How to efficiently build a tree from a flat structure?

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);
}

Here is a simple JavaScript algorithm to parse a flat table into a parent/child tree structure that runs in N time:

var table = [
    {parent_id: 0, id: 1, children: []},
    {parent_id: 0, id: 2, children: []},
    {parent_id: 0, id: 3, children: []},
    {parent_id: 1, id: 4, children: []},
    {parent_id: 1, id: 5, children: []},
    {parent_id: 1, id: 6, children: []},
    {parent_id: 2, id: 7, children: []},
    {parent_id: 7, id: 8, children: []},
    {parent_id: 8, id: 9, children: []},
    {parent_id: 3, id: 10, children: []}
];

var root = {id:0, parent_id: null, children: []};
var node_list = { 0 : root};

for (var i = 0; i < table.length; i++) {
    node_list[table[i].id] = table[i];
    node_list[table[i].parent_id].children.push(node_list[table[i].id]);
}

console.log(root);

Based on the answer of Mehrdad Afshari and the comment of Andrew Hanlon for a speedup, here is my take.

Important difference to the original task: A root node has ID==parentID.

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 Source { get; set; }
}

List<Node> BuildTreeAndGetRoots(List<MyObject> actualObjects)
{
    var lookup = new Dictionary<int, Node>();
    var rootNodes = new List<Node>();

    foreach (var item in actualObjects)
    {
        // add us to lookup
        Node ourNode;
        if (lookup.TryGetValue(item.ID, out ourNode))
        {   // was already found as a parent - register the actual object
            ourNode.Source = item;
        }
        else
        {
            ourNode = new Node() { Source = item };
            lookup.Add(item.ID, ourNode);
        }

        // hook into parent
        if (item.ParentID == item.ID)
        {   // is a root node
            rootNodes.Add(ourNode);
        }
        else
        {   // is a child row - so we have a parent
            Node parentNode;
            if (!lookup.TryGetValue(item.ParentID, out parentNode))
            {   // unknown parent, construct preliminary parent
                parentNode = new Node();
                lookup.Add(item.ParentID, parentNode);
            }
            parentNode.Children.Add(ourNode);
            ourNode.Parent = parentNode;
        }
    }

    return rootNodes;
}

Python solution

    def subtree(node, relationships):
        return {
            v: subtree(v, relationships) 
            for v in [x[0] for x in relationships if x[1] == node]
        }

For example:

    # (child, parent) pairs where -1 means no parent    
    flat_tree = [
         (1, -1),
         (4, 1),
         (10, 4),
         (11, 4),
         (16, 11),
         (17, 11),
         (24, 17),
         (25, 17),
         (5, 1),
         (8, 5),
         (9, 5),
         (7, 9),
         (12, 9),
         (22, 12),
         (23, 12),
         (2, 23),
         (26, 23),
         (27, 23),
         (20, 9),
         (21, 9)
        ]
    
    subtree(-1, flat_tree)

Produces:

JS version that returns one root or an array of roots each of which will have a Children array property containing the related children. Does not depend on ordered input, decently compact, and does not use recursion. Enjoy!

// creates a tree from a flat set of hierarchically related data
var MiracleGrow = function(treeData, key, parentKey)
{
    var keys = [];
    treeData.map(function(x){
        x.Children = [];
        keys.push(x[key]);
    });
    var roots = treeData.filter(function(x){return keys.indexOf(x[parentKey])==-1});
    var nodes = [];
    roots.map(function(x){nodes.push(x)});
    while(nodes.length > 0)
    {

        var node = nodes.pop();
        var children =  treeData.filter(function(x){return x[parentKey] == node[key]});
        children.map(function(x){
            node.Children.push(x);
            nodes.push(x)
        });
    }
    if (roots.length==1) return roots[0];
    return roots;
}


// demo/test data
var treeData = [

    {id:9, name:'Led Zep', parent:null},
    {id:10, name:'Jimmy', parent:9},
    {id:11, name:'Robert', parent:9},
    {id:12, name:'John', parent:9},

    {id:8, name:'Elec Gtr Strings', parent:5},
    {id:1, name:'Rush', parent:null},
    {id:2, name:'Alex', parent:1},
    {id:3, name:'Geddy', parent:1},
    {id:4, name:'Neil', parent:1},
    {id:5, name:'Gibson Les Paul', parent:2},
    {id:6, name:'Pearl Kit', parent:4},
    {id:7, name:'Rickenbacker', parent:3},

    {id:100, name:'Santa', parent:99},
    {id:101, name:'Elf', parent:100},

];
var root = MiracleGrow(treeData, "id", "parent")
console.log(root)

How to efficiently build a tree from a flat structure?

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