sagemathgh-38664: graphs: make init_short_digraph always sort neighbo…

…rs but without the extra log complexity (2nd try)

    
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This PR is based on the closed PR sagemath#38427 (by myself) that was breaking
too much doctests.

This PR improve the `init_short_digraph` function that is used to
initialize `StaticSparseCGraph` (used for immutable `Graph` and
`DiGraph`).

Before, a boolean parameter `sort_neighbors` was used to specify if we
wanted to sort the neighbors or not. It implied an extra `log` in the
complexity (as `qsort` was called).
With this PR, the neighbors are always sorted at no extra cost. It is
done by appending to the neighbors list the vertices in the correct
order so the call to `qsort` is not needed anymore.

This PR partly reverts sagemath#38198 and mostly reverts sagemath#37662


Contrary to PR sagemath#38427, I did not include the patch that remove the
sorting of vertices when StaticSparseGraph are initialized because it
was breaking too many doctests. Instead I added a option to disabled
said sorting and use it in my doctests to check that the new code works.

### 📝 Checklist

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- [x] I have created tests covering the changes.
- [ ] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

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URL: sagemath#38664
Reported by: cyrilbouvier
Reviewer(s): David Coudert

src/sage/graphs/asteroidal_triples.pyx

@@ -147,8 +147,7 @@ def is_asteroidal_triple_free(G, certificate=False):
     # module sage.graphs.base.static_sparse_graph
     cdef list int_to_vertex = list(G)
     cdef short_digraph sd
-    init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex,
-                       sort_neighbors=False)
+    init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex)
 
     cdef bitset_t seen
     bitset_init(seen, n)

src/sage/graphs/base/static_sparse_backend.pyx

@@ -425,7 +425,7 @@ cdef class StaticSparseCGraph(CGraph):
 
 cdef class StaticSparseBackend(CGraphBackend):
 
-    def __init__(self, G, loops=False, multiedges=False):
+    def __init__(self, G, loops=False, multiedges=False, sort=True):
         """
         A graph :mod:`backend <sage.graphs.base.graph_backends>` for static
         sparse graphs.
@@ -511,10 +511,11 @@ cdef class StaticSparseBackend(CGraphBackend):
             True
         """
         vertices = list(G)
-        try:
-            vertices.sort()
-        except TypeError:
-            pass
+        if sort:
+            try:
+                vertices.sort()
+            except TypeError:
+                pass
         cdef StaticSparseCGraph cg = <StaticSparseCGraph> StaticSparseCGraph(G, vertices)
         self._cg = cg
 

src/sage/graphs/base/static_sparse_graph.pxd

@@ -7,27 +7,19 @@ ctypedef unsigned int uint
 
 cdef extern from "stdlib.h":
     ctypedef void const_void "const void"
-    void qsort(void *base, int nmemb, int size,
-               int(*compar)(const_void *, const_void *)) nogil
-
     void *bsearch(const_void *key, const_void *base, size_t nmemb,
                   size_t size, int(*compar)(const_void *, const_void *)) nogil
 
-cdef extern from "search.h":
-    void *lfind(const_void *key, const_void *base, size_t *nmemb,
-                  size_t size, int(*compar)(const_void *, const_void *)) nogil
-
 ctypedef struct short_digraph_s:
     uint32_t * edges
     uint32_t ** neighbors
     PyObject * edge_labels
     int m
     int n
-    bint sorted_neighbors
 
 ctypedef short_digraph_s short_digraph[1]
 
-cdef int init_short_digraph(short_digraph g, G, edge_labelled=?, vertex_list=?, sort_neighbors=?) except -1
+cdef int init_short_digraph(short_digraph g, G, edge_labelled=?, vertex_list=?) except -1
 cdef void free_short_digraph(short_digraph g) noexcept
 cdef int init_reverse(short_digraph dst, short_digraph src) except -1
 cdef int out_degree(short_digraph g, int u) noexcept