Topological sort/Extracted top item

Topological sort/Extracted top item is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Sorting Algorithm
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Given a mapping between items, and items they depend on, a topological sort orders items so that no item precedes an item it depends upon.

The compiling of a design in the VHDL language has the constraint that a file must be compiled after any file containing definitions it depends on. A tool exists that extracts file dependencies.

• Assume the file names are single words, given without their file extensions.
• Files mentioned as only dependants, have no dependants of their own, but their order of compiling must be given.
• Any self dependencies should be ignored.

A top level file is defined as a file that:

1. Has dependents.
2. Is not itself the dependent of another file

Task Description

Given the following file dependencies as an example:

FILE    FILE DEPENDENCIES
====    =================
top1    des1 ip1 ip2
top2    des1 ip2 ip3
ip1     extra1 ip1a ipcommon
ip2     ip2a ip2b ip2c ipcommon
des1    des1a des1b des1c
des1a   des1a1 des1a2
des1c   des1c1 extra1

The task is to create a program that given a graph of the dependency:

1. Determines the top levels from the dependencies and show them.
2. Extracts a compile order of files to compile any given (usually top level) file.
3. Give a compile order for file top1.
4. Give a compile order for file top2.

You may show how to compile multiple top levels as a stretch goal

Note: this task differs from task Topological sort in that the order for compiling any file might not include all files; and that checks for dependency cycles are not mandated.

Related task

• Topological sort

11l

Translation of: Python

F _topx(data, tops, &_sofar) -> [[String]]
   ‘Recursive topological extractor’
   _sofar [+]= copy(tops)
   V depends = Set[String]()
   L(top) tops
      I top C data
         depends.update(data[top])
   I !depends.empty
      _topx(data, depends, &_sofar)
   [[String]] ordered
   V accum = Set[String]()
   L(i) (_sofar.len-1 .. 0).step(-1)
      ordered [+]= sorted(Array(_sofar[i] - accum))
      accum.update(_sofar[i])
   R ordered

F toplevels(&data)
   ‘
    Extract all top levels from dependency data
    Top levels are never dependents
   ’
   L(k, v) data
      v.discard(k)
   Set[String] dependents
   L(k, v) data
      dependents.update(v)
   R Set(data.keys()) - dependents

F topx(&data, tops)
   ‘Extract the set of top-level(s) in topological order’
   L(k, v) data
      v.discard(k)
   [Set[String]] _sofar
   R _topx(data, tops, &_sofar)

F printorder(order)
   ‘Prettyprint topological ordering’
   I !order.empty
      print(‘First: ’order[0].map(s -> String(s)).join(‘, ’))
   L(o) order[1..]
      print(‘ Then: ’o.map(s -> String(s)).join(‘, ’))

V data = [
   ‘top1’  = Set([‘ip1’, ‘des1’, ‘ip2’]),
   ‘top2’  = Set([‘ip2’, ‘des1’, ‘ip3’]),
   ‘des1’  = Set([‘des1a’, ‘des1b’, ‘des1c’]),
   ‘des1a’ = Set([‘des1a1’, ‘des1a2’]),
   ‘des1c’ = Set([‘des1c1’, ‘extra1’]),
   ‘ip2’   = Set([‘ip2a’, ‘ip2b’, ‘ip2c’, ‘ipcommon’]),
   ‘ip1’   = Set([‘ip1a’, ‘ipcommon’, ‘extra1’])
   ]

V tops = toplevels(&data)
print(‘The top levels of the dependency graph are: ’Array(tops).join(‘ ’))

L(t) sorted(Array(tops))
   print("\nThe compile order for top level: #. is...".format(t))
   printorder(topx(&data, Set([t])))
I tops.len > 1
   print("\nThe compile order for top levels: #. is...".format(sorted(Array(tops)).map(s -> String(s)).join(‘ and ’)))
   printorder(topx(&data, tops))

Output:

The top levels of the dependency graph are: top1 top2

The compile order for top level: top1 is...
First: des1a1, des1a2, des1c1, extra1
 Then: des1a, des1b, des1c, ip1a, ip2a, ip2b, ip2c, ipcommon
 Then: des1, ip1, ip2
 Then: top1

The compile order for top level: top2 is...
First: des1a1, des1a2, des1c1, extra1
 Then: des1a, des1b, des1c, ip2a, ip2b, ip2c, ipcommon
 Then: des1, ip2, ip3
 Then: top2

The compile order for top levels: top1 and top2 is...
First: des1a1, des1a2, des1c1, extra1
 Then: des1a, des1b, des1c, ip1a, ip2a, ip2b, ip2c, ipcommon
 Then: des1, ip1, ip2, ip3
 Then: top1, top2

C

Take code from Topological sort#c and add/change the following:

char input[] =	"top1    des1 ip1 ip2\n"
		"top2    des1 ip2 ip3\n"
		"ip1     extra1 ip1a ipcommon\n"
		"ip2     ip2a ip2b ip2c ipcommon\n"
		"des1    des1a des1b des1c\n"
		"des1a   des1a1 des1a2\n"
		"des1c   des1c1 extra1\n";

...
int find_name(item base, int len, const char *name)
{
	int i;
	for (i = 0; i < len; i++)
		if (!strcmp(base[i].name, name)) return i;
	return -1;
}

int depends_on(item base, int n1, int n2)
{
	int i;
	if (n1 == n2) return 1;
	for (i = 0; i < base[n1].n_deps; i++)
		if (depends_on(base, base[n1].deps[i], n2)) return 1;
	return 0;
}

void compile_order(item base, int n_items, int *top, int n_top)
{
	int i, j, lvl;
	int d = 0;
	printf("Compile order for:");
	for (i = 0; i < n_top; i++) {
		printf(" %s", base[top[i]].name);
		if (base[top[i]].depth > d)
			d = base[top[i]].depth;
	}
	printf("\n");

	for (lvl = 1; lvl <= d; lvl ++) {
		printf("level %d:", lvl);
		for (i = 0; i < n_items; i++) {
			if (base[i].depth != lvl) continue;
			for (j = 0; j < n_top; j++) {
				if (depends_on(base, top[j], i)) {
					printf(" %s", base[i].name);
					break;
				}
			}
		}
		printf("\n");
	}
	printf("\n");
}

int main()
{
	int i, n, bad = -1;
	item items;
	n = parse_input(&items);
 
	for (i = 0; i < n; i++)
		if (!items[i].depth && get_depth(items, i, bad) < 0) bad--;
 
	int top[3];
	top[0] = find_name(items, n, "top1");
	top[1] = find_name(items, n, "top2");
	top[2] = find_name(items, n, "ip1");

	compile_order(items, n, top, 1);
	compile_order(items, n, top + 1, 1);
	compile_order(items, n, top, 2);
	compile_order(items, n, top + 2, 1);

	return 0;
}

output (the last item is just to show that it doesn't have to be top level)

Compile order for: top1
level 1: extra1 ip1a ipcommon ip2a ip2b ip2c des1b des1a1 des1a2 des1c1
level 2: ip1 ip2 des1a des1c
level 3: des1
level 4: top1

Compile order for: top2
level 1: ip3 extra1 ipcommon ip2a ip2b ip2c des1b des1a1 des1a2 des1c1
level 2: ip2 des1a des1c
level 3: des1
level 4: top2

Compile order for: top1 top2
level 1: ip3 extra1 ip1a ipcommon ip2a ip2b ip2c des1b des1a1 des1a2 des1c1
level 2: ip1 ip2 des1a des1c
level 3: des1
level 4: top1 top2

Compile order for: ip1
level 1: extra1 ip1a ipcommon
level 2: ip1

Go

package main

import (
    "fmt"
    "strings"
)

var data = `
FILE    FILE DEPENDENCIES
====    =================
top1    des1 ip1 ip2
top2    des1 ip2 ip3
ip1     extra1 ip1a ipcommon
ip2     ip2a ip2b ip2c ipcommon
des1    des1a des1b des1c
des1a   des1a1 des1a2
des1c   des1c1 extra1`

func main() {
    g, dep, err := parseLibDep(data)
    if err != nil {
        fmt.Println(err)
        return
    }
    // Task 1: Determine top levels.  The input parser returns a list (dep)
    // of libraries that are dependants of at least one other library.
    // Top levels are then libraries in the graph that are not on this list.
    var tops []string
    for n := range g {
        if !dep[n] {
            tops = append(tops, n)
        }
    }
    fmt.Println("Top levels:", tops)
    // Task 2 is orderFrom method, below
    showOrder(g, "top1")         // Task 3
    showOrder(g, "top2")         // Task 4
    showOrder(g, "top1", "top2") // Stretch

    fmt.Println("Cycle examples:")
    // reparse with a cyclic dependency
    g, _, err = parseLibDep(data + `
des1a1  des1`)
    if err != nil {
        fmt.Println(err)
        return
    }
    showOrder(g, "top1")       // runs into cycle
    showOrder(g, "ip1", "ip2") // does not involve cycle
}

func showOrder(g graph, target ...string) {
    order, cyclic := g.orderFrom(target...)
    if cyclic == nil {
        reverse(order) // compile order is reverse of dependency order
        fmt.Println("Target", target, "order:", order)
    } else {
        fmt.Println("Target", target, "cyclic dependencies:", cyclic)
    }
}

func reverse(s []string) {
    last := len(s) - 1
    for i, e := range s[:len(s)/2] {
        s[i], s[last-i] = s[last-i], e
    }
}

type graph map[string][]string // adjacency list representation
type depList map[string]bool

// parseLibDep parses the text format of the task and returns a dependency
// graph and a list of nodes that are dependants of at least one other node.
func parseLibDep(data string) (g graph, d depList, err error) {
    lines := strings.Split(data, "\n")
    if len(lines) < 3 || !strings.HasPrefix(lines[2], "=") {
        return nil, nil, fmt.Errorf("data format")
    }
    lines = lines[3:]
    g = graph{}
    d = depList{}
    for _, line := range lines {
        libs := strings.Fields(line)
        if len(libs) == 0 {
            continue
        }
        lib := libs[0]
        var deps []string
        for _, dep := range libs[1:] {
            g[dep] = g[dep]
            if dep == lib {
                continue
            }
            for i := 0; ; i++ {
                if i == len(deps) {
                    deps = append(deps, dep)
                    d[dep] = true
                    break
                }
                if dep == deps[i] {
                    break
                }
            }
        }
        g[lib] = deps
    }
    return g, d, nil
}

// OrderFrom produces a topological ordering of the subgraph of g reachable
// from a set of start nodes, where the subgraph is a directed acyclic graph.
// If the subgraph contains a cycle, orderFrom returns the first cycle found
// and returns a nil order.  Cycles which are in the graph but not in the
// subgraph reachable from start are not detected.
func (g graph) orderFrom(start ...string) (order, cyclic []string) {
    L := make([]string, len(g))
    i := len(L)
    temp := map[string]bool{}
    perm := map[string]bool{}
    var cycleFound bool
    var cycleStart string
    var visit func(string)
    visit = func(n string) {
        switch {
        case temp[n]:
            cycleFound = true
            cycleStart = n
            return
        case perm[n]:
            return
        }
        temp[n] = true
        for _, m := range g[n] {
            visit(m)
            if cycleFound {
                if cycleStart > "" {
                    cyclic = append(cyclic, n)
                    if n == cycleStart {
                        cycleStart = ""
                    }
                }
                return
            }
        }
        delete(temp, n)
        perm[n] = true
        i--
        L[i] = n
    }
    for _, n := range start {
        if perm[n] {
            continue
        }
        visit(n)
        if cycleFound {
            return nil, cyclic
        }
    }
    return L[i:], nil
}

Output:

Top levels: [top1 top2]
Target [top1] order: [des1a1 des1a2 des1a des1b des1c1 extra1 des1c des1 ip1a ipcommon ip1 ip2a ip2b ip2c ip2 top1]
Target [top2] order: [des1a1 des1a2 des1a des1b des1c1 extra1 des1c des1 ip2a ip2b ip2c ipcommon ip2 ip3 top2]
Target [top1 top2] order: [des1a1 des1a2 des1a des1b des1c1 extra1 des1c des1 ip1a ipcommon ip1 ip2a ip2b ip2c ip2 top1 ip3 top2]
Cycle examples:
Target [top1] cyclic dependencies: [des1a1 des1a des1]
Target [ip1 ip2] order: [extra1 ip1a ipcommon ip1 ip2a ip2b ip2c ip2]

J

Derived from the topological sort implementation:

compileOrder=: dyad define
  targets=. ;: x
  parsed=. <@;:;._2 y
  names=. ~.({.&>parsed),targets,;parsed
  depends=. (> =@i.@#) names e.S:1 (#names){.parsed
  depends=. (+. +./ .*.~)^:_ depends
  b=. +./depends (] , #~) names e. targets
  names (</.~ \: ~.@])&(keep&#) +/"1 depends
  (b#names) (</.~ /: ~.@]) +/ }.+./ .*.~&(b#"1 b#depends)^:a: 1
)

topLevel=:  [: ({.&> -. [:;}.&.>) <@;:;._2

The changes include:

1. Added an argument for the target(s) we wish to find dependencies for
2. Make sure that these targets are included in our dependency structures
3. Make sure that things we can depend on are included in our dependency structures
4. Select these targets, and the things they depend on, once we know what depends on what
5. When ordering names by dependencies:
   1. only consider names and dependencies we want to keep
   2. extract names grouped by their dependency chain length

Example:

dependencies=: noun define
  top1    des1 ip1 ip2
  top2    des1 ip2 ip3
  ip1     extra1 ip1a ipcommon
  ip2     ip2a ip2b ip2c ipcommon
  des1    des1a des1b des1c
  des1a   des1a1 des1a2
  des1c   des1c1 extra1
)

   >topLevel dependencies
top1
top2

   ;:inv@> 'top1' compileOrder dependencies
extra1 ip1a ipcommon ip2a ip2b ip2c des1b des1a1 des1a2 des1c1
ip1 ip2 des1a des1c                                           
des1                                                          
top1                                                          

   ;:inv@> 'top2' compileOrder dependencies
ip3 extra1 ipcommon ip2a ip2b ip2c des1b des1a1 des1a2 des1c1
ip2 des1a des1c                                              
des1                                                         
top2                                                         

   ;:inv@> 'top1 top2' compileOrder dependencies
ip3 extra1 ip1a ipcommon ip2a ip2b ip2c des1b des1a1 des1a2 des1c1
ip1 ip2 des1a des1c                                               
des1                                                              
top1 top2

Java

Works with: Java version 8

import java.util.*;
import static java.util.Arrays.asList;
import static java.util.stream.Collectors.toList;

public class TopologicalSort2 {

    public static void main(String[] args) {
        String s = "top1,top2,ip1,ip2,ip3,ip1a,ip2a,ip2b,ip2c,ipcommon,des1,"
                + "des1a,des1b,des1c,des1a1,des1a2,des1c1,extra1";

        Graph g = new Graph(s, new int[][]{
            {0, 10}, {0, 2}, {0, 3},
            {1, 10}, {1, 3}, {1, 4},
            {2, 17}, {2, 5}, {2, 9},
            {3, 6}, {3, 7}, {3, 8}, {3, 9},
            {10, 11}, {10, 12}, {10, 13},
            {11, 14}, {11, 15},
            {13, 16}, {13, 17},});

        System.out.println("Top levels: " + g.toplevels());
        String[] files = {"top1", "top2", "ip1"};
        for (String f : files)
            System.out.printf("Compile order for %s %s%n", f, g.compileOrder(f));
    }
}

class Graph {
    List<String> vertices;
    boolean[][] adjacency;
    int numVertices;

    public Graph(String s, int[][] edges) {
        vertices = asList(s.split(","));
        numVertices = vertices.size();
        adjacency = new boolean[numVertices][numVertices];

        for (int[] edge : edges)
            adjacency[edge[0]][edge[1]] = true;
    }

    List<String> toplevels() {
        List<String> result = new ArrayList<>();
        // look for empty columns
        outer:
        for (int c = 0; c < numVertices; c++) {
            for (int r = 0; r < numVertices; r++) {
                if (adjacency[r][c])
                    continue outer;
            }
            result.add(vertices.get(c));
        }
        return result;
    }

    List<String> compileOrder(String item) {
        LinkedList<String> result = new LinkedList<>();
        LinkedList<Integer> queue = new LinkedList<>();

        queue.add(vertices.indexOf(item));

        while (!queue.isEmpty()) {
            int r = queue.poll();
            for (int c = 0; c < numVertices; c++) {
                if (adjacency[r][c] && !queue.contains(c)) {
                    queue.add(c);
                }
            }
            result.addFirst(vertices.get(r));
        }
        return result.stream().distinct().collect(toList());
    }
}

Top levels: [top1, top2]
Compile order for top1 [extra1, des1c1, des1a2, des1a1, des1c, des1b, des1a, ip2c, ip2b, ip2a, ipcommon, ip1a, des1, ip2, ip1, top1]
Compile order for top2 [extra1, des1c1, des1a2, des1a1, des1c, des1b, des1a, ipcommon, ip2c, ip2b, ip2a, des1, ip3, ip2, top2]
Compile order for ip1 [extra1, ipcommon, ip1a, ip1]

Julia

const topotext = """
top1    des1 ip1 ip2
top2    des1 ip2 ip3
ip1     extra1 ip1a ipcommon
ip2     ip2a ip2b ip2c ipcommon
des1    des1a des1b des1c
des1a   des1a1 des1a2
des1c   des1c1 extra1
"""

const topolines = map(x -> split(x, r"\s+", limit=2), split(strip(topotext), "\n"))
const topodict = Dict([p[1] => split(p[2], r"\s+") for p in topolines])

const dependents = collect(keys(topodict))
const dependencies = string.(unique(mapreduce(x -> topodict[x], vcat, dependents)))
const toplevel = string.(filter(x -> !(x in dependencies), dependents))

println("Top level files: ", toplevel)
println("Dependencies: $dependencies\n")

function compileorder(file, ddict)
    tocompile = [file]
    firstdependencies = get(ddict, file, [])
    if !isempty(firstdependencies)
        for f in firstdependencies
            append!(tocompile, reverse(compileorder(f, ddict)))
        end
    end
    return unique(reverse(tocompile))
end

for f in toplevel
    println("Compile order for $f: ", compileorder("top1", topodict))
end

Output:

Top level files: ["top2", "top1"]
Dependencies: ["des1a", "des1b", "des1c", "ip2a", "ip2b", "ip2c", "ipcommon", "des1c1", "extra1", "des1a1", "des1a2", "des1", "ip2", "ip3", "ip1", "ip1a"]

Compile order for top2: ["ipcommon", "ip2c", "ip2b", "ip2a", "ip2", "ip1a", "extra1", "ip1", "des1c1", "des1c", "des1b", "des1a2", "des1a1", "des1a", "des1", "top1"]
Compile order for top1: ["ipcommon", "ip2c", "ip2b", "ip2a", "ip2", "ip1a", "extra1", "ip1", "des1c1", "des1c", "des1b", "des1a2", "des1a1", "des1a", "des1", "top1"]

Kotlin

Translation of: Java

// version 1.1.51

import java.util.LinkedList

val s = "top1, top2, ip1, ip2, ip3, ip1a, ip2a, ip2b, ip2c, ipcommon, des1, " +
        "des1a, des1b, des1c, des1a1, des1a2, des1c1, extra1"

val deps = mutableListOf(
    0 to 10, 0 to 2, 0 to 3,
    1 to 10, 1 to 3, 1 to 4,
    2 to 17, 2 to 5, 2 to 9,
    3 to 6, 3 to 7, 3 to 8, 3 to 9,
    10 to 11, 10 to 12, 10 to 13,
    11 to 14, 11 to 15,
    13 to 16, 13 to 17
)

val files = listOf("top1", "top2", "ip1")

class Graph(s: String, edges: List<Pair<Int, Int>>) {

    val vertices = s.split(", ")
    val numVertices = vertices.size
    val adjacency = List(numVertices) { BooleanArray(numVertices) }

    init {
        for (edge in edges) adjacency[edge.first][edge.second] = true
    }

    fun topLevels(): List<String> {
        val result = mutableListOf<String>()
        // look for empty columns
        outer@ for (c in 0 until numVertices) {
            for (r in 0 until numVertices) {
                if (adjacency[r][c]) continue@outer
            }
            result.add(vertices[c])
        }
        return result
    }

    fun compileOrder(item: String): List<String> {
        val result = LinkedList<String>()
        val queue  = LinkedList<Int>()
        queue.add(vertices.indexOf(item))
        while (!queue.isEmpty()) {
            val r = queue.poll()
            for (c in 0 until numVertices) {
                if (adjacency[r][c] && !queue.contains(c)) queue.add(c)
            }
            result.addFirst(vertices[r])
        }
        return result.distinct().toList()
    }
}

fun main(args: Array<String>) {
    val g = Graph(s, deps)
    println("Top levels:  ${g.topLevels()}")
    for (f in files) println("\nCompile order for $f: ${g.compileOrder(f)}")
}

Output:

Top levels:  [top1, top2]

Compile order for top1: [extra1, des1c1, des1a2, des1a1, des1c, des1b, des1a, ip2c, ip2b, ip2a, ipcommon, ip1a, des1, ip2, ip1, top1]

Compile order for top2: [extra1, des1c1, des1a2, des1a1, des1c, des1b, des1a, ipcommon, ip2c, ip2b, ip2a, des1, ip3, ip2, top2]

Compile order for ip1: [extra1, ipcommon, ip1a, ip1]

Nim

Translation of: Python

import algorithm, sequtils, strutils, sets, tables

type
  StringSet = HashSet[string]
  StringSeq = seq[string]

const Empty: StringSet = initHashSet[string]()


func topLevels(data: Table[string, StringSet]): StringSet =
  ## Extract all top levels from dependency data.

  # Remove self dependencies.
  var data = data
  for key, values in data.mpairs:
    values.excl key

  let deps = toSeq(data.values).foldl(a + b)
  result = toSeq(data.keys).toHashSet - deps


func topx(data: Table[string, StringSet]; tops: StringSet;
          sofar: var seq[StringSet]): seq[StringSeq] =
  ## Recursive topological extractor.
  sofar = sofar & tops
  var depends: StringSet
  for top in tops:
    depends = depends + data.getOrDefault(top, Empty)
  if depends.card != 0: discard data.topx(depends, sofar)
  var accum = Empty
  for i in countdown(sofar.high, 0):
    result.add sorted(toSeq(sofar[i] - accum))
    accum = accum + sofar[i]


func topx(data: Table[string, StringSet]; tops = initHashSet[string]()): seq[StringSeq] =
  ## Extract the set of top-level(s) in topological order.

  # Remove self dependencies.
  var data = data
  for key, values in data.mpairs:
    values.excl key

  var tops = tops
  if tops.card == 0: tops = data.topLevels

  var sofar: seq[StringSet]
  result = data.topx(tops, sofar)


proc printOrder(order: seq[StringSeq]) =
  ## Prettyprint topological ordering.
  if order.len != 0:
    echo "First: ", order[0].join(", ")
  for i in 1..order.high:
    echo " Then: ", order[i].join(", ")


when isMainModule:

  const Data = {"top1":  ["ip1", "des1", "ip2"].toHashSet,
                "top2":  ["ip2", "des1", "ip3"].toHashSet,
                "des1":  ["des1a", "des1b", "des1c"].toHashSet,
                "des1a": ["des1a1", "des1a2"].toHashSet,
                "des1c": ["des1c1", "extra1"].toHashSet,
                "ip2":   ["ip2a", "ip2b", "ip2c", "ipcommon"].toHashSet,
                "ip1":   ["ip1a", "ipcommon", "extra1"].toHashSet}.toTable

  let tops = Data.topLevels()
  let topList = sorted(tops.toSeq)
  echo "The top levels of the dependency graph are: ", topList.join(", ")
  for t in topList:
    echo "\nThe compile order for top level “$#” is..." % t
    printOrder Data.topx([t].toHashSet)

  if tops.len > 1:
    echo "\nThe compile order for top levels $# is..." % topList.mapIt("“" & it & "”").join(" and ")
    printOrder Data.topx(tops)

Output:

The top levels of the dependency graph are: top1, top2

The compile order for top level “top1” is...
First: des1a1, des1a2, des1c1, extra1
 Then: des1a, des1b, des1c, ip1a, ip2a, ip2b, ip2c, ipcommon
 Then: des1, ip1, ip2
 Then: top1

The compile order for top level “top2” is...
First: des1a1, des1a2, des1c1, extra1
 Then: des1a, des1b, des1c, ip2a, ip2b, ip2c, ipcommon
 Then: des1, ip2, ip3
 Then: top2

The compile order for top levels “top1” and “top2” is...
First: des1a1, des1a2, des1c1, extra1
 Then: des1a, des1b, des1c, ip1a, ip2a, ip2b, ip2c, ipcommon
 Then: des1, ip1, ip2, ip3
 Then: top1, top2

Perl

#!/usr/bin/perl

use strict;
use warnings;
use List::Util qw( uniq );

my $deps = <<END;
top1    des1 ip1 ip2
top2    des1 ip2 ip3
ip1     extra1 ip1a ipcommon
ip2     ip2a ip2b ip2c ipcommon
des1    des1a des1b des1c
des1a   des1a1 des1a2
des1c   des1c1 extra1
END

sub before
  {
  map { $deps =~ /^$_\b(.+)/m ? before( split ' ', $1 ) : (), $_ } @_
  }

1 while $deps =~ s/^(\w+)\b.*?\K\h+\1\b//gm; # remove self dependencies
print "TOP LEVELS: @{[grep $deps !~ /\h$_\b/, $deps =~ /^\w+/gm]}\n";
print "\nTARGET $_ ORDER: @{[ uniq before split ]}\n"
  for $deps =~ /^\w+/gm, 'top1 top2';

Output:

TOP LEVELS: top1 top2

TARGET top1 ORDER: des1a1 des1a2 des1a des1b des1c1 extra1 des1c des1 ip1a ipcommon ip1 ip2a ip2b ip2c ip2 top1

TARGET top2 ORDER: des1a1 des1a2 des1a des1b des1c1 extra1 des1c des1 ip2a ip2b ip2c ipcommon ip2 ip3 top2

TARGET ip1 ORDER: extra1 ip1a ipcommon ip1

TARGET ip2 ORDER: ip2a ip2b ip2c ipcommon ip2

TARGET des1 ORDER: des1a1 des1a2 des1a des1b des1c1 extra1 des1c des1

TARGET des1a ORDER: des1a1 des1a2 des1a

TARGET des1c ORDER: des1c1 extra1 des1c

TARGET top1 top2 ORDER: des1a1 des1a2 des1a des1b des1c1 extra1 des1c des1 ip1a ipcommon ip1 ip2a ip2b ip2c ip2 top1 ip3 top2

Phix

Minor tweaks to the Topological_sort code: top_levels, propagate() and -1 now means "not required".

sequence names
enum RANK, NAME, DEP    -- content of names
-- rank is 1 for items to compile first, then 2, etc,
--      or 0 if cyclic dependencies prevent compilation.
--   -  and -1 now means "not required".
-- name is handy, and makes the result order alphabetic!
-- dep is a list of dependencies (indexes to other names)
 
function add_dependency(string name)
    integer k = find(name,vslice(names,NAME))
    if k=0 then
        names = append(names,{-1,name,{}})
        k = length(names)
    end if
    return k
end function
 
procedure propagate(integer t)
    if names[t][RANK]!=0 then
        names[t][RANK] = 0
        for i=1 to length(names[t][DEP]) do
            propagate(names[t][DEP][i])
        end for
    end if
end procedure
 
procedure topsort(string input, sequence tops)
    names = {}
    sequence lines = split(input,'\n')
    for i=1 to length(lines) do
        sequence line = split(lines[i]),
                 dependencies = {}
        integer k = add_dependency(line[1])
        for j=2 to length(line) do
            integer l = add_dependency(line[j])
            if l!=k then -- ignore self-references
                dependencies &= l
            end if
        end for
        names[k][DEP] = dependencies
    end for
 
    if tops={} then
        -- show top levels
        for i=1 to length(names) do
            for j=1 to length(names[i][DEP]) do
                integer ji = names[i][DEP][j]
                names[ji][RANK] = 0
            end for
        end for
        sequence top_levels = {}
        for i=1 to length(names) do
            if names[i][RANK]=-1 then
                top_levels = append(top_levels,names[i][NAME])
            end if      
        end for
        printf(1,"top levels: %s\n",{join(top_levels)})
        return
    end if
    -- Propagate required by setting RANK to 0:
    for i=1 to length(tops) do
        integer t = add_dependency(tops[i])
        propagate(t)
    end for
 
    -- Now populate names[RANK] iteratively:
    bool more = true
    integer rank = 0
    while more do
        more = false 
        rank += 1
        for i=1 to length(names) do
            if names[i][RANK]=0 then
                bool ok = true
                for j=1 to length(names[i][DEP]) do
                    integer ji = names[i][DEP][j],
                            nr = names[ji][RANK]
                    if nr=0 or nr=rank then
                        -- not yet compiled, or same pass
                        ok = false
                        exit
                    end if
                end for
                if ok then
                    names[i][RANK] = rank
                    more = true
                end if
            end if
        end for
    end while
 
    names = sort(names) -- (ie by [RANK=1] then [NAME=2])
    integer prank = -1
    for i=1 to length(names) do
        rank = names[i][RANK]
        if rank>-1 then
            puts(1,iff(rank=prank?" ":sprintf("\nlevel %d:",rank)))
            puts(1,names[i][NAME])
            prank = rank
        end if
    end for
    puts(1,"\n")
end procedure
 
constant input = """
top1    des1 ip1 ip2
top2    des1 ip2 ip3
ip1     extra1 ip1a ipcommon
ip2     ip2a ip2b ip2c ipcommon
des1    des1a des1b des1c
des1a   des1a1 des1a2
des1c   des1c1 extra1"""
 
topsort(input,{})
topsort(input,{"top1"})
topsort(input,{"top2"})
topsort(input,{"top1","top2"})
topsort(input,{"ip1"})

Output:

Items on the same line can be compiled at the same time, and each line is alphabetic.

top levels: top1 top2

level 1:des1a1 des1a2 des1b des1c1 extra1 ip1a ip2a ip2b ip2c ipcommon
level 2:des1a des1c ip1 ip2
level 3:des1
level 4:top1

level 1:des1a1 des1a2 des1b des1c1 extra1 ip2a ip2b ip2c ip3 ipcommon
level 2:des1a des1c ip2
level 3:des1
level 4:top2

level 1:des1a1 des1a2 des1b des1c1 extra1 ip1a ip2a ip2b ip2c ip3 ipcommon
level 2:des1a des1c ip1 ip2
level 3:des1
level 4:top1 top2

level 1:extra1 ip1a ipcommon
level 2:ip1

Python

Where the compile order between a subset of files is arbitrary, they are shown on the same line.

try:
    from functools import reduce
except: pass

# Python 3.x: def topx(data:'dict', tops:'set'=None) -> 'list':
def topx(data, tops=None):
    'Extract the set of top-level(s) in topological order'
    for k, v in data.items():
        v.discard(k) # Ignore self dependencies
    if tops is None:
        tops = toplevels(data)
    return _topx(data, tops, [], set())

def _topx(data, tops, _sofar, _sofar_set):
    'Recursive topological extractor'
    _sofar += [tops] # Accumulates order in reverse
    _sofar_set.union(tops)
    depends = reduce(set.union, (data.get(top, set()) for top in tops))
    if depends:
        _topx(data, depends, _sofar, _sofar_set)
    ordered, accum = [], set()
    for s in _sofar[::-1]:
        ordered += [sorted(s - accum)]
        accum |= s
    return ordered

def printorder(order):
    'Prettyprint topological ordering'
    if order:
        print("First: " + ', '.join(str(s) for s in order[0]))
    for o in order[1:]:
        print(" Then: " + ', '.join(str(s) for s in o))

def toplevels(data):
    '''\
    Extract all top levels from dependency data
    Top levels are never dependents
    '''
    for k, v in data.items():
        v.discard(k) # Ignore self dependencies
    dependents = reduce(set.union, data.values())
    return  set(data.keys()) - dependents

if __name__ == '__main__':
    data = dict(
        top1  = set('ip1 des1 ip2'.split()),
        top2  = set('ip2 des1 ip3'.split()),
        des1  = set('des1a des1b des1c'.split()),
        des1a = set('des1a1 des1a2'.split()),
        des1c = set('des1c1 extra1'.split()),
        ip2   = set('ip2a ip2b ip2c ipcommon'.split()),
        ip1   = set('ip1a ipcommon extra1'.split()),
        )

    tops = toplevels(data)
    print("The top levels of the dependency graph are: " + ' '.join(tops))

    for t in sorted(tops):
        print("\nThe compile order for top level: %s is..." % t)
        printorder(topx(data, set([t])))
    if len(tops) > 1:
        print("\nThe compile order for top levels: %s is..."
              % ' and '.join(str(s) for s in sorted(tops)) )
        printorder(topx(data, tops))

Sample Output

The top levels of the dependency graph are: top2 top1

The compile order for top level: top1 is...
First: des1a1, des1a2, des1c1, extra1
 Then: des1a, des1b, des1c, ip1a, ip2a, ip2b, ip2c, ipcommon
 Then: des1, ip1, ip2
 Then: top1

The compile order for top level: top2 is...
First: des1a1, des1a2, des1c1, extra1
 Then: des1a, des1b, des1c, ip2a, ip2b, ip2c, ipcommon
 Then: des1, ip2, ip3
 Then: top2

The compile order for top levels: top1 and top2 is...
First: des1a1, des1a2, des1c1, extra1
 Then: des1a, des1b, des1c, ip1a, ip2a, ip2b, ip2c, ipcommon
 Then: des1, ip1, ip2, ip3
 Then: top1, top2

Racket

#lang racket
(define dep-tree ; go straight for the hash, without parsing strings etc.
  #hash((top1  . (des1 ip1 ip2))
        (top2  . (des1 ip2 ip3))
        (ip1   . (extra1 ip1a ipcommon))
        (ip2   . (ip2a ip2b ip2c ipcommon))
        (des1  . (des1a des1b des1c))
        (des1a . (des1a1 des1a2))
        (des1c . (des1c1 extra1))))

(define (build-tree Deps Top)
  (define (build n b# d)
    (hash-set b# n d))  
  
  (define (inner-b-t node visited built# depth)
    (cond
      [(hash-ref built# node #f)
       built#]
      [(member node visited)
       (error 'build-tree "circular dependency tree at node: ~a" node)]
      [(hash-ref Deps node #f)
       =>
       (λ (deps)
         (define built#+
           (for/fold ((built# built#)) ((dependency deps))
             (if (equal? dependency node)
                 built#
                 (inner-b-t dependency (cons node visited) built# (add1 depth)))))
         (build node built#+ depth))]
      [else
       (build node built# depth)]))
  
  (define final-build# (inner-b-t Top null (hash) 1))
  
  (define levels# (for/fold ((hsh# (hash))) (([k v] (in-hash final-build#)))
                    (hash-update hsh# v (curry cons k) null)))

  (for/list ((lvl (in-list (sort (hash-keys levels#) >))))
    (hash-ref levels# lvl)))

(define (print-build-order Deps Top)
  (define build-order (build-tree Deps Top))
  (printf "To build: ~s~%" Top)
  (for ((round build-order)) (printf "Build: ~a~%" round))
  (newline))

(print-build-order dep-tree 'top1)
(print-build-order dep-tree 'top2)
(with-handlers [(exn? (λ (x) (displayln (exn-message x) (current-error-port))))]
  (build-tree #hash((top . (des1 ip1)) (ip1 . (net netip)) (netip . (mac ip1))) 'top))

Output:

To build: top1
Build: (extra1 des1c1 des1a2 des1a1)
Build: (ip2c ip2b ip2a ipcommon ip1a des1b des1c des1a)
Build: (des1 ip2 ip1)
Build: (top1)

To build: top2
Build: (extra1 des1c1 des1a2 des1a1)
Build: (ip2c ip2b ip2a ipcommon des1b des1c des1a)
Build: (ip3 des1 ip2)
Build: (top2)

build-tree: circular dependency tree at node: ip1

Raku

(formerly Perl 6)

sub top_topos ( %deps, *@top ) {
    my %ba;
    for %deps.kv -> $after, @befores {
        for @befores -> $before {
            %ba{$after}{$before} = 0 if $before ne $after;
            %ba{$before} //= {};
        }
    }

    if @top {
	my @want = @top;
	my %care;
	%care{@want} = 1 xx *;
	repeat while @want {
	    my @newwant;
	    for @want -> $before {
		if %ba{$before} {
		    for %ba{$before}.keys -> $after {
			if not %ba{$before}{$after} {
			    %ba{$before}{$after}++;
			    push @newwant, $after;
			}
		    }
		}
	    }
	    @want = @newwant;
	    %care{@want} = 1 xx *;
	}

	for %ba.keys -> $before {
	    %ba{$before}:delete unless %care{$before};
	}
    }
 
    my @levels;
    while %ba.grep( not *.value )».key -> @befores {
	push @levels, ~@befores.sort;
        %ba{@befores}:delete;
        for %ba.values { .{@befores}:delete }
    }
    if @top {
	say "For top-level-modules: ", @top;
	say "  $_" for @levels;
    }
    else {
	say "Top levels are: @levels[*-1]";
    }
 
    say "Cycle found! {%ba.keys.sort}" if %ba;
    say ''; 
}

my %deps =
    top1  =>  <des1 ip1 ip2>,
    top2  =>  <des1 ip2 ip3>,
    ip1   =>  <extra1 ip1a ipcommon>,
    ip2   =>  <ip2a ip2b ip2c ipcommon>,
    des1  =>  <des1a des1b des1c>,
    des1a =>  <des1a1 des1a2>,
    des1c =>  <des1c1 extra1>;
     
top_topos(%deps);
top_topos(%deps, 'top1');
top_topos(%deps, 'top2');
top_topos(%deps, 'ip1');
top_topos(%deps, 'top1', 'top2');

Output:

Top levels are: top1 top2

For top-level-modules: top1
  des1a1 des1a2 des1b des1c1 extra1 ip1a ip2a ip2b ip2c ipcommon
  des1a des1c ip1 ip2
  des1
  top1

For top-level-modules: top2
  des1a1 des1a2 des1b des1c1 extra1 ip2a ip2b ip2c ip3 ipcommon
  des1a des1c ip2
  des1
  top2

For top-level-modules: ip1
  extra1 ip1a ipcommon
  ip1

For top-level-modules: top1 top2
  des1a1 des1a2 des1b des1c1 extra1 ip1a ip2a ip2b ip2c ip3 ipcommon
  des1a des1c ip1 ip2
  des1
  top1 top2

REXX

Where the compile order between a subset of files is arbitrary, they are shown on the same line.
This REXX version can handle multiple top levels.

/*REXX program  displays the  compile  order  of jobs  (indicating the dependencies).   */
parse arg job                                    /*obtain optional argument from the CL.*/
jobL.=;   stage.=;    #.=0;      @.=;       JL=  /*define some handy─dandy variables.   */
tree.=;                      tree.1= '  top1     des1      ip1       ip2                 '
                             tree.2= '  top2     des1      ip2       ip3                 '
                             tree.3= '  ip1      extra1    ip1a      ipcommon            '
                             tree.4= '  ip2      ip2a      ip2b      ip2c       ipcommon '
                             tree.5= '  des1     des1a     des1b     des1c               '
                             tree.6= '  des1a    des1a1    des1a2                        '
                             tree.7= '  des1c    des1c1    extra1                        '
$=
              do j=1  while  tree.j\==''                               /*build job tree.*/
              parse var tree.j x deps;           @.x= space(deps)      /*extract jobs.  */
              if wordpos(x, $)==0  then $= $ x                         /*Unique? Add it.*/
                       do k=1  for words(@.x);   _= word(@.x, k)
                       if wordpos(_, $)==0  then $= space($ _)
                       end   /*k*/
              end            /*j*/
!.=;  !!.= !.                                                          /*init. 2 arrays.*/
              do j=1      for words($);          x= word($, j);        !.x.0= words(@.x)
                  do k=1  for !.x.0;         !.x.k= word(@.x, k);     !!.x.k= !.x.k
                  end   /*k*/                    /* [↑]  build arrays of job departments*/
              end       /*j*/

  do words($)                                    /*process all the jobs specified.      */
      do j=1  for words($);      x= word($, j);     z= words(@.x);      allN= 1;      m= 0
      if z==0  then do;  #.x=1;  iterate;  end   /*if no dependents, then skip this one.*/
         do k=1  for z;          y= !.x.k        /*examine all the stage numbers.       */
         if datatype(y, 'W')  then m= max(m, y)  /*find the highest stage number.       */
                              else do;  allN= 0  /*at least one entry isn't  numeric.   */
                                        if #.y\==0  then !.x.k= #.y
                                   end           /* [↑]  replace with a number.         */
         end   /*k*/
      if allN & m\==0  then #.x= max(#.x, m + 1) /*replace with the stage number max.   */
      end      /*j*/                             /* [↑]  maybe set the stage number.    */
  end          /*words($)*/

if job=''  then job= word(tree.1, 1)             /*Not specified?   Use 1st job in tree.*/
jobL.1= job                                      /*define the bottom level jobList.     */
s= 1                                             /*define the stage level for jobList.  */
        do j=1;              yyy= jobL.j
           do r=1  for words(yyy)                /*verify that there are no duplicates. */
               do c=1  while c<words(yyy);                    z= word(yyy,c)
               p= wordpos(z, yyy, c + 1);    if p\==0  then yyy= delword(yyy, p, 1)
               end   /*c*/                       /* [↑]   Duplicate?    Then delete it. */
           end       /*r*/
        jobL.j= yyy
        if yyy=''  then leave                    /*if null, then we're done with jobList*/
        z= words(yyy)                            /*number of jobs in the jobList.       */
        s= s+1                                   /*bump the stage number.               */
               do k=1  for z;    _= word(yyy, k) /*obtain a stage number for the job.   */
               jobL.s= jobL.s  @._               /*add a job to a stage.                */
               end   /*k*/
        end          /*j*/

   do k=1  for s;   JL= JL jobL.k                /*build a complete jobList  (JL).      */
   end   /*k*/

   do s=1  for words(JL);        _= word(JL, s)  /*process each job in the  jobList.    */
   level= #._                                    /*get the proper level for the job.    */
   stage.level= stage.level _                    /*assign a level to job stage number.  */
   end   /*s*/                                   /* [↑]  construct various job stages.  */

say '───────  The compile order for job: '       job        " ────────";              say
                                                 /* [↓]  display the stages for the job.*/
   do show=1  for s;     if stage.show\==''  then say show stage.show
   end   /*show*/                                /*stick a fork in it,  we're all done. */

output   when using the default input of:   top1

───────  The compile order for job:  top1  ─────── 

1  des1b extra1 ip1a ipcommon ip2a ip2b ip2c des1a1 des1a2 des1c1 extra1
2  ip1 ip2 des1a des1c
3  des1
4  top1

output   when using the input of:   top2

───────  The compile order for job:  top2  ───────

1  ip3 des1b ip2a ip2b ip2c ipcommon des1a1 des1a2 des1c1 extra1
2  ip2 des1a des1c
3  des1
4  top2

output   when using the input of:   top1 top2

───────  The compile order for job:  top1 top2  ───────

1  ip3 des1b extra1 ip1a ipcommon ip2a ip2b ip2c des1a1 des1a2 des1c1 extra1
2  ip1 ip2 des1a des1c
3  des1
4  top1 top2

Tcl

The topsort proc is taken from Topological sort#Tcl with {*} removed from the line commented so that results are returned by level:

package require Tcl 8.5
proc topsort {data} {
    # Clean the data
    dict for {node depends} $data {
        if {[set i [lsearch -exact $depends $node]] >= 0} {
            set depends [lreplace $depends $i $i]
            dict set data $node $depends
        }
        foreach node $depends {dict lappend data $node}
    }
    # Do the sort
    set sorted {}
    while 1 {
        # Find available nodes
        set avail [dict keys [dict filter $data value {}]]
        if {![llength $avail]} {
            if {[dict size $data]} {
                error "graph is cyclic, possibly involving nodes \"[dict keys $data]\""
            }
            return $sorted
        }
        lappend sorted $avail   ;# change here: [[Topological sort]] had {*}$avail
        # Remove from working copy of graph
        dict for {node depends} $data {
            foreach n $avail {
                if {[set i [lsearch -exact $depends $n]] >= 0} {
                    set depends [lreplace $depends $i $i]
                    dict set data $node $depends
                }
            }
        }
        foreach node $avail {
            dict unset data $node
        }
    }
}

# The changes to $data in this proc offer an interesting reflection on value semantics.
# Consider the value of $data seen by [dict for], by each invocation of [dict keys]
# and [dict unset] and how that affects the soundness of the loops.
proc tops {data} {
    dict for {k v} $data {
        foreach t [dict keys $data] {
            if {$t in $v} {
                dict unset data $t
            }
        }
    }
    dict keys $data
}

proc withdeps {dict tops {res {}}} {
    foreach top $tops {
        if {[dict exists $dict $top]} {
            set deps [dict get $dict $top]
            set res [dict merge  $res  [dict create $top $deps]  [withdeps $dict $deps]]
        }
    }
    return $res
}

proc parsetop {t} {
    set top {}
    foreach l [split $t \n] {
        catch {dict lappend top {*}$l}
    }
    return $top
}

set inputData {
        top1    des1 ip1 ip2
        top2    des1 ip2 ip3
        ip1     extra1 ip1a ipcommon
        ip2     ip2a ip2b ip2c ipcommon
        des1    des1a des1b des1c
        des1a   des1a1 des1a2
        des1c   des1c1 extra1
}

set d [parsetop $inputData]
pdict $d
set tops [tops $d]

puts "Tops: $tops\n"

set targets [list $tops {*}$tops]
foreach target $targets {
    puts "Target: $target"
    set i 0
    foreach deps [topsort [withdeps $d $target]] {
        puts "\tround [incr i]:\t$deps"
    }
}

Output:

Tops: top1 top2

Target: top1 top2
        round 1:        des1b des1a1 des1a2 des1c1 extra1 ip1a ipcommon ip2a ip2b ip2c ip3
        round 2:        des1a des1c ip1 ip2
        round 3:        des1
        round 4:        top1 top2
Target: top1
        round 1:        des1b des1a1 des1a2 des1c1 extra1 ip1a ipcommon ip2a ip2b ip2c
        round 2:        des1a des1c ip1 ip2
        round 3:        des1
        round 4:        top1
Target: top2
        round 1:        ip3 des1b des1a1 des1a2 des1c1 extra1 ip2a ip2b ip2c ipcommon
        round 2:        des1a des1c ip2
        round 3:        des1
        round 4:        top2

Wren

Translation of: Kotlin

Library: Wren-llist

Library: Wren-seq

import "/llist" for DLinkedList
import "/seq" for Lst

var s = "top1, top2, ip1, ip2, ip3, ip1a, ip2a, ip2b, ip2c, ipcommon, des1, " +
        "des1a, des1b, des1c, des1a1, des1a2, des1c1, extra1"

var deps = [
    [ 0, 10], [ 0,  2], [ 0,  3],
    [ 1, 10], [ 1,  3], [ 1,  4],
    [ 2, 17], [ 2,  5], [ 2,  9],
    [ 3,  6], [ 3,  7], [ 3,  8], [ 3,  9],
    [10, 11], [10, 12], [10, 13],
    [11, 14], [11, 15],
    [13, 16], [13, 17],
]

var files = ["top1", "top2", "ip1"]

class Graph {
    construct new(s, edges) {
        _vertices = s.split(", ")
        var nv = _vertices.count
        _adjacency = List.filled(nv, null)
        for (i in 0...nv) _adjacency[i] = List.filled(nv, false)
        for (edge in edges) _adjacency[edge[0]][edge[1]] = true
        _numVertices = nv
    }

    topLevels {
        var result = []
        // look for empty columns
        for (c in 0..._numVertices) {
            var outer = false
            for (r in 0..._numVertices) {
                if (_adjacency[r][c]) {
                    outer = true
                    break
                }
            }
            if (!outer) result.add(_vertices[c])
        }
        return result
    }

    compileOrder(item) {
        var result = DLinkedList.new()
        var queue  = DLinkedList.new()
        queue.add(Lst.indexOf(_vertices, item))
        while (!queue.isEmpty) {
            var r = queue.removeAt(0)
            for (c in 0..._numVertices) {
                if (_adjacency[r][c] && !queue.contains(c)) queue.add(c)
            }
            result.prepend(_vertices[r])
        }
        return Lst.distinct(result.toList)
    }
}

var g = Graph.new(s, deps)
System.print("Top levels: %(g.topLevels)")
for (f in files) System.print("\nCompile order for %(f): %(g.compileOrder(f))")

Output:

Top levels: [top1, top2]

Compile order for top1: [extra1, des1c1, des1a2, des1a1, des1c, des1b, des1a, ip2c, ip2b, ip2a, ipcommon, ip1a, des1, ip2, ip1, top1]

Compile order for top2: [extra1, des1c1, des1a2, des1a1, des1c, des1b, des1a, ipcommon, ip2c, ip2b, ip2a, des1, ip3, ip2, top2]

Compile order for ip1: [extra1, ipcommon, ip1a, ip1]