/*
   igraph library.
   Copyright (C) 2006-2020 The igraph development team

   This program is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 2 of the License, or
   (at your option) any later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with this program; if not, write to the Free Software
   Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
   02110-1301 USA

*/

#include "igraph_operators.h"

#include "igraph_constructors.h"
#include "igraph_interface.h"

#include "core/interruption.h"

/**
 * \function igraph_compose
 * \brief Calculates the composition of two graphs.
 *
 * The composition of graphs contains the same number of vertices as
 * the bigger graph of the two operands. It contains an (i,j) edge if
 * and only if there is a k vertex, such that the first graph
 * contains an (i,k) edge and the second graph a (k,j) edge.
 *
 * </para><para>
 * This is of course exactly the composition of two binary relations.
 *
 * </para><para>
 * The two graphs must have the same directedness, otherwise the function
 * returns with an error. Note that for undirected graphs the two relations
 * are by definition symmetric.
 *
 * \param res Pointer to an uninitialized graph object, the result
 *        will be stored here.
 * \param g1 The first operand, a graph object.
 * \param g2 The second operand, another graph object.
 * \param edge_map1 If not a null pointer, then it must be a pointer
 *        to an initialized vector, and a mapping from the edges of
 *        the result graph to the edges of the first graph is stored
 *        here.
 * \param edge_map2 If not a null pointer, then it must be a pointer
 *        to an initialized vector, and a mapping from the edges of
 *        the result graph to the edges of the second graph is stored
 *        here.
 * \return Error code.
 *
 * Time complexity: O(|V|*d1*d2), |V| is the number of vertices in the
 * first graph, d1 and d2 the average degree in the first and second
 * graphs.
 *
 * \example examples/simple/igraph_compose.c
 */
igraph_error_t igraph_compose(igraph_t *res,
                              const igraph_t *g1,
                              const igraph_t *g2,
                              igraph_vector_int_t *edge_map1,
                              igraph_vector_int_t *edge_map2) {

    const igraph_int_t no_of_nodes_left = igraph_vcount(g1);
    const igraph_int_t no_of_nodes_right = igraph_vcount(g2);
    const igraph_bool_t directed = igraph_is_directed(g1);
    const igraph_int_t no_of_nodes = no_of_nodes_left > no_of_nodes_right ?
                                             no_of_nodes_left : no_of_nodes_right;
    igraph_vector_int_t edges;
    igraph_vector_int_t neis1, neis2;

    if (directed != igraph_is_directed(g2)) {
        IGRAPH_ERROR("Cannot compose directed and undirected graph.",
                     IGRAPH_EINVAL);
    }

    IGRAPH_VECTOR_INT_INIT_FINALLY(&edges, 0);
    IGRAPH_VECTOR_INT_INIT_FINALLY(&neis1, 0);
    IGRAPH_VECTOR_INT_INIT_FINALLY(&neis2, 0);

    if (edge_map1) {
        igraph_vector_int_clear(edge_map1);
    }
    if (edge_map2) {
        igraph_vector_int_clear(edge_map2);
    }

    for (igraph_int_t i = 0; i < no_of_nodes_left; i++) {
        IGRAPH_ALLOW_INTERRUPTION();
        IGRAPH_CHECK(igraph_incident(g1, &neis1, i, IGRAPH_OUT, IGRAPH_LOOPS));
        while (!igraph_vector_int_empty(&neis1)) {
            const igraph_int_t con = igraph_vector_int_pop_back(&neis1);
            const igraph_int_t v1 = IGRAPH_OTHER(g1, con, i);
            if (v1 < no_of_nodes_right) {
                IGRAPH_CHECK(igraph_incident(g2, &neis2, v1, IGRAPH_OUT, IGRAPH_LOOPS));
            } else {
                continue;
            }
            while (!igraph_vector_int_empty(&neis2)) {
                const igraph_int_t con2 = igraph_vector_int_pop_back(&neis2);
                const igraph_int_t v2 = IGRAPH_OTHER(g2, con2, v1);
                IGRAPH_CHECK(igraph_vector_int_push_back(&edges, i));
                IGRAPH_CHECK(igraph_vector_int_push_back(&edges, v2));
                if (edge_map1) {
                    IGRAPH_CHECK(igraph_vector_int_push_back(edge_map1, con));
                }
                if (edge_map2) {
                    IGRAPH_CHECK(igraph_vector_int_push_back(edge_map2, con2));
                }
            }
        }
    }

    igraph_vector_int_destroy(&neis1);
    igraph_vector_int_destroy(&neis2);
    IGRAPH_FINALLY_CLEAN(2);

    IGRAPH_CHECK(igraph_create(res, &edges, no_of_nodes, directed));

    igraph_vector_int_destroy(&edges);
    IGRAPH_FINALLY_CLEAN(1);
    return IGRAPH_SUCCESS;
}
