How to efficiently build a tree from a flat structure

algorithmhierarchical-datalanguage-agnostictree

I have a bunch of objects in a flat structure. These objects have an ID and a ParentID property so they can be arranged in trees. They are in no particular order.
Each ParentID property does not necessarily matches with an ID in the structure. Therefore their could be several trees emerging from these objects.

How would you process these objects to create the resulting trees ?

I'm not so far from a solution but I'm sure it is far from optimal…

I need to create these trees to then insert Data into a database, in proper order.

There are no circular references. A Node is a RootNode when ParentID == null or when ParentID can't be found in the other objects

Best Answer

Store IDs of the objects in a hash table mapping to the specific object. Enumerate through all the objects and find their parent if it exists and update its parent pointer accordingly.

class MyObject
{ // The actual object
    public int ParentID { get; set; }
    public int ID { get; set; }
}

class Node
{
    public List<Node> Children = new List<Node>();
    public Node Parent { get; set; }
    public MyObject AssociatedObject { get; set; }
}

IEnumerable<Node> BuildTreeAndGetRoots(List<MyObject> actualObjects)
{
    Dictionary<int, Node> lookup = new Dictionary<int, Node>();
    actualObjects.ForEach(x => lookup.Add(x.ID, new Node { AssociatedObject = x }));
    foreach (var item in lookup.Values) {
        Node proposedParent;
        if (lookup.TryGetValue(item.AssociatedObject.ParentID, out proposedParent)) {
            item.Parent = proposedParent;
            proposedParent.Children.Add(item);
        }
    }
    return lookup.Values.Where(x => x.Parent == null);
}

Related Solutions

Sql – the most efficient/elegant way to parse a flat table into a tree

Now that MySQL 8.0 supports recursive queries, we can say that all popular SQL databases support recursive queries in standard syntax.

WITH RECURSIVE MyTree AS (
    SELECT * FROM MyTable WHERE ParentId IS NULL
    UNION ALL
    SELECT m.* FROM MyTABLE AS m JOIN MyTree AS t ON m.ParentId = t.Id
)
SELECT * FROM MyTree;

I tested recursive queries in MySQL 8.0 in my presentation Recursive Query Throwdown in 2017.

Below is my original answer from 2008:

There are several ways to store tree-structured data in a relational database. What you show in your example uses two methods:

Adjacency List (the "parent" column) and
Path Enumeration (the dotted-numbers in your name column).

Another solution is called Nested Sets, and it can be stored in the same table too. Read "Trees and Hierarchies in SQL for Smarties" by Joe Celko for a lot more information on these designs.

I usually prefer a design called Closure Table (aka "Adjacency Relation") for storing tree-structured data. It requires another table, but then querying trees is pretty easy.

I cover Closure Table in my presentation Models for Hierarchical Data with SQL and PHP and in my book SQL Antipatterns: Avoiding the Pitfalls of Database Programming.

CREATE TABLE ClosureTable (
  ancestor_id   INT NOT NULL REFERENCES FlatTable(id),
  descendant_id INT NOT NULL REFERENCES FlatTable(id),
  PRIMARY KEY (ancestor_id, descendant_id)
);

Store all paths in the Closure Table, where there is a direct ancestry from one node to another. Include a row for each node to reference itself. For example, using the data set you showed in your question:

INSERT INTO ClosureTable (ancestor_id, descendant_id) VALUES
  (1,1), (1,2), (1,4), (1,6),
  (2,2), (2,4),
  (3,3), (3,5),
  (4,4),
  (5,5),
  (6,6);

Now you can get a tree starting at node 1 like this:

SELECT f.* 
FROM FlatTable f 
  JOIN ClosureTable a ON (f.id = a.descendant_id)
WHERE a.ancestor_id = 1;

The output (in MySQL client) looks like the following:

+----+
| id |
+----+
|  1 | 
|  2 | 
|  4 | 
|  6 | 
+----+

In other words, nodes 3 and 5 are excluded, because they're part of a separate hierarchy, not descending from node 1.

Re: comment from e-satis about immediate children (or immediate parent). You can add a "path_length" column to the ClosureTable to make it easier to query specifically for an immediate child or parent (or any other distance).

INSERT INTO ClosureTable (ancestor_id, descendant_id, path_length) VALUES
  (1,1,0), (1,2,1), (1,4,2), (1,6,1),
  (2,2,0), (2,4,1),
  (3,3,0), (3,5,1),
  (4,4,0),
  (5,5,0),
  (6,6,0);

Then you can add a term in your search for querying the immediate children of a given node. These are descendants whose path_length is 1.

SELECT f.* 
FROM FlatTable f 
  JOIN ClosureTable a ON (f.id = a.descendant_id)
WHERE a.ancestor_id = 1
  AND path_length = 1;

+----+
| id |
+----+
|  2 | 
|  6 | 
+----+

Re comment from @ashraf: "How about sorting the whole tree [by name]?"

Here's an example query to return all nodes that are descendants of node 1, join them to the FlatTable that contains other node attributes such as name, and sort by the name.

SELECT f.name
FROM FlatTable f 
JOIN ClosureTable a ON (f.id = a.descendant_id)
WHERE a.ancestor_id = 1
ORDER BY f.name;

Re comment from @Nate:

SELECT f.name, GROUP_CONCAT(b.ancestor_id order by b.path_length desc) AS breadcrumbs
FROM FlatTable f 
JOIN ClosureTable a ON (f.id = a.descendant_id) 
JOIN ClosureTable b ON (b.descendant_id = a.descendant_id) 
WHERE a.ancestor_id = 1 
GROUP BY a.descendant_id 
ORDER BY f.name

+------------+-------------+
| name       | breadcrumbs |
+------------+-------------+
| Node 1     | 1           |
| Node 1.1   | 1,2         |
| Node 1.1.1 | 1,2,4       |
| Node 1.2   | 1,6         |
+------------+-------------+

A user suggested an edit today. SO moderators approved the edit, but I am reversing it.

The edit suggested that the ORDER BY in the last query above should be ORDER BY b.path_length, f.name, presumably to make sure the ordering matches the hierarchy. But this doesn't work, because it would order "Node 1.1.1" after "Node 1.2".

If you want the ordering to match the hierarchy in a sensible way, that is possible, but not simply by ordering by the path length. For example, see my answer to MySQL Closure Table hierarchical database - How to pull information out in the correct order.

R – What’s a good data structure for building equivalence classes on nodes of a tree

You seem to have two forms of equivalence to deal with. Plain equivalence (A), tracked as equivalence classes which are kept up to date and structural equivalence (D), for which you occasionally go build a single equivalence class and then throw it away.

It sounds to me like the problem would be conceptually simpler if you maintain equivalence classes for both plain and structural equivalence. If that introduces too much churn for the structural equivalence, you could maintain equivalence classes for some aspects of structural equivalence. Then you could find a balance where you can afford the maintenance of those equivalence classes but still greatly reduce the number of nodes to examine when building a list of structurally equivalent nodes.

Best Answer

Related Solutions

Sql – the most efficient/elegant way to parse a flat table into a tree

R – What’s a good data structure for building equivalence classes on nodes of a tree

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