/* -*- mode: C -*-  */
/*
   IGraph library.
   Copyright (C) 2003-2012  Gabor Csardi <csardi.gabor@gmail.com>
   334 Harvard street, Cambridge, MA 02139 USA

   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_memory.h"
#include "igraph_error.h"
#include "igraph_random.h"

#include <assert.h>
#include <string.h>         /* memcpy & co. */
#include <stdlib.h>
#include <stdarg.h>     /* va_start & co */
#include <math.h>


void igraph_qsort_r(void *a, size_t n, size_t es, void *thunk, int (*cmp)(void *, const void *, const void *));
void igraph_qsort(void *a, size_t n, size_t es, int (*cmp)(void *, const void *, const void *));


/**
 * \ingroup vector
 * \section about_igraph_vector_t_objects About \type igraph_vector_t objects
 *
 * <para>The \type igraph_vector_t data type is a simple and efficient
 * interface to arrays containing numbers. It is something
 * similar as (but much simpler than) the \type vector template
 * in the C++ standard library.</para>
 *
 * <para>Vectors are used extensively in \a igraph, all
 * functions which expect or return a list of numbers use
 * igraph_vector_t to achieve this.</para>
 *
 * <para>The \type igraph_vector_t type usually uses
 * O(n) space
 * to store n elements. Sometimes it
 * uses more, this is because vectors can shrink, but even if they
 * shrink, the current implementation does not free a single bit of
 * memory.</para>
 *
 * <para>The elements in an \type igraph_vector_t
 * object are indexed from zero, we follow the usual C convention
 * here.</para>
 *
 * <para>The elements of a vector always occupy a single block of
 * memory, the starting address of this memory block can be queried
 * with the \ref VECTOR macro. This way, vector objects can be used
 * with standard mathematical libraries, like the GNU Scientific
 * Library.</para>
 */

/**
 * \ingroup vector
 * \section igraph_vector_constructors_and_destructors Constructors and
 * Destructors
 *
 * <para>\type igraph_vector_t objects have to be initialized before using
 * them, this is analogous to calling a constructor on them. There are a
 * number of \type igraph_vector_t constructors, for your
 * convenience. \ref igraph_vector_init() is the basic constructor, it
 * creates a vector of the given length, filled with zeros.
 * \ref igraph_vector_copy() creates a new identical copy
 * of an already existing and initialized vector. \ref
 * igraph_vector_init_copy() creates a vector by copying a regular C array.
 * \ref igraph_vector_init_seq() creates a vector containing a regular
 * sequence with increment one.</para>
 *
 * <para>\ref igraph_vector_view() is a special constructor, it allows you to
 * handle a regular C array as a \type vector without copying
 * its elements.
 * </para>
 *
 * <para>If a \type igraph_vector_t object is not needed any more, it
 * should be destroyed to free its allocated memory by calling the
 * \type igraph_vector_t destructor, \ref igraph_vector_destroy().</para>
 *
 * <para> Note that vectors created by \ref igraph_vector_view() are special,
 * you mustn't call \ref igraph_vector_destroy() on these.</para>
 */

/**
 * \ingroup vector
 * \function igraph_vector_init
 * \brief Initializes a vector object (constructor).
 *
 * </para><para>
 * Every vector needs to be initialized before it can be used, and
 * there are a number of initialization functions or otherwise called
 * constructors. This function constructs a vector of the given size and
 * initializes each entry to 0. Note that \ref igraph_vector_null() can be
 * used to set each element of a vector to zero. However, if you want a
 * vector of zeros, it is much faster to use this function than to create a
 * vector and then invoke \ref igraph_vector_null().
 *
 * </para><para>
 * Every vector object initialized by this function should be
 * destroyed (ie. the memory allocated for it should be freed) when it
 * is not needed anymore, the \ref igraph_vector_destroy() function is
 * responsible for this.
 * \param v Pointer to a not yet initialized vector object.
 * \param size The size of the vector.
 * \return error code:
 *       \c IGRAPH_ENOMEM if there is not enough memory.
 *
 * Time complexity: operating system dependent, the amount of
 * \quote time \endquote required to allocate
 * O(n) elements,
 * n is the number of elements.
 */

int FUNCTION(igraph_vector, init)      (TYPE(igraph_vector)* v, int long size) {
    long int alloc_size = size > 0 ? size : 1;
    if (size < 0) {
        size = 0;
    }
    v->stor_begin = igraph_Calloc(alloc_size, BASE);
    if (v->stor_begin == 0) {
        IGRAPH_ERROR("cannot init vector", IGRAPH_ENOMEM);
    }
    v->stor_end = v->stor_begin + alloc_size;
    v->end = v->stor_begin + size;

    return 0;
}

/**
 * \ingroup vector
 * \function igraph_vector_view
 * \brief Handle a regular C array as a \type igraph_vector_t.
 *
 * </para><para>
 * This is a special \type igraph_vector_t constructor. It allows to
 * handle a regular C array as a \type igraph_vector_t temporarily.
 * Be sure that you \em don't ever call the destructor (\ref
 * igraph_vector_destroy()) on objects created by this constructor.
 * \param v Pointer to an uninitialized \type igraph_vector_t object.
 * \param data Pointer, the C array. It may not be \c NULL.
 * \param length The length of the C array.
 * \return Pointer to the vector object, the same as the
 *     \p v parameter, for convenience.
 *
 * Time complexity: O(1)
 */

const TYPE(igraph_vector)*FUNCTION(igraph_vector, view) (const TYPE(igraph_vector) *v,
        const BASE *data,
        long int length) {
    TYPE(igraph_vector) *v2 = (TYPE(igraph_vector)*)v;

    assert(data != 0);

    v2->stor_begin = (BASE*)data;
    v2->stor_end = (BASE*)data + length;
    v2->end = v2->stor_end;
    return v;
}

#ifndef BASE_COMPLEX

/**
 * \ingroup vector
 * \function igraph_vector_init_real
 * \brief Create an \type igraph_vector_t from the parameters.
 *
 * </para><para>
 * Because of how C and the C library handles variable length argument
 * lists, it is required that you supply real constants to this
 * function. This means that
 * \verbatim igraph_vector_t v;
 * igraph_vector_init_real(&amp;v, 5, 1,2,3,4,5); \endverbatim
 * is an error at runtime and the results are undefined. This is
 * the proper way:
 * \verbatim igraph_vector_t v;
 * igraph_vector_init_real(&amp;v, 5, 1.0,2.0,3.0,4.0,5.0); \endverbatim
 * \param v Pointer to an uninitialized \type igraph_vector_t object.
 * \param no Positive integer, the number of \type igraph_real_t
 *    parameters to follow.
 * \param ... The elements of the vector.
 * \return Error code, this can be \c IGRAPH_ENOMEM
 *     if there isn't enough memory to allocate the vector.
 *
 * \sa \ref igraph_vector_init_real_end(), \ref igraph_vector_init_int() for similar
 * functions.
 *
 * Time complexity: depends on the time required to allocate memory,
 * but at least O(n), the number of
 * elements in the vector.
 */

int FUNCTION(igraph_vector, init_real)(TYPE(igraph_vector) *v, int no, ...) {
    int i = 0;
    va_list ap;
    IGRAPH_CHECK(FUNCTION(igraph_vector, init)(v, no));

    va_start(ap, no);
    for (i = 0; i < no; i++) {
        VECTOR(*v)[i] = (BASE) va_arg(ap, double);
    }
    va_end(ap);

    return 0;
}

/**
 * \ingroup vector
 * \function igraph_vector_init_real_end
 * \brief Create an \type igraph_vector_t from the parameters.
 *
 * </para><para>
 * This constructor is similar to \ref igraph_vector_init_real(), the only
 * difference is that instead of giving the number of elements in the
 * vector, a special marker element follows the last real vector
 * element.
 * \param v Pointer to an uninitialized \type igraph_vector_t object.
 * \param endmark This element will signal the end of the vector. It
 *    will \em not be part of the vector.
 * \param ... The elements of the vector.
 * \return Error code, \c IGRAPH_ENOMEM if there
 *    isn't enough memory.
 *
 * \sa \ref igraph_vector_init_real() and \ref igraph_vector_init_int_end() for
 * similar functions.
 *
 * Time complexity: at least O(n) for
 * n elements plus the time
 * complexity of the memory allocation.
 */

int FUNCTION(igraph_vector, init_real_end)(TYPE(igraph_vector) *v,
        BASE endmark, ...) {
    int i = 0, n = 0;
    va_list ap;

    va_start(ap, endmark);
    while (1) {
        BASE num = (BASE) va_arg(ap, double);
        if (num == endmark) {
            break;
        }
        n++;
    }
    va_end(ap);

    IGRAPH_CHECK(FUNCTION(igraph_vector, init)(v, n));
    IGRAPH_FINALLY(FUNCTION(igraph_vector, destroy), v);

    va_start(ap, endmark);
    for (i = 0; i < n; i++) {
        VECTOR(*v)[i] = (BASE) va_arg(ap, double);
    }
    va_end(ap);

    IGRAPH_FINALLY_CLEAN(1);
    return 0;
}

/**
 * \ingroup vector
 * \function igraph_vector_init_int
 * \brief Create an \type igraph_vector_t containing the parameters.
 *
 * </para><para>
 * This function is similar to \ref igraph_vector_init_real(), but it expects
 * \type int parameters. It is important that all parameters
 * should be of this type, otherwise the result of the function call
 * is undefined.
 * \param v Pointer to an uninitialized \type igraph_vector_t object.
 * \param no The number of \type int parameters to follow.
 * \param ... The elements of the vector.
 * \return Error code, \c IGRAPH_ENOMEM if there is
 *    not enough memory.
 * \sa \ref igraph_vector_init_real() and igraph_vector_init_int_end(), these are
 *    similar functions.
 *
 * Time complexity: at least O(n) for
 * n elements plus the time
 * complexity of the memory allocation.
 */

int FUNCTION(igraph_vector, init_int)(TYPE(igraph_vector) *v, int no, ...) {
    int i = 0;
    va_list ap;
    IGRAPH_CHECK(FUNCTION(igraph_vector, init)(v, no));

    va_start(ap, no);
    for (i = 0; i < no; i++) {
        VECTOR(*v)[i] = (BASE) va_arg(ap, int);
    }
    va_end(ap);

    return 0;
}

/**
 * \ingroup vector
 * \function igraph_vector_init_int_end
 * \brief Create an \type igraph_vector_t from the parameters.
 *
 * </para><para>
 * This constructor is similar to \ref igraph_vector_init_int(), the only
 * difference is that instead of giving the number of elements in the
 * vector, a special marker element follows the last real vector
 * element.
 * \param v Pointer to an uninitialized \type igraph_vector_t object.
 * \param endmark This element will signal the end of the vector. It
 *    will \em not be part of the vector.
 * \param ... The elements of the vector.
 * \return Error code, \c IGRAPH_ENOMEM if there
 *    isn't enough memory.
 *
 * \sa \ref igraph_vector_init_int() and \ref igraph_vector_init_real_end() for
 * similar functions.
 *
 * Time complexity: at least O(n) for
 * n elements plus the time
 * complexity of the memory allocation.
 */

int FUNCTION(igraph_vector_init, int_end)(TYPE(igraph_vector) *v, int endmark, ...) {
    int i = 0, n = 0;
    va_list ap;

    va_start(ap, endmark);
    while (1) {
        int num = va_arg(ap, int);
        if (num == endmark) {
            break;
        }
        n++;
    }
    va_end(ap);

    IGRAPH_CHECK(FUNCTION(igraph_vector, init)(v, n));
    IGRAPH_FINALLY(FUNCTION(igraph_vector, destroy), v);

    va_start(ap, endmark);
    for (i = 0; i < n; i++) {
        VECTOR(*v)[i] = (BASE) va_arg(ap, int);
    }
    va_end(ap);

    IGRAPH_FINALLY_CLEAN(1);
    return 0;
}

#endif /* ifndef BASE_COMPLEX */

/**
 * \ingroup vector
 * \function igraph_vector_destroy
 * \brief Destroys a vector object.
 *
 * </para><para>
 * All vectors initialized by \ref igraph_vector_init() should be properly
 * destroyed by this function. A destroyed vector needs to be
 * reinitialized by \ref igraph_vector_init(), \ref igraph_vector_init_copy() or
 * another constructor.
 * \param v Pointer to the (previously initialized) vector object to
 *        destroy.
 *
 * Time complexity: operating system dependent.
 */

void FUNCTION(igraph_vector, destroy)   (TYPE(igraph_vector)* v) {
    assert(v != 0);
    if (v->stor_begin != 0) {
        igraph_Free(v->stor_begin);
        v->stor_begin = NULL;
    }
}

/**
 * \ingroup vector
 * \function igraph_vector_capacity
 * \brief Returns the allocated capacity of the vector
 *
 * Note that this might be different from the size of the vector (as
 * queried by \ref igraph_vector_size(), and specifies how many elements
 * the vector can hold, without reallocation.
 * \param v Pointer to the (previously initialized) vector object
 *          to query.
 * \return The allocated capacity.
 *
 * \sa \ref igraph_vector_size().
 *
 * Time complexity: O(1).
 */

long int FUNCTION(igraph_vector, capacity)(const TYPE(igraph_vector)*v) {
    return v->stor_end - v->stor_begin;
}

/**
 * \ingroup vector
 * \function igraph_vector_reserve
 * \brief Reserves memory for a vector.
 *
 * </para><para>
 * \a igraph vectors are flexible, they can grow and
 * shrink. Growing
 * however occasionally needs the data in the vector to be copied.
 * In order to avoid this, you can call this function to reserve space for
 * future growth of the vector.
 *
 * </para><para>
 * Note that this function does \em not change the size of the
 * vector. Let us see a small example to clarify things: if you
 * reserve space for 100 elements and the size of your
 * vector was (and still is) 60, then you can surely add additional 40
 * elements to your vector before it will be copied.
 * \param v The vector object.
 * \param size The new \em allocated size of the vector.
 * \return Error code:
 *         \c IGRAPH_ENOMEM if there is not enough memory.
 *
 * Time complexity: operating system dependent, should be around
 * O(n), n
 * is the new allocated size of the vector.
 */

int FUNCTION(igraph_vector, reserve)   (TYPE(igraph_vector)* v, long int size) {
    long int actual_size = FUNCTION(igraph_vector, size)(v);
    BASE *tmp;
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    if (size <= FUNCTION(igraph_vector, size)(v)) {
        return 0;
    }

    tmp = igraph_Realloc(v->stor_begin, (size_t) size, BASE);
    if (tmp == 0) {
        IGRAPH_ERROR("cannot reserve space for vector", IGRAPH_ENOMEM);
    }
    v->stor_begin = tmp;
    v->stor_end = v->stor_begin + size;
    v->end = v->stor_begin + actual_size;

    return 0;
}

/**
 * \ingroup vector
 * \function igraph_vector_empty
 * \brief Decides whether the size of the vector is zero.
 *
 * \param v The vector object.
 * \return Non-zero number (true) if the size of the vector is zero and
 *         zero (false) otherwise.
 *
 * Time complexity: O(1).
 */

igraph_bool_t FUNCTION(igraph_vector, empty)     (const TYPE(igraph_vector)* v) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    return v->stor_begin == v->end;
}

/**
 * \ingroup vector
 * \function igraph_vector_size
 * \brief Gives the size (=length) of the vector.
 *
 * \param v The vector object
 * \return The size of the vector.
 *
 * Time complexity: O(1).
 */

long int FUNCTION(igraph_vector, size)      (const TYPE(igraph_vector)* v) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    return v->end - v->stor_begin;
}

/**
 * \ingroup vector
 * \function igraph_vector_clear
 * \brief Removes all elements from a vector.
 *
 * </para><para>
 * This function simply sets the size of the vector to zero, it does
 * not free any allocated memory. For that you have to call
 * \ref igraph_vector_destroy().
 * \param v The vector object.
 *
 * Time complexity: O(1).
 */

void FUNCTION(igraph_vector, clear)     (TYPE(igraph_vector)* v) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    v->end = v->stor_begin;
}

/**
 * \ingroup vector
 * \function igraph_vector_push_back
 * \brief Appends one element to a vector.
 *
 * </para><para>
 * This function resizes the vector to be one element longer and
 * sets the very last element in the vector to \p e.
 * \param v The vector object.
 * \param e The element to append to the vector.
 * \return Error code:
 *         \c IGRAPH_ENOMEM: not enough memory.
 *
 * Time complexity: operating system dependent. What is important is that
 * a sequence of n
 * subsequent calls to this function has time complexity
 * O(n), even if there
 * hadn't been any space reserved for the new elements by
 * \ref igraph_vector_reserve(). This is implemented by a trick similar to the C++
 * \type vector class: each time more memory is allocated for a
 * vector, the size of the additionally allocated memory is the same
 * as the vector's current length. (We assume here that the time
 * complexity of memory allocation is at most linear.)
 */

int FUNCTION(igraph_vector, push_back) (TYPE(igraph_vector)* v, BASE e) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);

    /* full, allocate more storage */
    if (v->stor_end == v->end) {
        long int new_size = FUNCTION(igraph_vector, size)(v) * 2;
        if (new_size == 0) {
            new_size = 1;
        }
        IGRAPH_CHECK(FUNCTION(igraph_vector, reserve)(v, new_size));
    }

    *(v->end) = e;
    v->end += 1;

    return 0;
}

/**
 * \ingroup vector
 * \function igraph_vector_insert
 * \brief Inserts a single element into a vector.
 *
 * Note that this function does not do range checking. Insertion will shift the
 * elements from the position given to the end of the vector one position to the
 * right, and the new element will be inserted in the empty space created at
 * the given position. The size of the vector will increase by one.
 *
 * \param v The vector object.
 * \param pos The position where the new element is to be inserted.
 * \param value The new element to be inserted.
 */
int FUNCTION(igraph_vector, insert)(TYPE(igraph_vector) *v, long int pos,
                                    BASE value) {
    size_t size = (size_t) FUNCTION(igraph_vector, size)(v);
    IGRAPH_CHECK(FUNCTION(igraph_vector, resize)(v, (long) size + 1));
    if (pos < size) {
        memmove(v->stor_begin + pos + 1, v->stor_begin + pos,
                sizeof(BASE) * (size - (size_t) pos));
    }
    v->stor_begin[pos] = value;
    return 0;
}

/**
 * \ingroup vector
 * \section igraph_vector_accessing_elements Accessing elements
 *
 * <para>The simplest way to access an element of a vector is to use the
 * \ref VECTOR macro. This macro can be used both for querying and setting
 * \type igraph_vector_t elements. If you need a function, \ref
 * igraph_vector_e() queries and \ref igraph_vector_set() sets an element of a
 * vector. \ref igraph_vector_e_ptr() returns the address of an element.</para>
 *
 * <para>\ref igraph_vector_tail() returns the last element of a non-empty
 * vector. There is no <function>igraph_vector_head()</function> function
 * however, as it is easy to write <code>VECTOR(v)[0]</code>
 * instead.</para>
 */

/**
 * \ingroup vector
 * \function igraph_vector_e
 * \brief Access an element of a vector.
 * \param v The \type igraph_vector_t object.
 * \param pos The position of the element, the index of the first
 *    element is zero.
 * \return The desired element.
 * \sa \ref igraph_vector_e_ptr() and the \ref VECTOR macro.
 *
 * Time complexity: O(1).
 */

BASE FUNCTION(igraph_vector, e)         (const TYPE(igraph_vector)* v, long int pos) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    return * (v->stor_begin + pos);
}

/**
 * \ingroup vector
 * \function igraph_vector_e_ptr
 * \brief Get the address of an element of a vector
 * \param v The \type igraph_vector_t object.
 * \param pos The position of the element, the position of the first
 *   element is zero.
 * \return Pointer to the desired element.
 * \sa \ref igraph_vector_e() and the \ref VECTOR macro.
 *
 * Time complexity: O(1).
 */

BASE* FUNCTION(igraph_vector, e_ptr)  (const TYPE(igraph_vector)* v, long int pos) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    return v->stor_begin + pos;
}

/**
 * \ingroup vector
 * \function igraph_vector_set
 * \brief Assignment to an element of a vector.
 * \param v The \type igraph_vector_t element.
 * \param pos Position of the element to set.
 * \param value New value of the element.
 * \sa \ref igraph_vector_e().
 */

void FUNCTION(igraph_vector, set)       (TYPE(igraph_vector)* v,
        long int pos, BASE value) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    *(v->stor_begin + pos) = value;
}

/**
 * \ingroup vector
 * \function igraph_vector_null
 * \brief Sets each element in the vector to zero.
 *
 * </para><para>
 * Note that \ref igraph_vector_init() sets the elements to zero as well, so
 * it makes no sense to call this function on a just initialized
 * vector. Thus if you want to construct a vector of zeros, then you should
 * use \ref igraph_vector_init().
 * \param v The vector object.
 *
 * Time complexity: O(n), the size of
 * the vector.
 */

void FUNCTION(igraph_vector, null)      (TYPE(igraph_vector)* v) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    if (FUNCTION(igraph_vector, size)(v) > 0) {
        memset(v->stor_begin, 0,
               sizeof(BASE) * (size_t) FUNCTION(igraph_vector, size)(v));
    }
}

/**
 * \function igraph_vector_fill
 * \brief Fill a vector with a constant element
 *
 * Sets each element of the vector to the supplied constant.
 * \param vector The vector to work on.
 * \param e The element to fill with.
 *
 * Time complexity: O(n), the size of the vector.
 */

void FUNCTION(igraph_vector, fill)      (TYPE(igraph_vector)* v, BASE e) {
    BASE *ptr;
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    for (ptr = v->stor_begin; ptr < v->end; ptr++) {
        *ptr = e;
    }
}

/**
 * \ingroup vector
 * \function igraph_vector_tail
 * \brief Returns the last element in a vector.
 *
 * </para><para>
 * It is an error to call this function on an empty vector, the result
 * is undefined.
 * \param v The vector object.
 * \return The last element.
 *
 * Time complexity: O(1).
 */

BASE FUNCTION(igraph_vector, tail)(const TYPE(igraph_vector) *v) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    return *((v->end) - 1);
}

/**
 * \ingroup vector
 * \function igraph_vector_pop_back
 * \brief Removes and returns the last element of a vector.
 *
 * </para><para>
 * It is an error to call this function with an empty vector.
 * \param v The vector object.
 * \return The removed last element.
 *
 * Time complexity: O(1).
 */

BASE FUNCTION(igraph_vector, pop_back)(TYPE(igraph_vector)* v) {
    BASE tmp;
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    assert(v->end != v->stor_begin);
    tmp = FUNCTION(igraph_vector, e)(v, FUNCTION(igraph_vector, size)(v) - 1);
    v->end -= 1;
    return tmp;
}

#ifndef NOTORDERED

/**
 * \ingroup vector
 * \function igraph_vector_sort_cmp
 * \brief Internal comparison function of vector elements, used by
 * \ref igraph_vector_sort().
 */

int FUNCTION(igraph_vector, sort_cmp)(const void *a, const void *b) {
    const BASE *da = (const BASE *) a;
    const BASE *db = (const BASE *) b;

    return (*da > *db) - (*da < *db);
}

/**
 * \ingroup vector
 * \function igraph_vector_sort
 * \brief Sorts the elements of the vector into ascending order.
 *
 * </para><para>
 * This function uses the built-in sort function of the C library.
 * \param v Pointer to an initialized vector object.
 *
 * Time complexity: should be
 * O(nlogn) for
 * n
 * elements.
 */

void FUNCTION(igraph_vector, sort)(TYPE(igraph_vector) *v) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    igraph_qsort(v->stor_begin, (size_t) FUNCTION(igraph_vector, size)(v),
                 sizeof(BASE), FUNCTION(igraph_vector, sort_cmp));
}

/**
 * Ascending comparison function passed to qsort from  igraph_vector_qsort_ind
 */
int FUNCTION(igraph_vector, i_qsort_ind_cmp_asc)(const void *p1, const void *p2) {
    BASE **pa = (BASE **) p1;
    BASE **pb = (BASE **) p2;
    if ( **pa < **pb ) {
        return -1;
    }
    if ( **pa > **pb) {
        return 1;
    }
    return 0;
}

/**
 * Descending comparison function passed to qsort from  igraph_vector_qsort_ind
 */
int FUNCTION(igraph_vector, i_qsort_ind_cmp_desc)(const void *p1, const void *p2) {
    BASE **pa = (BASE **) p1;
    BASE **pb = (BASE **) p2;
    if ( **pa < **pb ) {
        return 1;
    }
    if ( **pa > **pb) {
        return -1;
    }
    return 0;
}

/**
 * \function igraph_vector_qsort_ind
 * \brief Return a permutation of indices that sorts a vector
 *
 * Takes an unsorted array \c v as input and computes an array of
 * indices inds such that v[ inds[i] ], with i increasing from 0, is
 * an ordered array (either ascending or descending, depending on
 * \v order). The order of indices for identical elements is not
 * defined.
 *
 * \param v the array to be sorted
 * \param inds the output array of indices. this must be initialized,
 *         but will be resized
 * \param descending whether the output array should be sorted in descending
 *        order.
 * \return Error code.
 *
 * This routine uses the C library qsort routine.
 * Algorithm: 1) create an array of pointers to the elements of v. 2)
 * Pass this array to qsort. 3) after sorting the difference between
 * the pointer value and the first pointer value gives its original
 * position in the array. Use this to set the values of inds.
 *
 * Some tests show that this routine is faster than
 * igraph_vector_heapsort_ind by about 10 percent
 * for small vectors to a factor of two for large vectors.
 */

long int FUNCTION(igraph_vector, qsort_ind)(TYPE(igraph_vector) *v,
        igraph_vector_t *inds, igraph_bool_t descending) {
    long int i;
    BASE **vind, *first;
    size_t n = (size_t) FUNCTION(igraph_vector, size)(v);
    IGRAPH_CHECK(igraph_vector_resize(inds, (long) n));
    if (n == 0) {
        return 0;
    }
    vind = igraph_Calloc(n, BASE*);
    if (vind == 0) {
        IGRAPH_ERROR("igraph_vector_qsort_ind failed", IGRAPH_ENOMEM);
    }
    for (i = 0; i < n; i++) {
        vind[i] = &VECTOR(*v)[i];
    }
    first = vind[0];
    if (descending) {
        igraph_qsort(vind, n, sizeof(BASE**), FUNCTION(igraph_vector, i_qsort_ind_cmp_desc));
    } else {
        igraph_qsort(vind, n, sizeof(BASE**), FUNCTION(igraph_vector, i_qsort_ind_cmp_asc));
    }
    for (i = 0; i < n; i++) {
        VECTOR(*inds)[i] = vind[i] - first;
    }
    igraph_Free(vind);
    return 0;
}

#endif

/**
 * \ingroup vector
 * \function igraph_vector_resize
 * \brief Resize the vector.
 *
 * </para><para>
 * Note that this function does not free any memory, just sets the
 * size of the vector to the given one. It can on the other hand
 * allocate more memory if the new size is larger than the previous
 * one. In this case the newly appeared elements in the vector are
 * \em not set to zero, they are uninitialized.
 * \param v The vector object
 * \param newsize The new size of the vector.
 * \return Error code,
 *         \c IGRAPH_ENOMEM if there is not enough
 *         memory. Note that this function \em never returns an error
 *         if the vector is made smaller.
 * \sa \ref igraph_vector_reserve() for allocating memory for future
 * extensions of a vector. \ref igraph_vector_resize_min() for
 * deallocating the unnneded memory for a vector.
 *
 * Time complexity: O(1) if the new
 * size is smaller, operating system dependent if it is larger. In the
 * latter case it is usually around
 * O(n),
 * n is the new size of the vector.
 */

int FUNCTION(igraph_vector, resize)(TYPE(igraph_vector)* v, long int newsize) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    IGRAPH_CHECK(FUNCTION(igraph_vector, reserve)(v, newsize));
    v->end = v->stor_begin + newsize;
    return 0;
}

/**
 * \ingroup vector
 * \function igraph_vector_resize_min
 * \brief Deallocate the unused memory of a vector.
 *
 * </para><para>
 * Note that this function involves additional memory allocation and
 * may result an out-of-memory error.
 * \param v Pointer to an initialized vector.
 * \return Error code.
 *
 * \sa \ref igraph_vector_resize(), \ref igraph_vector_reserve().
 *
 * Time complexity: operating system dependent.
 */

int FUNCTION(igraph_vector, resize_min)(TYPE(igraph_vector)*v) {
    size_t size;
    BASE *tmp;
    if (v->stor_end == v->end) {
        return 0;
    }

    size = (size_t) (v->end - v->stor_begin);
    tmp = igraph_Realloc(v->stor_begin, size, BASE);
    if (tmp == 0) {
        IGRAPH_ERROR("cannot resize vector", IGRAPH_ENOMEM);
    } else {
        v->stor_begin = tmp;
        v->stor_end = v->end = v->stor_begin + size;
    }

    return 0;
}

#ifndef NOTORDERED

/**
 * \ingroup vector
 * \function igraph_vector_max
 * \brief Gives the maximum element of the vector.
 *
 * </para><para>
 * If the size of the vector is zero, an arbitrary number is
 * returned.
 * \param v The vector object.
 * \return The maximum element.
 *
 * Time complexity: O(n),
 * n is the size of the vector.
 */

BASE FUNCTION(igraph_vector, max)(const TYPE(igraph_vector)* v) {
    BASE max;
    BASE *ptr;
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    max = *(v->stor_begin);
    ptr = v->stor_begin + 1;
    while (ptr < v->end) {
        if ((*ptr) > max) {
            max = *ptr;
        }
        ptr++;
    }
    return max;
}

/**
 * \ingroup vector
 * \function igraph_vector_which_max
 * \brief Gives the position of the maximum element of the vector.
 *
 * </para><para>
 * If the size of the vector is zero, -1 is
 * returned.
 * \param v The vector object.
 * \return The position of the first maximum element.
 *
 * Time complexity: O(n),
 * n is the size of the vector.
 */

long int FUNCTION(igraph_vector, which_max)(const TYPE(igraph_vector)* v) {
    long int which = -1;
    if (!FUNCTION(igraph_vector, empty)(v)) {
        BASE max;
        BASE *ptr;
        long int pos;
        assert(v != NULL);
        assert(v->stor_begin != NULL);
        max = *(v->stor_begin); which = 0;
        ptr = v->stor_begin + 1; pos = 1;
        while (ptr < v->end) {
            if ((*ptr) > max) {
                max = *ptr;
                which = pos;
            }
            ptr++; pos++;
        }
    }
    return which;
}

/**
 * \function igraph_vector_min
 * \brief Smallest element of a vector.
 *
 * The vector must be non-empty.
 * \param v The input vector.
 * \return The smallest element of \p v.
 *
 * Time complexity: O(n), the number of elements.
 */

BASE FUNCTION(igraph_vector, min)(const TYPE(igraph_vector)* v) {
    BASE min;
    BASE *ptr;
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    min = *(v->stor_begin);
    ptr = v->stor_begin + 1;
    while (ptr < v->end) {
        if ((*ptr) < min) {
            min = *ptr;
        }
        ptr++;
    }
    return min;
}

/**
 * \function igraph_vector_which_min
 * \brief Index of the smallest element.
 *
 * The vector must be non-empty.
 * If the smallest element is not unique, then the index of the first
 * is returned.
 * \param v The input vector.
 * \return Index of the smallest element.
 *
 * Time complexity: O(n), the number of elements.
 */

long int FUNCTION(igraph_vector, which_min)(const TYPE(igraph_vector)* v) {
    long int which = -1;
    if (!FUNCTION(igraph_vector, empty)(v)) {
        BASE min;
        BASE *ptr;
        long int pos;
        assert(v != NULL);
        assert(v->stor_begin != NULL);
        min = *(v->stor_begin); which = 0;
        ptr = v->stor_begin + 1; pos = 1;
        while (ptr < v->end) {
            if ((*ptr) < min) {
                min = *ptr;
                which = pos;
            }
            ptr++; pos++;
        }
    }
    return which;
}

#endif

/**
 * \ingroup vector
 * \function igraph_vector_init_copy
 * \brief Initializes a vector from an ordinary C array (constructor).
 *
 * \param v Pointer to an uninitialized vector object.
 * \param data A regular C array.
 * \param length The length of the C array.
 * \return Error code:
 *         \c IGRAPH_ENOMEM if there is not enough memory.
 *
 * Time complexity: operating system specific, usually
 * O(\p length).
 */

int FUNCTION(igraph_vector, init_copy)(TYPE(igraph_vector) *v,
                                       const BASE *data, long int length) {
    v->stor_begin = igraph_Calloc(length, BASE);
    if (v->stor_begin == 0) {
        IGRAPH_ERROR("cannot init vector from array", IGRAPH_ENOMEM);
    }
    v->stor_end = v->stor_begin + length;
    v->end = v->stor_end;
    memcpy(v->stor_begin, data, (size_t) length * sizeof(BASE));

    return 0;
}

/**
 * \ingroup vector
 * \function igraph_vector_copy_to
 * \brief Copies the contents of a vector to a C array.
 *
 * </para><para>
 * The C array should have sufficient length.
 * \param v The vector object.
 * \param to The C array.
 *
 * Time complexity: O(n),
 * n is the size of the vector.
 */

void FUNCTION(igraph_vector, copy_to)(const TYPE(igraph_vector) *v, BASE *to) {

    assert(v != NULL);
    assert(v->stor_begin != NULL);
    if (v->end != v->stor_begin) {
        memcpy(to, v->stor_begin, sizeof(BASE) * (size_t) (v->end - v->stor_begin));
    }
}

/**
 * \ingroup vector
 * \function igraph_vector_copy
 * \brief Initializes a vector from another vector object (constructor).
 *
 * </para><para>
 * The contents of the existing vector object will be copied to
 * the new one.
 * \param to Pointer to a not yet initialized vector object.
 * \param from The original vector object to copy.
 * \return Error code:
 *         \c IGRAPH_ENOMEM if there is not enough memory.
 *
 * Time complexity: operating system dependent, usually
 * O(n),
 * n is the size of the vector.
 */

int FUNCTION(igraph_vector, copy)(TYPE(igraph_vector) *to,
                                  const TYPE(igraph_vector) *from) {
    assert(from != NULL);
    assert(from->stor_begin != NULL);
    to->stor_begin = igraph_Calloc(FUNCTION(igraph_vector, size)(from), BASE);
    if (to->stor_begin == 0) {
        IGRAPH_ERROR("cannot copy vector", IGRAPH_ENOMEM);
    }
    to->stor_end = to->stor_begin + FUNCTION(igraph_vector, size)(from);
    to->end = to->stor_end;
    memcpy(to->stor_begin, from->stor_begin,
           (size_t) FUNCTION(igraph_vector, size)(from) * sizeof(BASE));

    return 0;
}

/**
 * \ingroup vector
 * \function igraph_vector_sum
 * \brief Calculates the sum of the elements in the vector.
 *
 * </para><para>
 * For the empty vector 0.0 is returned.
 * \param v The vector object.
 * \return The sum of the elements.
 *
 * Time complexity: O(n), the size of
 * the vector.
 */

BASE FUNCTION(igraph_vector, sum)(const TYPE(igraph_vector) *v) {
    BASE res = ZERO;
    BASE *p;
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    for (p = v->stor_begin; p < v->end; p++) {
#ifdef SUM
        SUM(res, res, *p);
#else
        res += *p;
#endif
    }
    return res;
}

igraph_real_t FUNCTION(igraph_vector, sumsq)(const TYPE(igraph_vector) *v) {
    igraph_real_t res = 0.0;
    BASE *p;
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    for (p = v->stor_begin; p < v->end; p++) {
#ifdef SQ
        res += SQ(*p);
#else
        res += (*p) * (*p);
#endif
    }
    return res;
}

/**
 * \ingroup vector
 * \function igraph_vector_prod
 * \brief Calculates the product of the elements in the vector.
 *
 * </para><para>
 * For the empty vector one (1) is returned.
 * \param v The vector object.
 * \return The product of the elements.
 *
 * Time complexity: O(n), the size of
 * the vector.
 */

BASE FUNCTION(igraph_vector, prod)(const TYPE(igraph_vector) *v) {
    BASE res = ONE;
    BASE *p;
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    for (p = v->stor_begin; p < v->end; p++) {
#ifdef PROD
        PROD(res, res, *p);
#else
        res *= *p;
#endif
    }
    return res;
}

/**
 * \ingroup vector
 * \function igraph_vector_cumsum
 * \brief Calculates the cumulative sum of the elements in the vector.
 *
 * </para><para>
 * \param to An initialized vector object that will store the cumulative
 *           sums. Element i of this vector will store the sum of the elements
 *           of the 'from' vector, up to and including element i.
 * \param from The input vector.
 * \return Error code.
 *
 * Time complexity: O(n), the size of the vector.
 */

int FUNCTION(igraph_vector, cumsum)(TYPE(igraph_vector) *to,
                                    const TYPE(igraph_vector) *from) {
    BASE res = ZERO;
    BASE *p, *p2;

    assert(from != NULL);
    assert(from->stor_begin != NULL);
    assert(to != NULL);
    assert(to->stor_begin != NULL);

    IGRAPH_CHECK(FUNCTION(igraph_vector, resize)(to, FUNCTION(igraph_vector, size)(from)));

    for (p = from->stor_begin, p2 = to->stor_begin; p < from->end; p++, p2++) {
#ifdef SUM
        SUM(res, res, *p);
#else
        res += *p;
#endif
        *p2 = res;
    }

    return 0;
}

#ifndef NOTORDERED

/**
 * \ingroup vector
 * \function igraph_vector_init_seq
 * \brief Initializes a vector with a sequence.
 *
 * </para><para>
 * The vector will contain the numbers \p from,
 * \p from+1, ..., \p to.
 * \param v Pointer to an uninitialized vector object.
 * \param from The lower limit in the sequence (inclusive).
 * \param to The upper limit in the sequence (inclusive).
 * \return Error code:
 *         \c IGRAPH_ENOMEM: out of memory.
 *
 * Time complexity: O(n), the number
 * of elements in the vector.
 */

int FUNCTION(igraph_vector, init_seq)(TYPE(igraph_vector) *v,
                                      BASE from, BASE to) {
    BASE *p;
    IGRAPH_CHECK(FUNCTION(igraph_vector, init)(v, (long int) (to - from + 1)));

    for (p = v->stor_begin; p < v->end; p++) {
        *p = from++;
    }

    return 0;
}

#endif

/**
 * \ingroup vector
 * \function igraph_vector_remove_section
 * \brief Deletes a section from a vector.
 *
 * </para><para>
 * Note that this function does not do range checking. The result is
 * undefined if you supply invalid limits.
 * \param v The vector object.
 * \param from The position of the first element to remove.
 * \param to The position of the first element \em not to remove.
 *
 * Time complexity: O(n-from),
 * n is the number of elements in the
 * vector.
 */

void FUNCTION(igraph_vector, remove_section)(TYPE(igraph_vector) *v,
        long int from, long int to) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    /* Not removing from the end? */
    if (to < FUNCTION(igraph_vector, size)(v)) {
        memmove(v->stor_begin + from, v->stor_begin + to,
                sizeof(BASE) * (size_t) (v->end - v->stor_begin - to));
    }
    v->end -= (to - from);
}

/**
 * \ingroup vector
 * \function igraph_vector_remove
 * \brief Removes a single element from a vector.
 *
 * Note that this function does not do range checking.
 * \param v The vector object.
 * \param elem The position of the element to remove.
 *
 * Time complexity: O(n-elem),
 * n is the number of elements in the
 * vector.
 */

void FUNCTION(igraph_vector, remove)(TYPE(igraph_vector) *v, long int elem) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    FUNCTION(igraph_vector, remove_section)(v, elem, elem + 1);
}

/**
 * \ingroup vector
 * \function igraph_vector_move_interval
 * \brief Copies a section of a vector.
 *
 * </para><para>
 * The result of this function is undefined if the source and target
 * intervals overlap.
 * \param v The vector object.
 * \param begin The position of the first element to move.
 * \param end The position of the first element \em not to move.
 * \param to The target position.
 * \return Error code, the current implementation always returns with
 *    success.
 *
 * Time complexity: O(end-begin).
 */

int FUNCTION(igraph_vector, move_interval)(TYPE(igraph_vector) *v,
        long int begin, long int end,
        long int to) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    memcpy(v->stor_begin + to, v->stor_begin + begin,
           sizeof(BASE) * (size_t) (end - begin));

    return 0;
}

int FUNCTION(igraph_vector, move_interval2)(TYPE(igraph_vector) *v,
        long int begin, long int end,
        long int to) {
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    memmove(v->stor_begin + to, v->stor_begin + begin,
            sizeof(BASE) * (size_t) (end - begin));

    return 0;
}

/**
 * \ingroup vector
 * \function igraph_vector_permdelete
 * \brief Remove elements of a vector (for internal use).
 */

void FUNCTION(igraph_vector, permdelete)(TYPE(igraph_vector) *v,
        const igraph_vector_t *index, long int nremove) {
    long int i, n;
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    n = FUNCTION(igraph_vector, size)(v);
    for (i = 0; i < n; i++) {
        if (VECTOR(*index)[i] != 0) {
            VECTOR(*v)[ (long int)VECTOR(*index)[i] - 1 ] = VECTOR(*v)[i];
        }
    }
    v->end -= nremove;
}

#ifndef NOTORDERED

/**
 * \ingroup vector
 * \function igraph_vector_isininterval
 * \brief Checks if all elements of a vector are in the given
 * interval.
 *
 * \param v The vector object.
 * \param low The lower limit of the interval (inclusive).
 * \param high The higher limit of the interval (inclusive).
 * \return True (positive integer) if all vector elements are in the
 *   interval, false (zero) otherwise.
 *
 * Time complexity: O(n), the number
 * of elements in the vector.
 */

igraph_bool_t FUNCTION(igraph_vector, isininterval)(const TYPE(igraph_vector) *v,
        BASE low,
        BASE high) {
    BASE *ptr;
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    for (ptr = v->stor_begin; ptr < v->end; ptr++) {
        if (*ptr < low || *ptr > high) {
            return 0;
        }
    }
    return 1;
}

/**
 * \ingroup vector
 * \function igraph_vector_any_smaller
 * \brief Checks if any element of a vector is smaller than a limit.
 *
 * \param v The \type igraph_vector_t object.
 * \param limit The limit.
 * \return True (positive integer) if the vector contains at least one
 *   smaller element than \p limit, false (zero)
 *   otherwise.
 *
 * Time complexity: O(n), the number
 * of elements in the vector.
 */

igraph_bool_t FUNCTION(igraph_vector, any_smaller)(const TYPE(igraph_vector) *v,
        BASE limit) {
    BASE *ptr;
    assert(v != NULL);
    assert(v->stor_begin != NULL);
    for (ptr = v->stor_begin; ptr < v->end; ptr++) {
        if (*ptr < limit) {
            return 1;
        }
    }
    return 0;
}

#endif

/**
 * \ingroup vector
 * \function igraph_vector_all_e
 * \brief Are all elements equal?
 *
 * \param lhs The first vector.
 * \param rhs The second vector.
 * \return Positive integer (=true) if the elements in the \p lhs are all
 *    equal to the corresponding elements in \p rhs. Returns \c 0
 *    (=false) if the lengths of the vectors don't match.
 *
 * Time complexity: O(n), the length of the vectors.
 */

igraph_bool_t FUNCTION(igraph_vector, all_e)(const TYPE(igraph_vector) *lhs,
        const TYPE(igraph_vector) *rhs) {
    long int i, s;
    assert(lhs != 0);
    assert(rhs != 0);
    assert(lhs->stor_begin != 0);
    assert(rhs->stor_begin != 0);

    s = FUNCTION(igraph_vector, size)(lhs);
    if (s != FUNCTION(igraph_vector, size)(rhs)) {
        return 0;
    } else {
        for (i = 0; i < s; i++) {
            BASE l = VECTOR(*lhs)[i];
            BASE r = VECTOR(*rhs)[i];
#ifdef EQ
            if (!EQ(l, r)) {
#else
            if (l != r) {
#endif
                return 0;
            }
        }
        return 1;
    }
}

igraph_bool_t
FUNCTION(igraph_vector, is_equal)(const TYPE(igraph_vector) *lhs,
                                  const TYPE(igraph_vector) *rhs) {
    return FUNCTION(igraph_vector, all_e)(lhs, rhs);
}

#ifndef NOTORDERED

/**
 * \ingroup vector
 * \function igraph_vector_all_l
 * \brief Are all elements less?
 *
 * \param lhs The first vector.
 * \param rhs The second vector.
 * \return Positive integer (=true) if the elements in the \p lhs are all
 *    less than the corresponding elements in \p rhs. Returns \c 0
 *    (=false) if the lengths of the vectors don't match.
 *
 * Time complexity: O(n), the length of the vectors.
 */

igraph_bool_t FUNCTION(igraph_vector, all_l)(const TYPE(igraph_vector) *lhs,
        const TYPE(igraph_vector) *rhs) {
    long int i, s;
    assert(lhs != 0);
    assert(rhs != 0);
    assert(lhs->stor_begin != 0);
    assert(rhs->stor_begin != 0);

    s = FUNCTION(igraph_vector, size)(lhs);
    if (s != FUNCTION(igraph_vector, size)(rhs)) {
        return 0;
    } else {
        for (i = 0; i < s; i++) {
            BASE l = VECTOR(*lhs)[i];
            BASE r = VECTOR(*rhs)[i];
            if (l >= r) {
                return 0;
            }
        }
        return 1;
    }
}

/**
 * \ingroup vector
 * \function igraph_vector_all_g
 * \brief Are all elements greater?
 *
 * \param lhs The first vector.
 * \param rhs The second vector.
 * \return Positive integer (=true) if the elements in the \p lhs are all
 *    greater than the corresponding elements in \p rhs. Returns \c 0
 *    (=false) if the lengths of the vectors don't match.
 *
 * Time complexity: O(n), the length of the vectors.
 */

igraph_bool_t FUNCTION(igraph_vector, all_g)(const TYPE(igraph_vector) *lhs,
        const TYPE(igraph_vector) *rhs) {

    long int i, s;
    assert(lhs != 0);
    assert(rhs != 0);
    assert(lhs->stor_begin != 0);
    assert(rhs->stor_begin != 0);

    s = FUNCTION(igraph_vector, size)(lhs);
    if (s != FUNCTION(igraph_vector, size)(rhs)) {
        return 0;
    } else {
        for (i = 0; i < s; i++) {
            BASE l = VECTOR(*lhs)[i];
            BASE r = VECTOR(*rhs)[i];
            if (l <= r) {
                return 0;
            }
        }
        return 1;
    }
}

/**
 * \ingroup vector
 * \function igraph_vector_all_le
 * \brief Are all elements less or equal?
 *
 * \param lhs The first vector.
 * \param rhs The second vector.
 * \return Positive integer (=true) if the elements in the \p lhs are all
 *    less than or equal to the corresponding elements in \p
 *    rhs. Returns \c 0 (=false) if the lengths of the vectors don't
 *    match.
 *
 * Time complexity: O(n), the length of the vectors.
 */

igraph_bool_t
FUNCTION(igraph_vector, all_le)(const TYPE(igraph_vector) *lhs,
                                const TYPE(igraph_vector) *rhs) {
    long int i, s;
    assert(lhs != 0);
    assert(rhs != 0);
    assert(lhs->stor_begin != 0);
    assert(rhs->stor_begin != 0);

    s = FUNCTION(igraph_vector, size)(lhs);
    if (s != FUNCTION(igraph_vector, size)(rhs)) {
        return 0;
    } else {
        for (i = 0; i < s; i++) {
            BASE l = VECTOR(*lhs)[i];
            BASE r = VECTOR(*rhs)[i];
            if (l > r) {
                return 0;
            }
        }
        return 1;
    }
}

/**
 * \ingroup vector
 * \function igraph_vector_all_ge
 * \brief Are all elements greater or equal?
 *
 * \param lhs The first vector.
 * \param rhs The second vector.
 * \return Positive integer (=true) if the elements in the \p lhs are all
 *    greater than or equal to the corresponding elements in \p
 *    rhs. Returns \c 0 (=false) if the lengths of the vectors don't
 *    match.
 *
 * Time complexity: O(n), the length of the vectors.
 */

igraph_bool_t
FUNCTION(igraph_vector, all_ge)(const TYPE(igraph_vector) *lhs,
                                const TYPE(igraph_vector) *rhs) {
    long int i, s;
    assert(lhs != 0);
    assert(rhs != 0);
    assert(lhs->stor_begin != 0);
    assert(rhs->stor_begin != 0);

    s = FUNCTION(igraph_vector, size)(lhs);
    if (s != FUNCTION(igraph_vector, size)(rhs)) {
        return 0;
    } else {
        for (i = 0; i < s; i++) {
            BASE l = VECTOR(*lhs)[i];
            BASE r = VECTOR(*rhs)[i];
            if (l < r) {
                return 0;
            }
        }
        return 1;
    }
}

#endif

igraph_bool_t FUNCTION(igraph_i_vector, binsearch_slice)(const TYPE(igraph_vector) *v,
        BASE what, long int *pos,
        long int start, long int end);

#ifndef NOTORDERED

/**
 * \ingroup vector
 * \function igraph_vector_binsearch
 * \brief Finds an element by binary searching a sorted vector.
 *
 * </para><para>
 * It is assumed that the vector is sorted. If the specified element
 * (\p what) is not in the vector, then the
 * position of where it should be inserted (to keep the vector sorted)
 * is returned.
 * \param v The \type igraph_vector_t object.
 * \param what The element to search for.
 * \param pos Pointer to a \type long int. This is set to the
 *   position of an instance of \p what in the
 *   vector if it is present. If \p v does not
 *   contain \p what then
 *   \p pos is set to the position to which it
 *   should be inserted (to keep the the vector sorted of course).
 * \return Positive integer (true) if \p what is
 *   found in the vector, zero (false) otherwise.
 *
 * Time complexity: O(log(n)),
 * n is the number of elements in
 * \p v.
 */

igraph_bool_t FUNCTION(igraph_vector, binsearch)(const TYPE(igraph_vector) *v,
        BASE what, long int *pos) {
    return FUNCTION(igraph_i_vector, binsearch_slice)(v, what, pos,
            0, FUNCTION(igraph_vector, size)(v));
}

igraph_bool_t FUNCTION(igraph_i_vector, binsearch_slice)(const TYPE(igraph_vector) *v,
        BASE what, long int *pos,
        long int start, long int end) {
    long int left  = start;
    long int right = end - 1;

    while (left <= right) {
        /* (right + left) / 2 could theoretically overflow for long vectors */
        long int middle = left + ((right - left) >> 1);
        if (VECTOR(*v)[middle] > what) {
            right = middle - 1;
        } else if (VECTOR(*v)[middle] < what) {
            left = middle + 1;
        } else {
            if (pos != 0) {
                *pos = middle;
            }
            return 1;
        }
    }

    /* if we are here, the element was not found */
    if (pos != 0) {
        *pos = left;
    }

    return 0;
}

/**
 * \ingroup vector
 * \function igraph_vector_binsearch2
 * \brief Binary search, without returning the index.
 *
 * </para><para>
 * It is assumed that the vector is sorted.
 * \param v The \type igraph_vector_t object.
 * \param what The element to search for.
 * \return Positive integer (true) if \p what is
 *   found in the vector, zero (false) otherwise.
 *
 * Time complexity: O(log(n)),
 * n is the number of elements in
 * \p v.
 */

igraph_bool_t FUNCTION(igraph_vector, binsearch2)(const TYPE(igraph_vector) *v,
        BASE what) {
    long int left = 0;
    long int right = FUNCTION(igraph_vector, size)(v) - 1;

    while (left <= right) {
        /* (right + left) / 2 could theoretically overflow for long vectors */
        long int middle = left + ((right - left) >> 1);
        if (what < VECTOR(*v)[middle]) {
            right = middle - 1;
        } else if (what > VECTOR(*v)[middle]) {
            left = middle + 1;
        } else {
            return 1;
        }
    }

    return 0;
}

#endif

/**
 * \function igraph_vector_scale
 * \brief Multiply all elements of a vector by a constant
 *
 * \param v The vector.
 * \param by The constant.
 * \return Error code. The current implementation always returns with success.
 *
 * Added in version 0.2.</para><para>
 *
 * Time complexity: O(n), the number of elements in a vector.
 */

void FUNCTION(igraph_vector, scale)(TYPE(igraph_vector) *v, BASE by) {
    long int i;
    for (i = 0; i < FUNCTION(igraph_vector, size)(v); i++) {
#ifdef PROD
        PROD(VECTOR(*v)[i], VECTOR(*v)[i], by);
#else
        VECTOR(*v)[i] *= by;
#endif
    }
}

/**
 * \function igraph_vector_add_constant
 * \brief Add a constant to the vector.
 *
 * \p plus is added to every element of \p v. Note that overflow
 * might happen.
 * \param v The input vector.
 * \param plus The constant to add.
 *
 * Time complexity: O(n), the number of elements.
 */

void FUNCTION(igraph_vector, add_constant)(TYPE(igraph_vector) *v, BASE plus) {
    long int i, n = FUNCTION(igraph_vector, size)(v);
    for (i = 0; i < n; i++) {
#ifdef SUM
        SUM(VECTOR(*v)[i], VECTOR(*v)[i], plus);
#else
        VECTOR(*v)[i] += plus;
#endif
    }
}

/**
 * \function igraph_vector_contains
 * \brief Linear search in a vector.
 *
 * Check whether the supplied element is included in the vector, by
 * linear search.
 * \param v The input vector.
 * \param e The element to look for.
 * \return \c TRUE if the element is found and \c FALSE otherwise.
 *
 * Time complexity: O(n), the length of the vector.
 */

igraph_bool_t FUNCTION(igraph_vector, contains)(const TYPE(igraph_vector) *v,
        BASE e) {
    BASE *p = v->stor_begin;
    while (p < v->end) {
#ifdef EQ
        if (EQ(*p, e)) {
#else
        if (*p == e) {
#endif
            return 1;
        }
        p++;
    }
    return 0;
}

/**
 * \function igraph_vector_search
 * \brief Search from a given position
 *
 * The supplied element \p what is searched in vector \p v, starting
 * from element index \p from. If found then the index of the first
 * instance (after \p from) is stored in \p pos.
 * \param v The input vector.
 * \param from The index to start searching from. No range checking is
 *     performed.
 * \param what The element to find.
 * \param pos If not \c NULL then the index of the found element is
 *    stored here.
 * \return Boolean, \c TRUE if the element was found, \c FALSE
 *   otherwise.
 *
 * Time complexity: O(m), the number of elements to search, the length
 * of the vector minus the \p from argument.
 */

igraph_bool_t FUNCTION(igraph_vector, search)(const TYPE(igraph_vector) *v,
        long int from, BASE what,
        long int *pos) {
    long int i, n = FUNCTION(igraph_vector, size)(v);
    for (i = from; i < n; i++) {
#ifdef EQ
        if (EQ(VECTOR(*v)[i], what)) {
            break;
        }
#else
        if (VECTOR(*v)[i] == what) {
            break;
        }
#endif
    }

    if (i < n) {
        if (pos != 0) {
            *pos = i;
        }
        return 1;
    } else {
        return 0;
    }
}

#ifndef NOTORDERED

/**
 * \function igraph_vector_filter_smaller
 * \ingroup internal
 */

int FUNCTION(igraph_vector, filter_smaller)(TYPE(igraph_vector) *v,
        BASE elem) {
    long int i = 0, n = FUNCTION(igraph_vector, size)(v);
    long int s;
    while (i < n && VECTOR(*v)[i] < elem) {
        i++;
    }
    s = i;

    while (s < n && VECTOR(*v)[s] == elem) {
        s++;
    }

    FUNCTION(igraph_vector, remove_section)(v, 0, i + (s - i) / 2);
    return 0;
}

#endif

/**
 * \function igraph_vector_append
 * \brief Append a vector to another one.
 *
 * The target vector will be resized (except when \p from is empty).
 * \param to The vector to append to.
 * \param from The vector to append, it is kept unchanged.
 * \return Error code.
 *
 * Time complexity: O(n), the number of elements in the new vector.
 */

int FUNCTION(igraph_vector, append)(TYPE(igraph_vector) *to,
                                    const TYPE(igraph_vector) *from) {
    long tosize, fromsize;

    tosize = FUNCTION(igraph_vector, size)(to);
    fromsize = FUNCTION(igraph_vector, size)(from);
    IGRAPH_CHECK(FUNCTION(igraph_vector, resize)(to, tosize + fromsize));
    memcpy(to->stor_begin + tosize, from->stor_begin,
           sizeof(BASE) * (size_t) fromsize);
    to->end = to->stor_begin + tosize + fromsize;

    return 0;
}

/**
 * \function igraph_vector_get_interval
 */

int FUNCTION(igraph_vector, get_interval)(const TYPE(igraph_vector) *v,
        TYPE(igraph_vector) *res,
        long int from, long int to) {
    IGRAPH_CHECK(FUNCTION(igraph_vector, resize)(res, to - from));
    memcpy(res->stor_begin, v->stor_begin + from,
           (size_t) (to - from) * sizeof(BASE));
    return 0;
}

#ifndef NOTORDERED

/**
 * \function igraph_vector_maxdifference
 * \brief The maximum absolute difference of \p m1 and \p m2
 *
 * The element with the largest absolute value in \p m1 - \p m2 is
 * returned. Both vectors must be non-empty, but they not need to have
 * the same length, the extra elements in the longer vector are ignored.
 * \param m1 The first vector.
 * \param m2 The second vector.
 * \return The maximum absolute difference of \p m1 and \p m2.
 *
 * Time complexity: O(n), the number of elements in the shorter
 * vector.
 */

igraph_real_t FUNCTION(igraph_vector, maxdifference)(const TYPE(igraph_vector) *m1,
        const TYPE(igraph_vector) *m2) {
    long int n1 = FUNCTION(igraph_vector, size)(m1);
    long int n2 = FUNCTION(igraph_vector, size)(m2);
    long int n = n1 < n2 ? n1 : n2;
    long int i;
    igraph_real_t diff = 0.0;

    for (i = 0; i < n; i++) {
        igraph_real_t d = fabs((igraph_real_t)(VECTOR(*m1)[i]) -
                               (igraph_real_t)(VECTOR(*m2)[i]));
        if (d > diff) {
            diff = d;
        }
    }

    return diff;
}

#endif

/**
 * \function igraph_vector_update
 * \brief Update a vector from another one.
 *
 * After this operation the contents of \p to will be exactly the same
 * as that of \p from. The vector \p to will be resized if it was originally 
 * shorter or longer than \p from.
 * \param to The vector to update.
 * \param from The vector to update from.
 * \return Error code.
 *
 * Time complexity: O(n), the number of elements in \p from.
 */

int FUNCTION(igraph_vector, update)(TYPE(igraph_vector) *to,
                                    const TYPE(igraph_vector) *from) {
    size_t n = (size_t) FUNCTION(igraph_vector, size)(from);
    FUNCTION(igraph_vector, resize)(to, (long) n);
    memcpy(to->stor_begin, from->stor_begin, sizeof(BASE)*n);
    return 0;
}

/**
 * \function igraph_vector_swap
 * \brief Swap elements of two vectors.
 *
 * The two vectors must have the same length, otherwise an error
 * happens.
 * \param v1 The first vector.
 * \param v2 The second vector.
 * \return Error code.
 *
 * Time complexity: O(n), the length of the vectors.
 */

int FUNCTION(igraph_vector, swap)(TYPE(igraph_vector) *v1, TYPE(igraph_vector) *v2) {

    long int i, n1 = FUNCTION(igraph_vector, size)(v1);
    long int n2 = FUNCTION(igraph_vector, size)(v2);
    if (n1 != n2) {
        IGRAPH_ERROR("Vectors must have the same number of elements for swapping",
                     IGRAPH_EINVAL);
    }

    for (i = 0; i < n1; i++) {
        BASE tmp;
        tmp = VECTOR(*v1)[i];
        VECTOR(*v1)[i] = VECTOR(*v2)[i];
        VECTOR(*v2)[i] = tmp;
    }
    return 0;
}

/**
 * \function igraph_vector_swap_elements
 * \brief Swap two elements in a vector.
 *
 * Note that currently no range checking is performed.
 * \param v The input vector.
 * \param i Index of the first element.
 * \param j Index of the second element (may be the same as the
 * first one).
 * \return Error code, currently always \c IGRAPH_SUCCESS.
 *
 * Time complexity: O(1).
 */

int FUNCTION(igraph_vector, swap_elements)(TYPE(igraph_vector) *v,
        long int i, long int j) {
    BASE tmp = VECTOR(*v)[i];
    VECTOR(*v)[i] = VECTOR(*v)[j];
    VECTOR(*v)[j] = tmp;

    return 0;
}

/**
 * \function igraph_vector_reverse
 * \brief Reverse the elements of a vector.
 *
 * The first element will be last, the last element will be
 * first, etc.
 * \param v The input vector.
 * \return Error code, currently always \c IGRAPH_SUCCESS.
 *
 * Time complexity: O(n), the number of elements.
 */

int FUNCTION(igraph_vector, reverse)(TYPE(igraph_vector) *v) {

    long int n = FUNCTION(igraph_vector, size)(v), n2 = n / 2;
    long int i, j;
    for (i = 0, j = n - 1; i < n2; i++, j--) {
        BASE tmp;
        tmp = VECTOR(*v)[i];
        VECTOR(*v)[i] = VECTOR(*v)[j];
        VECTOR(*v)[j] = tmp;
    }
    return 0;
}

/**
 * \ingroup vector
 * \function igraph_vector_shuffle
 * \brief Shuffles a vector in-place using the Fisher-Yates method
 *
 * </para><para>
 * The Fisher-Yates shuffle ensures that every permutation is
 * equally probable when using a proper randomness source. Of course
 * this does not apply to pseudo-random generators as the cycle of
 * these generators is less than the number of possible permutations
 * of the vector if the vector is long enough.
 * \param v The vector object.
 * \return Error code, currently always \c IGRAPH_SUCCESS.
 *
 * Time complexity: O(n),
 * n is the number of elements in the
 * vector.
 *
 * </para><para>
 * References:
 * \clist
 * \cli (Fisher &amp; Yates 1963)
 *   R. A. Fisher and F. Yates. \emb Statistical Tables for Biological,
 *   Agricultural and Medical Research. \eme Oliver and Boyd, 6th edition,
 *   1963, page 37.
 * \cli (Knuth 1998)
 *   D. E. Knuth. \emb Seminumerical Algorithms, \eme volume 2 of \emb The Art
 *   of Computer Programming. \eme Addison-Wesley, 3rd edition, 1998, page 145.
 * \endclist
 *
 * \example examples/simple/igraph_fisher_yates_shuffle.c
 */

int FUNCTION(igraph_vector, shuffle)(TYPE(igraph_vector) *v) {
    long int n = FUNCTION(igraph_vector, size)(v);
    long int k;
    BASE dummy;

    RNG_BEGIN();
    while (n > 1) {
        k = RNG_INTEGER(0, n - 1);
        n--;
        dummy = VECTOR(*v)[n];
        VECTOR(*v)[n] = VECTOR(*v)[k];
        VECTOR(*v)[k] = dummy;
    }
    RNG_END();

    return IGRAPH_SUCCESS;
}

/**
 * \function igraph_vector_add
 * \brief Add two vectors.
 *
 * Add the elements of \p v2 to \p v1, the result is stored in \p
 * v1. The two vectors must have the same length.
 * \param v1 The first vector, the result will be stored here.
 * \param v2 The second vector, its contents will be unchanged.
 * \return Error code.
 *
 * Time complexity: O(n), the number of elements.
 */

int FUNCTION(igraph_vector, add)(TYPE(igraph_vector) *v1,
                                 const TYPE(igraph_vector) *v2) {

    long int n1 = FUNCTION(igraph_vector, size)(v1);
    long int n2 = FUNCTION(igraph_vector, size)(v2);
    long int i;
    if (n1 != n2) {
        IGRAPH_ERROR("Vectors must have the same number of elements for swapping",
                     IGRAPH_EINVAL);
    }

    for (i = 0; i < n1; i++) {
#ifdef SUM
        SUM(VECTOR(*v1)[i], VECTOR(*v1)[i], VECTOR(*v2)[i]);
#else
        VECTOR(*v1)[i] += VECTOR(*v2)[i];
#endif
    }

    return 0;
}

/**
 * \function igraph_vector_sub
 * \brief Subtract a vector from another one.
 *
 * Subtract the elements of \p v2 from \p v1, the result is stored in
 * \p v1. The two vectors must have the same length.
 * \param v1 The first vector, to subtract from. The result is stored
 *    here.
 * \param v2 The vector to subtract, it will be unchanged.
 * \return Error code.
 *
 * Time complexity: O(n), the length of the vectors.
 */

int FUNCTION(igraph_vector, sub)(TYPE(igraph_vector) *v1,
                                 const TYPE(igraph_vector) *v2) {

    long int n1 = FUNCTION(igraph_vector, size)(v1);
    long int n2 = FUNCTION(igraph_vector, size)(v2);
    long int i;
    if (n1 != n2) {
        IGRAPH_ERROR("Vectors must have the same number of elements for swapping",
                     IGRAPH_EINVAL);
    }

    for (i = 0; i < n1; i++) {
#ifdef DIFF
        DIFF(VECTOR(*v1)[i], VECTOR(*v1)[i], VECTOR(*v2)[i]);
#else
        VECTOR(*v1)[i] -= VECTOR(*v2)[i];
#endif
    }

    return 0;
}

/**
 * \function igraph_vector_mul
 * \brief Multiply two vectors.
 *
 * \p v1 will be multiplied by \p v2, elementwise. The two vectors
 * must have the same length.
 * \param v1 The first vector, the result will be stored here.
 * \param v2 The second vector, it is left unchanged.
 * \return Error code.
 *
 * Time complexity: O(n), the number of elements.
 */

int FUNCTION(igraph_vector, mul)(TYPE(igraph_vector) *v1,
                                 const TYPE(igraph_vector) *v2) {

    long int n1 = FUNCTION(igraph_vector, size)(v1);
    long int n2 = FUNCTION(igraph_vector, size)(v2);
    long int i;
    if (n1 != n2) {
        IGRAPH_ERROR("Vectors must have the same number of elements for swapping",
                     IGRAPH_EINVAL);
    }

    for (i = 0; i < n1; i++) {
#ifdef PROD
        PROD(VECTOR(*v1)[i], VECTOR(*v1)[i], VECTOR(*v2)[i]);
#else
        VECTOR(*v1)[i] *= VECTOR(*v2)[i];
#endif
    }

    return 0;
}

/**
 * \function igraph_vector_div
 * \brief Divide a vector by another one.
 *
 * \p v1 is divided by \p v2, elementwise. They must have the same length. If the
 * base type of the vector can generate divide by zero errors then
 * please make sure that \p v2 contains no zero if you want to avoid
 * trouble.
 * \param v1 The dividend. The result is also stored here.
 * \param v2 The divisor, it is left unchanged.
 * \return Error code.
 *
 * Time complexity: O(n), the length of the vectors.
 */

int FUNCTION(igraph_vector, div)(TYPE(igraph_vector) *v1,
                                 const TYPE(igraph_vector) *v2) {

    long int n1 = FUNCTION(igraph_vector, size)(v1);
    long int n2 = FUNCTION(igraph_vector, size)(v2);
    long int i;
    if (n1 != n2) {
        IGRAPH_ERROR("Vectors must have the same number of elements for swapping",
                     IGRAPH_EINVAL);
    }

    for (i = 0; i < n1; i++) {
#ifdef DIV
        DIV(VECTOR(*v1)[i], VECTOR(*v1)[i], VECTOR(*v2)[i]);
#else
        VECTOR(*v1)[i] /= VECTOR(*v2)[i];
#endif
    }

    return 0;
}

#ifndef NOABS

int FUNCTION(igraph_vector, abs)(TYPE(igraph_vector) *v) {
#ifdef UNSIGNED
    /* Nothing do to, unsigned type */
#else
    long int i, n = FUNCTION(igraph_vector, size)(v);
    for (i = 0; i < n; i++) {
        VECTOR(*v)[i] = VECTOR(*v)[i] >= 0 ? VECTOR(*v)[i] : -VECTOR(*v)[i];
    }
#endif

    return 0;
}

#endif

#ifndef NOTORDERED

/**
 * \function igraph_vector_minmax
 * \brief Minimum and maximum elements of a vector.
 *
 * Handy if you want to have both the smallest and largest element of
 * a vector. The vector is only traversed once. The vector must by non-empty.
 * \param v The input vector. It must contain at least one element.
 * \param min Pointer to a base type variable, the minimum is stored
 *     here.
 * \param max Pointer to a base type variable, the maximum is stored
 *     here.
 * \return Error code.
 *
 * Time complexity: O(n), the number of elements.
 */

int FUNCTION(igraph_vector, minmax)(const TYPE(igraph_vector) *v,
                                    BASE *min, BASE *max) {
    long int n = FUNCTION(igraph_vector, size)(v);
    long int i;
    *min = *max = VECTOR(*v)[0];
    for (i = 1; i < n; i++) {
        BASE tmp = VECTOR(*v)[i];
        if (tmp > *max) {
            *max = tmp;
        } else if (tmp < *min) {
            *min = tmp;
        }
    }
    return 0;
}

/**
 * \function igraph_vector_which_minmax
 * \brief Index of the minimum and maximum elements
 *
 * Handy if you need the indices of the smallest and largest
 * elements. The vector is traversed only once. The vector must to
 * non-empty.
 * \param v The input vector. It must contain at least one element.
 * \param which_min The index of the minimum element will be stored
 *   here.
 * \param which_max The index of the maximum element will be stored
 *   here.
 * \return Error code.
 *
 * Time complexity: O(n), the number of elements.
 */

int FUNCTION(igraph_vector, which_minmax)(const TYPE(igraph_vector) *v,
        long int *which_min, long int *which_max) {

    long int n = FUNCTION(igraph_vector, size)(v);
    long int i;
    BASE min, max;
    *which_min = *which_max = 0;
    min = max = VECTOR(*v)[0];
    for (i = 1; i < n; i++) {
        BASE tmp = VECTOR(*v)[i];
        if (tmp > max) {
            max = tmp;
            *which_max = i;
        } else if (tmp < min) {
            min = tmp;
            *which_min = i;
        }
    }
    return 0;
}

#endif

/**
 * \function igraph_vector_isnull
 * \brief Are all elements zero?
 *
 * Checks whether all elements of a vector are zero.
 * \param v The input vector
 * \return Boolean, \c TRUE if the vector contains only zeros, \c
 *    FALSE otherwise.
 *
 * Time complexity: O(n), the number of elements.
 */

igraph_bool_t FUNCTION(igraph_vector, isnull)(const TYPE(igraph_vector) *v) {

    long int n = FUNCTION(igraph_vector, size)(v);
    long int i = 0;

#ifdef EQ
    while (i < n && EQ(VECTOR(*v)[i], ZERO)) {
#else
    while (i < n && VECTOR(*v)[i] == ZERO) {
#endif
        i++;
    }

    return i == n;
}

#ifndef NOTORDERED

int FUNCTION(igraph_i_vector, intersect_sorted)(
    const TYPE(igraph_vector) *v1, long int begin1, long int end1,
    const TYPE(igraph_vector) *v2, long int begin2, long int end2,
    TYPE(igraph_vector) *result);

/**
 * \function igraph_vector_intersect_sorted
 * \brief Calculates the intersection of two sorted vectors
 *
 * The elements that are contained in both vectors are stored in the result
 * vector. All three vectors must be initialized.
 *
 * </para><para>
 * Instead of the naive intersection which takes O(n), this function uses
 * the set intersection method of Ricardo Baeza-Yates, which is more efficient
 * when one of the vectors is significantly smaller than the other, and
 * gives similar performance on average when the two vectors are equal.
 *
 * </para><para>
 * The algorithm keeps the multiplicities of the elements: if an element appears
 * k1 times in the first vector and k2 times in the second, the result
 * will include that element min(k1, k2) times.
 *
 * </para><para>
 * Reference: Baeza-Yates R: A fast set intersection algorithm for sorted
 * sequences. In: Lecture Notes in Computer Science, vol. 3109/2004, pp.
 * 400--408, 2004. Springer Berlin/Heidelberg. ISBN: 978-3-540-22341-2.
 *
 * \param v1 the first vector
 * \param v2 the second vector
 * \param result the result vector, which will also be sorted.
 *
 * Time complexity: O(m log(n)) where m is the size of the smaller vector
 * and n is the size of the larger one.
 */
int FUNCTION(igraph_vector, intersect_sorted)(const TYPE(igraph_vector) *v1,
        const TYPE(igraph_vector) *v2, TYPE(igraph_vector) *result) {
    long int size1, size2;

    size1 = FUNCTION(igraph_vector, size)(v1);
    size2 = FUNCTION(igraph_vector, size)(v2);

    FUNCTION(igraph_vector, clear)(result);

    if (size1 == 0 || size2 == 0) {
        return 0;
    }

    IGRAPH_CHECK(FUNCTION(igraph_i_vector, intersect_sorted)(
                     v1, 0, size1, v2, 0, size2, result));
    return 0;
}

int FUNCTION(igraph_i_vector, intersect_sorted)(
    const TYPE(igraph_vector) *v1, long int begin1, long int end1,
    const TYPE(igraph_vector) *v2, long int begin2, long int end2,
    TYPE(igraph_vector) *result) {
    long int size1, size2, probe1, probe2;

    if (begin1 == end1 || begin2 == end2) {
        return 0;
    }

    size1 = end1 - begin1;
    size2 = end2 - begin2;

    if (size1 < size2) {
        probe1 = begin1 + (size1 >> 1);      /* pick the median element */
        FUNCTION(igraph_i_vector, binsearch_slice)(v2, VECTOR(*v1)[probe1], &probe2, begin2, end2);
        IGRAPH_CHECK(FUNCTION(igraph_i_vector, intersect_sorted)(
                         v1, begin1, probe1, v2, begin2, probe2, result
                     ));
        if (!(probe2 == end2 || VECTOR(*v1)[probe1] < VECTOR(*v2)[probe2])) {
            IGRAPH_CHECK(FUNCTION(igraph_vector, push_back)(result, VECTOR(*v2)[probe2]));
            probe2++;
        }
        IGRAPH_CHECK(FUNCTION(igraph_i_vector, intersect_sorted)(
                         v1, probe1 + 1, end1, v2, probe2, end2, result
                     ));
    } else {
        probe2 = begin2 + (size2 >> 1);      /* pick the median element */
        FUNCTION(igraph_i_vector, binsearch_slice)(v1, VECTOR(*v2)[probe2], &probe1, begin1, end1);
        IGRAPH_CHECK(FUNCTION(igraph_i_vector, intersect_sorted)(
                         v1, begin1, probe1, v2, begin2, probe2, result
                     ));
        if (!(probe1 == end1 || VECTOR(*v2)[probe2] < VECTOR(*v1)[probe1])) {
            IGRAPH_CHECK(FUNCTION(igraph_vector, push_back)(result, VECTOR(*v2)[probe2]));
            probe1++;
        }
        IGRAPH_CHECK(FUNCTION(igraph_i_vector, intersect_sorted)(
                         v1, probe1, end1, v2, probe2 + 1, end2, result
                     ));
    }

    return 0;
}

/**
 * \function igraph_vector_difference_sorted
 * \brief Calculates the difference between two sorted vectors (considered as sets)
 *
 * The elements that are contained in only the first vector but not the second are
 * stored in the result vector. All three vectors must be initialized.
 *
 * \param v1 the first vector
 * \param v2 the second vector
 * \param result the result vector
 */
int FUNCTION(igraph_vector, difference_sorted)(const TYPE(igraph_vector) *v1,
        const TYPE(igraph_vector) *v2, TYPE(igraph_vector) *result) {
    long int i, j, i0, j0;
    i0 = FUNCTION(igraph_vector, size)(v1);
    j0 = FUNCTION(igraph_vector, size)(v2);
    i = j = 0;

    if (i0 == 0) {
        /* v1 is empty, this is easy */
        FUNCTION(igraph_vector, clear)(result);
        return IGRAPH_SUCCESS;
    }

    if (j0 == 0) {
        /* v2 is empty, this is easy */
        IGRAPH_CHECK(FUNCTION(igraph_vector, resize)(result, i0));
        memcpy(result->stor_begin, v1->stor_begin, sizeof(BASE) * (size_t) i0);
        return IGRAPH_SUCCESS;
    }

    FUNCTION(igraph_vector, clear)(result);

    /* Copy the part of v1 that is less than the first element of v2 */
    while (i < i0 && VECTOR(*v1)[i] < VECTOR(*v2)[j]) {
        i++;
    }
    if (i > 0) {
        IGRAPH_CHECK(FUNCTION(igraph_vector, resize)(result, i));
        memcpy(result->stor_begin, v1->stor_begin, sizeof(BASE) * (size_t) i);
    }

    while (i < i0 && j < j0) {
        BASE element = VECTOR(*v1)[i];
        if (element == VECTOR(*v2)[j]) {
            i++; j++;
            while (i < i0 && VECTOR(*v1)[i] == element) {
                i++;
            }
            while (j < j0 && VECTOR(*v2)[j] == element) {
                j++;
            }
        } else if (element < VECTOR(*v2)[j]) {
            IGRAPH_CHECK(FUNCTION(igraph_vector, push_back)(result, element));
            i++;
        } else {
            j++;
        }
    }
    if (i < i0) {
        long int oldsize = FUNCTION(igraph_vector, size)(result);
        IGRAPH_CHECK(FUNCTION(igraph_vector, resize)(result, oldsize + i0 - i));
        memcpy(result->stor_begin + oldsize, v1->stor_begin + i,
               sizeof(BASE) * (size_t) (i0 - i));
    }

    return 0;
}

#endif

#if defined(OUT_FORMAT)

#ifndef USING_R
int FUNCTION(igraph_vector, print)(const TYPE(igraph_vector) *v) {
    long int i, n = FUNCTION(igraph_vector, size)(v);
    if (n != 0) {
#ifdef PRINTFUNC
        PRINTFUNC(VECTOR(*v)[0]);
#else
        printf(OUT_FORMAT, VECTOR(*v)[0]);
#endif
    }
    for (i = 1; i < n; i++) {
#ifdef PRINTFUNC
        putchar(' '); PRINTFUNC(VECTOR(*v)[i]);
#else
        printf(" " OUT_FORMAT, VECTOR(*v)[i]);
#endif
    }
    printf("\n");
    return 0;
}

int FUNCTION(igraph_vector, printf)(const TYPE(igraph_vector) *v,
                                    const char *format) {
    long int i, n = FUNCTION(igraph_vector, size)(v);
    if (n != 0) {
        printf(format, VECTOR(*v)[0]);
    }
    for (i = 1; i < n; i++) {
        putchar(' '); printf(format, VECTOR(*v)[i]);
    }
    printf("\n");
    return 0;
}

#endif

int FUNCTION(igraph_vector, fprint)(const TYPE(igraph_vector) *v, FILE *file) {
    long int i, n = FUNCTION(igraph_vector, size)(v);
    if (n != 0) {
#ifdef FPRINTFUNC
        FPRINTFUNC(file, VECTOR(*v)[0]);
#else
        fprintf(file, OUT_FORMAT, VECTOR(*v)[0]);
#endif
    }
    for (i = 1; i < n; i++) {
#ifdef FPRINTFUNC
        fputc(' ', file); FPRINTFUNC(file, VECTOR(*v)[i]);
#else
        fprintf(file, " " OUT_FORMAT, VECTOR(*v)[i]);
#endif
    }
    fprintf(file, "\n");
    return 0;
}

#endif

int FUNCTION(igraph_vector, index)(const TYPE(igraph_vector) *v,
                                   TYPE(igraph_vector) *newv,
                                   const igraph_vector_t *idx) {

    long int i, newlen = igraph_vector_size(idx);
    IGRAPH_CHECK(FUNCTION(igraph_vector, resize)(newv, newlen));

    for (i = 0; i < newlen; i++) {
        long int j = (long int) VECTOR(*idx)[i];
        VECTOR(*newv)[i] = VECTOR(*v)[j];
    }

    return 0;
}

int FUNCTION(igraph_vector, index_int)(TYPE(igraph_vector) *v,
                                       const igraph_vector_int_t *idx) {
    BASE *tmp;
    int i, n = igraph_vector_int_size(idx);

    tmp = igraph_Calloc(n, BASE);
    if (!tmp) {
        IGRAPH_ERROR("Cannot index vector", IGRAPH_ENOMEM);
    }

    for (i = 0; i < n; i++) {
        tmp[i] = VECTOR(*v)[ VECTOR(*idx)[i] ];
    }

    igraph_Free(v->stor_begin);
    v->stor_begin = tmp;
    v->stor_end = v->end = tmp + n;

    return 0;
}
