number of tree nodes needs to be close to 2^64 for the above condition to occur.

use outils::prelude::*;                // The resulting tree is shown below:
                                       //
let mut aaforest = AaForest::new(10);  //       -- (3) --
                                       //      /         \
let mut indices = Vec::new();          //    (1)         (5)
indices.push(aaforest.insert(0));      //   /   \       /   \
                                       // (0)   (2)    (4)   (6)
for i in 1..7 {
    indices.push(aaforest.insert(i));
    aaforest.append(indices[i-1], indices[i]);
}

assert!(aaforest.is_smaller(indices[0], indices[3]));
assert!(!aaforest.is_smaller(indices[3], indices[1]));

impl<V> Tgf for AaForest<V> where
    V: ValueType, 

fn to_tgf(&self) -> String

Returns a TGF representation of Self.

impl<V> Traversable<V, usize> for AaForest<V> where
    V: ValueType, 

fn root(&self, node: NodeIndex) -> Option<NodeIndex>

Returns the index of the root node of the tree containing the tree node indexed by node. In case of an invalid index, None is returned.

fn value(&self, node: NodeIndex) -> Option<&V>

Immutably access the value stored in the tree node indexed by node.

fn value_mut(&mut self, node: NodeIndex) -> Option<&mut V>

Mutably access the value stored in the tree node indexed by node.

fn parent(&self, node: NodeIndex) -> Option<NodeIndex>

Returns the index of parent node tree node indexed by node.

fn child(&self, node: NodeIndex, pos: usize) -> Option<NodeIndex>

Returns the index of the child node at position pos of the tree node indexed by node.

Note that a binary tree node will always have two children, i.e. that even if the left child (pos == 0) is empty, the right child (pos == 1) might contain a value. In case of a leaf node, both children will be empty:

use outils::prelude::*;

let mut aaforest = AaForest::new(10);
let n1 = aaforest.insert(1);
let n2 = aaforest.insert(2);
aaforest.append(n1, n2);

// At this point, the AA algorithm has not had to rotate the tree, so that
// `n2` will be the right child of `n1`:

assert_eq!(aaforest.child(n1, 0), None);
assert_eq!(aaforest.child(n1, 1), Some(n2));

fn child_count(&self, node: NodeIndex) -> usize

Returns the number of child nodes of the tree node indexed by node.

Note that a binary tree node will always have two children, i.e. that even if the left child is empty, the right child might contain a value. In case of a leaf node, both children will be empty, but the number of (empty) children will still be 2:

use outils::prelude::*;

let mut aaforest = AaForest::new(10);
let n1 = aaforest.insert(1);
let n2 = aaforest.insert(2);
aaforest.append(n1, n2);

// At this point, the AA algorithm has not had to rotate the tree, so that
// `n2` will be the right child of `n1`:

assert_eq!(aaforest.child_count(n1), 2);
assert_eq!(aaforest.child_count(n2), 2);
assert_eq!(aaforest.child_count(NodeIndex(999)), 0); // Invalid index => no children

fn node_count(&self) -> usize

Returns the total number of tree nodes of the forest trees in self.

impl<'slf, V> Values<'slf, V, usize> for AaForest<V> where
    V: 'slf + ValueType, 

fn values(&'slf self) -> Box<dyn Iterator<Item = (NodeIndex, &'slf V)> + 'slf>

Returns a boxed iterator over the stored values and their corresponding tree node indices held by self. The values are not returned in any particular order.