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fib.c

/*-
 * Copyright 1997-2003 John-Mark Gurney.
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 *    $Id: fib.c,v 1.2 2007-07-04 22:44:39 martin-s Exp $
 *
 */

#include <fib.h>
#include <fibpriv.h>

#include <limits.h>
#include <stdlib.h>

#define swap(type, a, b)            \
            do {              \
                  type c;           \
                  c = a;            \
                  a = b;            \
                  b = c;            \
            } while (0)       \

#define INT_BITS        (sizeof(int) * 8)
static inline int
ceillog2(unsigned int a)
{
      int oa;
      int i;
      int b;

      oa = a;
      b = INT_BITS / 2;
      i = 0;
      while (b) {
            i = (i << 1);
            if (a >= (1 << b)) {
                  a /= (1 << b);
                  i = i | 1;
            } else
                  a &= (1 << b) - 1;
            b /= 2;
      }
      if ((1 << i) == oa)
            return i;
      else
            return i + 1;
}

/*
 * Private Heap Functions
 */
static void
fh_deleteel(struct fibheap *h, struct fibheap_el *x)
{
      void *data;
      int key;

      data = x->fhe_data;
      key = x->fhe_key;

      if (!h->fh_keys)
            fh_replacedata(h, x, h->fh_neginf);
      else
            fh_replacekey(h, x, INT_MIN);
      if (fh_extractminel(h) != x) {
            /*
             * XXX - This should never happen as fh_replace should set it
             * to min.
             */
            abort();
      }

      x->fhe_data = data;
      x->fhe_key = key;
}

static void
fh_initheap(struct fibheap *new)
{
      new->fh_cmp_fnct = NULL;
      new->fh_neginf = NULL;
      new->fh_n = 0;
      new->fh_Dl = -1;
      new->fh_cons = NULL;
      new->fh_min = NULL;
      new->fh_root = NULL;
      new->fh_keys = 0;
#ifdef FH_STATS
      new->fh_maxn = 0;
      new->fh_ninserts = 0;
      new->fh_nextracts = 0;
#endif
}

static void
fh_destroyheap(struct fibheap *h)
{
      h->fh_cmp_fnct = NULL;
      h->fh_neginf = NULL;
      if (h->fh_cons != NULL)
            free(h->fh_cons);
      h->fh_cons = NULL;
      free(h);
}

/*
 * Public Heap Functions
 */
struct fibheap *
fh_makekeyheap()
{
      struct fibheap *n;

      if ((n = malloc(sizeof *n)) == NULL)
            return NULL;

      fh_initheap(n);
      n->fh_keys = 1;

      return n;
}

struct fibheap *
fh_makeheap()
{
      struct fibheap *n;

      if ((n = malloc(sizeof *n)) == NULL)
            return NULL;

      fh_initheap(n);

      return n;
}

voidcmp
fh_setcmp(struct fibheap *h, voidcmp fnct)
{
      voidcmp oldfnct;
      
      oldfnct = h->fh_cmp_fnct;
      h->fh_cmp_fnct = fnct;

      return oldfnct;
}

void *
fh_setneginf(struct fibheap *h, void *data)
{
      void *old;

      old = h->fh_neginf;
      h->fh_neginf = data;

      return old;
}

struct fibheap *
fh_union(struct fibheap *ha, struct fibheap *hb)
{
      struct fibheap_el *x;

      if (ha->fh_root == NULL || hb->fh_root == NULL) {
            /* either one or both are empty */
            if (ha->fh_root == NULL) {
                  fh_destroyheap(ha);
                  return hb;
            } else {
                  fh_destroyheap(hb);
                  return ha;
            }
      }
      ha->fh_root->fhe_left->fhe_right = hb->fh_root;
      hb->fh_root->fhe_left->fhe_right = ha->fh_root;
      x = ha->fh_root->fhe_left;
      ha->fh_root->fhe_left = hb->fh_root->fhe_left;
      hb->fh_root->fhe_left = x;
      ha->fh_n += hb->fh_n;
      /*
       * we probably should also keep stats on number of unions
       */

      /* set fh_min if necessary */
      if (fh_compare(ha, hb->fh_min, ha->fh_min) < 0)
            ha->fh_min = hb->fh_min;

      fh_destroyheap(hb);
      return ha;
}

void
fh_deleteheap(struct fibheap *h)
{
      /*
       * We could do this even faster by walking each binomial tree, but
       * this is simpler to code.
       */
      while (h->fh_min != NULL)
            fhe_destroy(fh_extractminel(h));

      fh_destroyheap(h);
}

/*
 * Public Key Heap Functions
 */
struct fibheap_el *
fh_insertkey(struct fibheap *h, int key, void *data)
{
      struct fibheap_el *x;

      if ((x = fhe_newelem()) == NULL)
            return NULL;

      /* just insert on root list, and make sure it's not the new min */
      x->fhe_data = data;
      x->fhe_key = key;

      fh_insertel(h, x);

      return x;
}

int
fh_minkey(struct fibheap *h)
{
      if (h->fh_min == NULL)
            return INT_MIN;
      return h->fh_min->fhe_key;
}

int
fh_replacekey(struct fibheap *h, struct fibheap_el *x, int key)
{
      int ret;

      ret = x->fhe_key;
      (void)fh_replacekeydata(h, x, key, x->fhe_data);

      return ret;
}

#include <stdio.h>

void *
fh_replacekeydata(struct fibheap *h, struct fibheap_el *x, int key, void *data)
{
      void *odata;
      int okey;
      struct fibheap_el *y;
      int r;

      odata = x->fhe_data;
      okey = x->fhe_key;

      /*
       * we can increase a key by deleting and reinserting, that
       * requires O(lgn) time.
       */
      if ((r = fh_comparedata(h, key, data, x)) > 0) {
            printf("fh_comparedata r=%d key=%d data=%p\n", r, key, data);
            /* XXX - bad code! */
            abort();
            fh_deleteel(h, x);

            x->fhe_data = data;
            x->fhe_key = key;

            fh_insertel(h, x);

            return odata;
      }

      x->fhe_data = data;
      x->fhe_key = key;

      /* because they are equal, we don't have to do anything */
      if (r == 0)
            return odata;

      y = x->fhe_p;

      if (h->fh_keys && okey == key)
            return odata;

      if (y != NULL && fh_compare(h, x, y) <= 0) {
            fh_cut(h, x, y);
            fh_cascading_cut(h, y);
      }

      /*
       * the = is so that the call from fh_delete will delete the proper
       * element.
       */
      if (fh_compare(h, x, h->fh_min) <= 0)
            h->fh_min = x;

      return odata;
}

/*
 * Public void * Heap Functions
 */
/*
 * this will return these values:
 *    NULL  failed for some reason
 *    ptr   token to use for manipulation of data
 */
struct fibheap_el *
fh_insert(struct fibheap *h, void *data)
{
      struct fibheap_el *x;

      if ((x = fhe_newelem()) == NULL)
            return NULL;

      /* just insert on root list, and make sure it's not the new min */
      x->fhe_data = data;

      fh_insertel(h, x);

      return x;
}

void *
fh_min(struct fibheap *h)
{
      if (h->fh_min == NULL)
            return NULL;
      return h->fh_min->fhe_data;
}

void *
fh_extractmin(struct fibheap *h)
{
      struct fibheap_el *z;
      void *ret;

      ret = NULL;

      if (h->fh_min != NULL) {
            z = fh_extractminel(h);
            ret = z->fhe_data;
#ifndef NO_FREE
            fhe_destroy(z);
#endif

      }

      return ret;
}

void *
fh_replacedata(struct fibheap *h, struct fibheap_el *x, void *data)
{
      return fh_replacekeydata(h, x, x->fhe_key, data);
}

void *
fh_delete(struct fibheap *h, struct fibheap_el *x)
{
      void *k;

      k = x->fhe_data;
      if (!h->fh_keys)
            fh_replacedata(h, x, h->fh_neginf);
      else
            fh_replacekey(h, x, INT_MIN);
      fh_extractmin(h);

      return k;
}

/*
 * Statistics Functions
 */
#ifdef FH_STATS
int
fh_maxn(struct fibheap *h)
{
      return h->fh_maxn;
}

int
fh_ninserts(struct fibheap *h)
{
      return h->fh_ninserts;
}

int
fh_nextracts(struct fibheap *h)
{
      return h->fh_nextracts;
}
#endif

/*
 * begin of private element fuctions
 */
static struct fibheap_el *
fh_extractminel(struct fibheap *h)
{
      struct fibheap_el *ret;
      struct fibheap_el *x, *y, *orig;

      ret = h->fh_min;

      orig = NULL;
      /* put all the children on the root list */
      /* for true consistancy, we should use fhe_remove */
      for(x = ret->fhe_child; x != orig && x != NULL;) {
            if (orig == NULL)
                  orig = x;
            y = x->fhe_right;
            x->fhe_p = NULL;
            fh_insertrootlist(h, x);
            x = y;
      }
      /* remove minimum from root list */
      fh_removerootlist(h, ret);
      h->fh_n--;

      /* if we aren't empty, consolidate the heap */
      if (h->fh_n == 0)
            h->fh_min = NULL;
      else {
            h->fh_min = ret->fhe_right;
            fh_consolidate(h);
      }

#ifdef FH_STATS
      h->fh_nextracts++;
#endif

      return ret;
}

static void
fh_insertrootlist(struct fibheap *h, struct fibheap_el *x)
{
      if (h->fh_root == NULL) {
            h->fh_root = x;
            x->fhe_left = x;
            x->fhe_right = x;
            return;
      }

      fhe_insertafter(h->fh_root, x);
}

static void
fh_removerootlist(struct fibheap *h, struct fibheap_el *x)
{
      if (x->fhe_left == x)
            h->fh_root = NULL;
      else
            h->fh_root = fhe_remove(x);
}

static void
fh_consolidate(struct fibheap *h)
{
      struct fibheap_el **a;
      struct fibheap_el *w;
      struct fibheap_el *y;
      struct fibheap_el *x;
      int i;
      int d;
      int D;

      fh_checkcons(h);

      /* assign a the value of h->fh_cons so I don't have to rewrite code */
      D = h->fh_Dl + 1;
      a = h->fh_cons;

      for (i = 0; i < D; i++)
            a[i] = NULL;

      while ((w = h->fh_root) != NULL) {
            x = w;
            fh_removerootlist(h, w);
            d = x->fhe_degree;
            /* XXX - assert that d < D */
            while(a[d] != NULL) {
                  y = a[d];
                  if (fh_compare(h, x, y) > 0)
                        swap(struct fibheap_el *, x, y);
                  fh_heaplink(h, y, x);
                  a[d] = NULL;
                  d++;
            }
            a[d] = x;
      }
      h->fh_min = NULL;
      for (i = 0; i < D; i++)
            if (a[i] != NULL) {
                  fh_insertrootlist(h, a[i]);
                  if (h->fh_min == NULL || fh_compare(h, a[i],
                      h->fh_min) < 0)
                        h->fh_min = a[i];
            }
}

static void
fh_heaplink(struct fibheap *h, struct fibheap_el *y, struct fibheap_el *x)
{
      /* make y a child of x */
      if (x->fhe_child == NULL)
            x->fhe_child = y;
      else
            fhe_insertbefore(x->fhe_child, y);
      y->fhe_p = x;
      x->fhe_degree++;
      y->fhe_mark = 0;
}

static void
fh_cut(struct fibheap *h, struct fibheap_el *x, struct fibheap_el *y)
{
      fhe_remove(x);
      y->fhe_degree--;
      fh_insertrootlist(h, x);
      x->fhe_p = NULL;
      x->fhe_mark = 0;
}

static void
fh_cascading_cut(struct fibheap *h, struct fibheap_el *y)
{
      struct fibheap_el *z;

      while ((z = y->fhe_p) != NULL) {
            if (y->fhe_mark == 0) {
                  y->fhe_mark = 1;
                  return;
            } else {
                  fh_cut(h, y, z);
                  y = z;
            }
      }
}

/*
 * begining of handling elements of fibheap
 */
static struct fibheap_el *
fhe_newelem()
{
      struct fibheap_el *e;

      if ((e = malloc(sizeof *e)) == NULL)
            return NULL;

      fhe_initelem(e);

      return e;
}

static void
fhe_initelem(struct fibheap_el *e)
{
      e->fhe_degree = 0;
      e->fhe_mark = 0;
      e->fhe_p = NULL;
      e->fhe_child = NULL;
      e->fhe_left = e;
      e->fhe_right = e;
      e->fhe_data = NULL;
}

static void
fhe_insertafter(struct fibheap_el *a, struct fibheap_el *b)
{
      if (a == a->fhe_right) {
            a->fhe_right = b;
            a->fhe_left = b;
            b->fhe_right = a;
            b->fhe_left = a;
      } else {
            b->fhe_right = a->fhe_right;
            a->fhe_right->fhe_left = b;
            a->fhe_right = b;
            b->fhe_left = a;
      }
}

static inline void
fhe_insertbefore(struct fibheap_el *a, struct fibheap_el *b)
{
      fhe_insertafter(a->fhe_left, b);
}

static struct fibheap_el *
fhe_remove(struct fibheap_el *x)
{
      struct fibheap_el *ret;

      if (x == x->fhe_left)
            ret = NULL;
      else
            ret = x->fhe_left;

      /* fix the parent pointer */
      if (x->fhe_p != NULL && x->fhe_p->fhe_child == x)
            x->fhe_p->fhe_child = ret;

      x->fhe_right->fhe_left = x->fhe_left;
      x->fhe_left->fhe_right = x->fhe_right;

      /* clear out hanging pointers */
      x->fhe_p = NULL;
      x->fhe_left = x;
      x->fhe_right = x;

      return ret;
}

static void
fh_checkcons(struct fibheap *h)
{
      int oDl;

      /* make sure we have enough memory allocated to "reorganize" */
      if (h->fh_Dl == -1 || h->fh_n > (1 << h->fh_Dl)) {
            oDl = h->fh_Dl;
            if ((h->fh_Dl = ceillog2(h->fh_n) + 1) < 8)
                  h->fh_Dl = 8;
            if (oDl != h->fh_Dl)
                  h->fh_cons = (struct fibheap_el **)realloc(h->fh_cons,
                      sizeof *h->fh_cons * (h->fh_Dl + 1));
            if (h->fh_cons == NULL)
                  abort();
      }
}

static int
fh_compare(struct fibheap *h, struct fibheap_el *a, struct fibheap_el *b)
{
      if (h->fh_keys) {
            if (a->fhe_key < b->fhe_key)
                  return -1;
            if (a->fhe_key == b->fhe_key)
                  return 0;
            return 1;
      } else
            return h->fh_cmp_fnct(a->fhe_data, b->fhe_data);
}

static int
fh_comparedata(struct fibheap *h, int key, void *data, struct fibheap_el *b)
{
      struct fibheap_el a;

      a.fhe_key = key;
      a.fhe_data = data;

      return fh_compare(h, &a, b);
}

static void
fh_insertel(struct fibheap *h, struct fibheap_el *x)
{
      fh_insertrootlist(h, x);

      if (h->fh_min == NULL || (h->fh_keys ? x->fhe_key < h->fh_min->fhe_key
          : h->fh_cmp_fnct(x->fhe_data, h->fh_min->fhe_data) < 0))
            h->fh_min = x;

      h->fh_n++;

#ifdef FH_STATS
      if (h->fh_n > h->fh_maxn)
            h->fh_maxn = h->fh_n;
      h->fh_ninserts++;
#endif

}

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