gh-39223: avoid some conversions to `short_digraph` in `distances_all_pairs.pyx`
    
Similarly to #39216, we avoid the conversion to `short_digraph` in
`distances_all_pairs.pyx` when the input graph is an instance of
`StaticSparseBackend`.

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- [x] The description explains in detail what this PR is about.
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- [ ] I have updated the documentation and checked the documentation
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### ⌛ Dependencies

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URL: #39223
Reported by: David Coudert
Reviewer(s): Frédéric Chapoton

Author: Release Manager

src/sage/graphs/distances_all_pairs.pyx

@@ -122,17 +122,18 @@ Functions
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.data_structures.binary_matrix cimport *
 from libc.string cimport memset
 from libc.stdint cimport uint64_t, UINT64_MAX
 from libc.stdint cimport uint32_t, INT32_MAX, UINT32_MAX
 from cysignals.memory cimport sig_malloc, sig_calloc, sig_free
 from cysignals.signals cimport sig_on, sig_off
 from memory_allocator cimport MemoryAllocator
 
+from sage.data_structures.binary_matrix cimport *
 from sage.graphs.base.c_graph cimport CGraphBackend
 from sage.graphs.base.c_graph cimport CGraph
-
+from sage.graphs.base.static_sparse_backend cimport StaticSparseCGraph
+from sage.graphs.base.static_sparse_backend cimport StaticSparseBackend
 from sage.graphs.base.static_sparse_graph cimport (short_digraph,
                                                    init_short_digraph,
                                                    init_reverse,
@@ -446,15 +447,15 @@ def distances_all_pairs(G):
         sage: g = graphs.PetersenGraph()
         sage: distances_all_pairs(g)
         {0: {0: 0, 1: 1, 2: 2, 3: 2, 4: 1, 5: 1, 6: 2, 7: 2, 8: 2, 9: 2},
-        1: {0: 1, 1: 0, 2: 1, 3: 2, 4: 2, 5: 2, 6: 1, 7: 2, 8: 2, 9: 2},
-        2: {0: 2, 1: 1, 2: 0, 3: 1, 4: 2, 5: 2, 6: 2, 7: 1, 8: 2, 9: 2},
-        3: {0: 2, 1: 2, 2: 1, 3: 0, 4: 1, 5: 2, 6: 2, 7: 2, 8: 1, 9: 2},
-        4: {0: 1, 1: 2, 2: 2, 3: 1, 4: 0, 5: 2, 6: 2, 7: 2, 8: 2, 9: 1},
-        5: {0: 1, 1: 2, 2: 2, 3: 2, 4: 2, 5: 0, 6: 2, 7: 1, 8: 1, 9: 2},
-        6: {0: 2, 1: 1, 2: 2, 3: 2, 4: 2, 5: 2, 6: 0, 7: 2, 8: 1, 9: 1},
-        7: {0: 2, 1: 2, 2: 1, 3: 2, 4: 2, 5: 1, 6: 2, 7: 0, 8: 2, 9: 1},
-        8: {0: 2, 1: 2, 2: 2, 3: 1, 4: 2, 5: 1, 6: 1, 7: 2, 8: 0, 9: 2},
-        9: {0: 2, 1: 2, 2: 2, 3: 2, 4: 1, 5: 2, 6: 1, 7: 1, 8: 2, 9: 0}}
+         1: {0: 1, 1: 0, 2: 1, 3: 2, 4: 2, 5: 2, 6: 1, 7: 2, 8: 2, 9: 2},
+         2: {0: 2, 1: 1, 2: 0, 3: 1, 4: 2, 5: 2, 6: 2, 7: 1, 8: 2, 9: 2},
+         3: {0: 2, 1: 2, 2: 1, 3: 0, 4: 1, 5: 2, 6: 2, 7: 2, 8: 1, 9: 2},
+         4: {0: 1, 1: 2, 2: 2, 3: 1, 4: 0, 5: 2, 6: 2, 7: 2, 8: 2, 9: 1},
+         5: {0: 1, 1: 2, 2: 2, 3: 2, 4: 2, 5: 0, 6: 2, 7: 1, 8: 1, 9: 2},
+         6: {0: 2, 1: 1, 2: 2, 3: 2, 4: 2, 5: 2, 6: 0, 7: 2, 8: 1, 9: 1},
+         7: {0: 2, 1: 2, 2: 1, 3: 2, 4: 2, 5: 1, 6: 2, 7: 0, 8: 2, 9: 1},
+         8: {0: 2, 1: 2, 2: 2, 3: 1, 4: 2, 5: 1, 6: 1, 7: 2, 8: 0, 9: 2},
+         9: {0: 2, 1: 2, 2: 2, 3: 2, 4: 1, 5: 2, 6: 1, 7: 1, 8: 2, 9: 0}}
     """
     from sage.rings.infinity import Infinity
 
@@ -1806,6 +1807,17 @@ def diameter(G, algorithm=None, source=None):
         sage: G = graphs.PathGraph(1)
         sage: diameter(G, algorithm='iFUB')
         0
+
+    Immutable graphs::
+
+        sage: G = graphs.RandomGNP(10, .5)
+        sage: G._backend
+        <sage.graphs.base.sparse_graph.SparseGraphBackend ...>
+        sage: H = Graph(G, immutable=True)
+        sage: H._backend
+        <sage.graphs.base.static_sparse_backend.StaticSparseBackend ...>
+        sage: diameter(G, algorithm='iFUB') == diameter(H, algorithm='iFUB')
+        True
     """
     cdef uint32_t n = G.order()
     if n <= 1:
@@ -1832,9 +1844,16 @@ def diameter(G, algorithm=None, source=None):
     # Copying the whole graph to obtain the list of neighbors quicker than by
     # calling out_neighbors. This data structure is well documented in the
     # module sage.graphs.base.static_sparse_graph
-    cdef list int_to_vertex = list(G)
+    cdef list int_to_vertex
+    cdef StaticSparseCGraph cg
     cdef short_digraph sd
-    init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex)
+    if isinstance(G, StaticSparseBackend):
+        cg = <StaticSparseCGraph> G._cg
+        sd = <short_digraph> cg.g
+        int_to_vertex = cg._vertex_to_labels
+    else:
+        int_to_vertex = list(G)
+        init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex)
     cdef short_digraph rev_sd  # to store copy of sd with edges reversed
 
     # and we map the source to an int in [0,n-1]
@@ -1849,7 +1868,8 @@ def diameter(G, algorithm=None, source=None):
         bitset_init(seen, n)
         tab = <uint32_t*> sig_malloc(2* n * sizeof(uint32_t))
         if not tab:
-            free_short_digraph(sd)
+            if not isinstance(G, StaticSparseBackend):
+                free_short_digraph(sd)
             bitset_free(seen)
             raise MemoryError()
 
@@ -1875,7 +1895,8 @@ def diameter(G, algorithm=None, source=None):
     else:  # algorithm == 'iFUB'
         LB = diameter_iFUB(sd, isource)
 
-    free_short_digraph(sd)
+    if not isinstance(G, StaticSparseBackend):
+        free_short_digraph(sd)
 
     if LB < 0 or LB > n:
         from sage.rings.infinity import Infinity
@@ -1926,6 +1947,17 @@ def radius_DHV(G):
         Traceback (most recent call last):
         ...
         TypeError: this method works for unweighted undirected graphs only
+
+    Immutable graphs::
+
+        sage: G = graphs.RandomGNP(10, .5)
+        sage: G._backend
+        <sage.graphs.base.sparse_graph.SparseGraphBackend ...>
+        sage: H = Graph(G, immutable=True)
+        sage: H._backend
+        <sage.graphs.base.static_sparse_backend.StaticSparseBackend ...>
+        sage: radius_DHV(G) == radius_DHV(H)
+        True
     """
     if G.is_directed():
         raise TypeError("this method works for unweighted undirected graphs only")
@@ -1934,9 +1966,16 @@ def radius_DHV(G):
     if n <= 1:
         return 0
 
-    cdef list int_to_vertex = list(G)
+    cdef list int_to_vertex
+    cdef StaticSparseCGraph cg
     cdef short_digraph sd
-    init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex)
+    if isinstance(G, StaticSparseBackend):
+        cg = <StaticSparseCGraph> G._cg
+        sd = <short_digraph> cg.g
+        int_to_vertex = cg._vertex_to_labels
+    else:
+        int_to_vertex = list(G)
+        init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex)
 
     cdef uint32_t source, ecc_source
     cdef uint32_t antipode, ecc_antipode
@@ -1946,6 +1985,8 @@ def radius_DHV(G):
     cdef MemoryAllocator mem = MemoryAllocator()
     cdef uint32_t * distances = <uint32_t *>mem.malloc(3 * n * sizeof(uint32_t))
     if not distances:
+        if not isinstance(G, StaticSparseBackend):
+            free_short_digraph(sd)
         raise MemoryError()
 
     cdef uint32_t * waiting_list = distances + n
@@ -1987,7 +2028,8 @@ def radius_DHV(G):
                 LB = ecc_lower_bound[v]
                 source = v  # vertex with minimum eccentricity lower bound
 
-    free_short_digraph(sd)
+    if not isinstance(G, StaticSparseBackend):
+        free_short_digraph(sd)
     bitset_free(seen)
     if UB == UINT32_MAX:
         from sage.rings.infinity import Infinity
@@ -2041,6 +2083,19 @@ def wiener_index(G):
         Traceback (most recent call last):
         ...
         ValueError: Wiener index is not defined for the empty graph
+
+    TESTS:
+
+    Immutable graphs::
+
+        sage: G = graphs.RandomGNP(10, .5)
+        sage: G._backend
+        <sage.graphs.base.sparse_graph.SparseGraphBackend ...>
+        sage: H = Graph(G, immutable=True)
+        sage: H._backend
+        <sage.graphs.base.static_sparse_backend.StaticSparseBackend ...>
+        sage: G.wiener_index() == H.wiener_index()
+        True
     """
     if not G:
         raise ValueError("Wiener index is not defined for the empty graph")
@@ -2052,8 +2107,13 @@ def wiener_index(G):
     # Copying the whole graph to obtain the list of neighbors quicker than by
     # calling out_neighbors.  This data structure is well documented in the
     # module sage.graphs.base.static_sparse_graph
+    cdef StaticSparseCGraph cg
     cdef short_digraph sd
-    init_short_digraph(sd, G, edge_labelled=False, vertex_list=list(G))
+    if isinstance(G, StaticSparseBackend):
+        cg = <StaticSparseCGraph> G._cg
+        sd = <short_digraph> cg.g
+    else:
+        init_short_digraph(sd, G, edge_labelled=False, vertex_list=list(G))
 
     # allocated some data structures
     cdef bitset_t seen
@@ -2074,7 +2134,8 @@ def wiener_index(G):
         for v in range(0 if G.is_directed() else (u + 1), n):
             s += distances[v]
 
-    free_short_digraph(sd)
+    if not isinstance(G, StaticSparseBackend):
+        free_short_digraph(sd)
     bitset_free(seen)
 
     if s == UINT64_MAX:
@@ -2342,6 +2403,18 @@ def szeged_index(G, algorithm=None):
         Traceback (most recent call last):
         ...
         ValueError: the 'low' algorithm cannot be used on digraphs
+
+    Immutable graphs::
+
+        sage: G = graphs.RandomGNP(10, .3)
+        sage: G.add_edges(graphs.RandomTree(10).edges())
+        sage: G._backend
+        <sage.graphs.base.sparse_graph.SparseGraphBackend ...>
+        sage: H = Graph(G, immutable=True)
+        sage: H._backend
+        <sage.graphs.base.static_sparse_backend.StaticSparseBackend ...>
+        sage: szeged_index(G) == szeged_index(H)
+        True
     """
     if not G.is_connected():
         raise ValueError("the Szeged index is defined for connected graphs only")
@@ -2364,16 +2437,23 @@ def szeged_index(G, algorithm=None):
     if G.order() <= 1:
         return 0
 
+    cdef StaticSparseCGraph cg
     cdef short_digraph sd
-    init_short_digraph(sd, G, edge_labelled=False, vertex_list=list(G))
+    if isinstance(G, StaticSparseBackend):
+        cg = <StaticSparseCGraph> G._cg
+        sd = <short_digraph> cg.g
+    else:
+        init_short_digraph(sd, G, edge_labelled=False, vertex_list=list(G))
+
     cdef uint64_t s
 
     if algorithm == "low":
         s = c_szeged_index_low_memory(sd)
     else:
         s = c_szeged_index_high_memory(sd)
 
-    free_short_digraph(sd)
+    if not isinstance(G, StaticSparseBackend):
+        free_short_digraph(sd)
     return s
 
 
@@ -2441,13 +2521,31 @@ def distances_distribution(G):
         sage: D = digraphs.DeBruijn(2,3)                                                # needs sage.combinat
         sage: D.distances_distribution()                                                # needs sage.combinat
         {1: 1/4, 2: 11/28, 3: 5/14}
+
+    TESTS:
+
+    Immutable graphs::
+
+        sage: G = graphs.RandomGNP(10, .5)
+        sage: G._backend
+        <sage.graphs.base.sparse_graph.SparseGraphBackend ...>
+        sage: H = Graph(G, immutable=True)
+        sage: H._backend
+        <sage.graphs.base.static_sparse_backend.StaticSparseBackend ...>
+        sage: G.distances_distribution() == H.distances_distribution()
+        True
     """
     cdef size_t n = G.order()
     if n <= 1:
         return {}
 
+    cdef StaticSparseCGraph cg
     cdef short_digraph sd
-    init_short_digraph(sd, G, edge_labelled=False, vertex_list=list(G))
+    if isinstance(G, StaticSparseBackend):
+        cg = <StaticSparseCGraph> G._cg
+        sd = <short_digraph> cg.g
+    else:
+        init_short_digraph(sd, G, edge_labelled=False, vertex_list=list(G))
 
     cdef MemoryAllocator mem = MemoryAllocator()
     cdef uint32_t * distances = <uint32_t *> mem.allocarray(2 * n, sizeof(uint32_t))
@@ -2470,7 +2568,8 @@ def distances_distribution(G):
             for v in range(n):
                 count[distances[v]] += 1
 
-    free_short_digraph(sd)
+    if not isinstance(G, StaticSparseBackend):
+        free_short_digraph(sd)
     bitset_free(seen)
 
     from sage.rings.infinity import Infinity
@@ -2554,6 +2653,17 @@ def antipodal_graph(G):
         Antipodal graph of Graph on 1 vertex: Looped graph on 1 vertex
         sage: antipodal_graph(Graph(2)).edges(sort=True, labels=False)
         [(0, 1)]
+
+    Immutable graphs::
+
+        sage: G = graphs.RandomGNP(10, .5)
+        sage: G._backend
+        <sage.graphs.base.sparse_graph.SparseGraphBackend ...>
+        sage: H = Graph(G, immutable=True)
+        sage: H._backend
+        <sage.graphs.base.static_sparse_backend.StaticSparseBackend ...>
+        sage: antipodal_graph(G).is_isomorphic(antipodal_graph(H))
+        True
     """
     if not G:
         raise ValueError("the antipodal graph of the empty graph is not defined")
@@ -2577,9 +2687,16 @@ def antipodal_graph(G):
             A.add_edges(itertools.product(c1, c2))
         return A
 
-    cdef list int_to_vertex = list(G)
+    cdef list int_to_vertex
+    cdef StaticSparseCGraph cg
     cdef short_digraph sd
-    init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex)
+    if isinstance(G, StaticSparseBackend):
+        cg = <StaticSparseCGraph> G._cg
+        sd = <short_digraph> cg.g
+        int_to_vertex = cg._vertex_to_labels
+    else:
+        int_to_vertex = list(G)
+        init_short_digraph(sd, G, edge_labelled=False, vertex_list=int_to_vertex)
 
     cdef MemoryAllocator mem = MemoryAllocator()
     cdef uint32_t * distances = <uint32_t *> mem.allocarray(2 * n, sizeof(uint32_t))
@@ -2607,7 +2724,8 @@ def antipodal_graph(G):
                     A.add_edge(u, int_to_vertex[vj])
                 j -= 1
 
-    free_short_digraph(sd)
+    if not isinstance(G, StaticSparseBackend):
+        free_short_digraph(sd)
     bitset_free(seen)
 
     A.add_vertices(G)