Topological sort/Extracted top item
Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.
For comparing various sorts, see compare sorts.
For other sorting algorithms, see sorting algorithms, or:
Heap sort | Merge sort | Patience sort | Quick sort
O(n log2n) sorts
Shell Sort
O(n2) sorts
Bubble sort |
Cocktail sort |
Cocktail sort with shifting bounds |
Comb sort |
Cycle sort |
Gnome sort |
Insertion sort |
Selection sort |
Strand sort
other sorts
Bead sort |
Bogo sort |
Common sorted list |
Composite structures sort |
Custom comparator sort |
Counting sort |
Disjoint sublist sort |
External sort |
Jort sort |
Lexicographical sort |
Natural sorting |
Order by pair comparisons |
Order disjoint list items |
Order two numerical lists |
Object identifier (OID) sort |
Pancake sort |
Quickselect |
Permutation sort |
Radix sort |
Ranking methods |
Remove duplicate elements |
Sleep sort |
Stooge sort |
[Sort letters of a string] |
Three variable sort |
Topological sort |
Tree sort
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:
- Has dependents.
- 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:
- Determines the top levels from the dependencies and show them.
- Extracts a compile order of files to compile any given (usually top level) file.
- Give a compile order for file top1.
- 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
C
Take code from Topological sort#c and add/change the following: <lang c>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; }</lang>output (the last item is just to show that it doesn't have to be top level)<lang>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</lang>
Go
<lang 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
}</lang>
- 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:
<lang j>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 </lang>
The changes include:
- Added an argument for the target(s) we wish to find dependencies for
- Make sure that these targets are included in our dependency structures
- Make sure that things we can depend on are included in our dependency structures
- Select these targets, and the things they depend on, once we know what depends on what
- When ordering names by dependencies:
- only consider names and dependencies we want to keep
- extract names grouped by their dependency chain length
Example:
<lang j>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 </lang>
Java
<lang java>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()); }
}</lang>
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
<lang 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
</lang>
- 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
<lang scala>// 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)}")
}</lang>
- 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]
Perl
<lang 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';</lang>
- 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". <lang Phix>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],no_empty:=true), 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"})</lang>
- 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. <lang python>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))</lang>
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>#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))</lang>
- 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) <lang perl6>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');</lang>
- 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.
<lang REXX>/*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. */</lang>
- 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:
<lang Tcl>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" }
}</lang>
- 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
<lang ecmascript>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))")</lang>
- 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]