# algorithm - whatwg - what is the html living standard

## Graph serialization (3)

I'm looking for a simple algorithm to 'serialize' a directed graph. In particular I've got a set of files with interdependencies on their execution order, and I want to find the correct order at compile time. I know it must be a fairly common thing to do - compilers do it all the time - but my google-fu has been weak today. What's the 'go-to' algorithm for this?

Topological Sort (From Wikipedia):

In graph theory, a topological sort or topological ordering of a directed acyclic graph (DAG) is a linear ordering of its nodes in which each node comes before all nodes to which it has outbound edges. Every DAG has one or more topological sorts.

Pseudo code:

```
L ← Empty list where we put the sorted elements
Q ← Set of all nodes with no incoming edges
while Q is non-empty do
remove a node n from Q
insert n into L
for each node m with an edge e from n to m do
remove edge e from the graph
if m has no other incoming edges then
insert m into Q
if graph has edges then
output error message (graph has a cycle)
else
output message (proposed topologically sorted order: L)
```

I would expect tools that need this simply walk the tree in a depth-first manner and when they hit a leaf, just process it (e.g. compile) and remove it from the graph (or mark it as processed, and treat nodes with all leaves processed as leaves).

As long as it's a DAG, this simple stack-based walk should be trivial.

If the graph contains cycles, how can there exist allowed execution orders for your files? It seems to me that if the graph contains cycles, then you have no solution, and this is reported correctly by the above algorithm.