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New module 'array-mergesort'.
author Bruno Haible <bruno@clisp.org>
date Mon, 16 Feb 2009 03:14:41 +0100
parents 66432f187008
children 8efaede722cf
files ChangeLog lib/array-mergesort.h modules/array-mergesort
diffstat 3 files changed, 301 insertions(+), 0 deletions(-) [+]
line wrap: on
line diff
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,9 @@
+2009-02-15  Bruno Haible  <bruno@clisp.org>
+
+	New module 'array-mergesort'.
+	* modules/array-mergesort: New file.
+	* lib/array-mergesort.h: New file.
+
 2009-02-15  Bruno Haible  <bruno@clisp.org>
 
 	Fix 2009-02-07 commit.
new file mode 100644
--- /dev/null
+++ b/lib/array-mergesort.h
@@ -0,0 +1,274 @@
+/* Stable-sorting of an array using mergesort.
+   Copyright (C) 2009 Free Software Foundation, Inc.
+   Written by Bruno Haible <bruno@clisp.org>, 2009.
+
+   This program is free software: you can redistribute it and/or modify it
+   under the terms of the GNU Lesser General Public License as published
+   by the Free Software Foundation; either version 3 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
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public License
+   along with this program.  If not, see <http://www.gnu.org/licenses/>.  */
+
+/* This file implements stable sorting of an array, using the mergesort
+   algorithm.
+   Worst-case running time for an array of length N is O(N log N).
+   Unlike the mpsort module, the algorithm here attempts to minimize not
+   only the number of comparisons, but also the number of copying operations.
+
+   Before including this file, you need to define
+     ELEMENT      The type of every array element.
+     COMPARE      A two-argument macro that takes two 'const ELEMENT *'
+                  pointers and returns a negative, zero, or positive 'int'
+                  value if the element pointed to by the first argument is,
+                  respectively, less, equal, or greater than the element
+                  pointed to by the second argument.
+     STATIC       The storage class of the functions being defined.
+   Before including this file, you also need to include:
+     #include <stddef.h>
+ */
+
+/* Merge the sorted arrays src1[0..n1-1] and src2[0..n2-1] into
+   dst[0..n1+n2-1].  In case of ambiguity, put the elements of src1
+   before the elements of src2.
+   n1 and n2 must be > 0.
+   The arrays src1 and src2 must not overlap the dst array, except that
+   src1 may be dst[n2..n1+n2-1], or src2 may be dst[n1..n1+n2-1].  */
+static void
+merge (const ELEMENT *src1, size_t n1,
+       const ELEMENT *src2, size_t n2,
+       ELEMENT *dst)
+{
+  for (;;) /* while (n1 > 0 && n2 > 0) */
+    {
+      if (COMPARE (src1, src2) <= 0)
+	{
+	  *dst++ = *src1++;
+	  n1--;
+	  if (n1 == 0)
+	    break;
+	}
+      else
+	{
+	  *dst++ = *src2++;
+	  n2--;
+	  if (n2 == 0)
+	    break;
+	}
+    }
+  /* Here n1 == 0 || n2 == 0 but also n1 > 0 || n2 > 0.  */
+  if (n1 > 0)
+    {
+      if (dst != src1)
+	do
+	  {
+	    *dst++ = *src1++;
+	    n1--;
+	  }
+	while (n1 > 0);
+    }
+  else /* n2 > 0 */
+    {
+      if (dst != src2)
+	do
+	  {
+	    *dst++ = *src2++;
+	    n2--;
+	  }
+	while (n2 > 0);
+    }
+}
+
+/* Sort src[0..n-1] into dst[0..n-1], using tmp[0..n/2-1] as temporary
+   (scratch) storage.
+   The arrays src, dst, tmp must not overlap.  */
+STATIC void
+merge_sort_fromto (const ELEMENT *src, ELEMENT *dst, size_t n, ELEMENT *tmp)
+{
+  switch (n)
+    {
+    case 0:
+      return;
+    case 1:
+      /* Nothing to do.  */
+      dst[0] = src[0];
+      return;
+    case 2:
+      /* Trivial case.  */
+      if (COMPARE (&src[0], &src[1]) <= 0)
+	{
+	  /* src[0] <= src[1] */
+	  dst[0] = src[0];
+	  dst[1] = src[1];
+	}
+      else
+	{
+	  dst[0] = src[1];
+	  dst[1] = src[0];
+	}
+      break;
+    case 3:
+      /* Simple case.  */
+      if (COMPARE (&src[0], &src[1]) <= 0)
+	{
+	  if (COMPARE (&src[1], &src[2]) <= 0)
+	    {
+	      /* src[0] <= src[1] <= src[2] */
+	      dst[0] = src[0];
+	      dst[1] = src[1];
+	      dst[2] = src[2];
+	    }
+	  else if (COMPARE (&src[0], &src[2]) <= 0)
+	    {
+	      /* src[0] <= src[2] < src[1] */
+	      dst[0] = src[0];
+	      dst[1] = src[2];
+	      dst[2] = src[1];
+	    }
+	  else
+	    {
+	      /* src[2] < src[0] <= src[1] */
+	      dst[0] = src[2];
+	      dst[1] = src[0];
+	      dst[2] = src[1];
+	    }
+	}
+      else
+	{
+	  if (COMPARE (&src[0], &src[2]) <= 0)
+	    {
+	      /* src[1] < src[0] <= src[2] */
+	      dst[0] = src[1];
+	      dst[1] = src[0];
+	      dst[2] = src[2];
+	    }
+	  else if (COMPARE (&src[1], &src[2]) <= 0)
+	    {
+	      /* src[1] <= src[2] < src[0] */
+	      dst[0] = src[1];
+	      dst[1] = src[2];
+	      dst[2] = src[0];
+	    }
+	  else
+	    {
+	      /* src[2] < src[1] < src[0] */
+	      dst[0] = src[2];
+	      dst[1] = src[1];
+	      dst[2] = src[0];
+	    }
+	}
+      break;
+    default:
+      {
+	size_t n1 = n / 2;
+	size_t n2 = (n + 1) / 2;
+	/* Note: n1 + n2 = n, n1 <= n2.  */
+	/* Sort src[n1..n-1] into dst[n1..n-1], scratching tmp[0..n2/2-1].  */
+	merge_sort_fromto (src + n1, dst + n1, n2, tmp);
+	/* Sort src[0..n1-1] into tmp[0..n1-1], scratching dst[0..n1-1].  */
+	merge_sort_fromto (src, tmp, n1, dst);
+	/* Merge the two half results.  */
+	merge (tmp, n1, dst + n1, n2, dst);
+      }
+      break;
+    }
+}
+
+/* Sort src[0..n-1], using tmp[0..n-1] as temporary (scratch) storage.
+   The arrays src, tmp must not overlap. */
+STATIC void
+merge_sort_inplace (ELEMENT *src, size_t n, ELEMENT *tmp)
+{
+  switch (n)
+    {
+    case 0:
+    case 1:
+      /* Nothing to do.  */
+      return;
+    case 2:
+      /* Trivial case.  */
+      if (COMPARE (&src[0], &src[1]) <= 0)
+	{
+	  /* src[0] <= src[1] */
+	}
+      else
+	{
+	  ELEMENT t = src[0];
+	  src[0] = src[1];
+	  src[1] = t;
+	}
+      break;
+    case 3:
+      /* Simple case.  */
+      if (COMPARE (&src[0], &src[1]) <= 0)
+	{
+	  if (COMPARE (&src[1], &src[2]) <= 0)
+	    {
+	      /* src[0] <= src[1] <= src[2] */
+	    }
+	  else if (COMPARE (&src[0], &src[2]) <= 0)
+	    {
+	      /* src[0] <= src[2] < src[1] */
+	      ELEMENT t = src[1];
+	      src[1] = src[2];
+	      src[2] = t;
+	    }
+	  else
+	    {
+	      /* src[2] < src[0] <= src[1] */
+	      ELEMENT t = src[0];
+	      src[0] = src[2];
+	      src[2] = src[1];
+	      src[1] = t;
+	    }
+	}
+      else
+	{
+	  if (COMPARE (&src[0], &src[2]) <= 0)
+	    {
+	      /* src[1] < src[0] <= src[2] */
+	      ELEMENT t = src[0];
+	      src[0] = src[1];
+	      src[1] = t;
+	    }
+	  else if (COMPARE (&src[1], &src[2]) <= 0)
+	    {
+	      /* src[1] <= src[2] < src[0] */
+	      ELEMENT t = src[0];
+	      src[0] = src[1];
+	      src[1] = src[2];
+	      src[2] = t;
+	    }
+	  else
+	    {
+	      /* src[2] < src[1] < src[0] */
+	      ELEMENT t = src[0];
+	      src[0] = src[2];
+	      src[2] = t;
+	    }
+	}
+      break;
+    default:
+      {
+	size_t n1 = n / 2;
+	size_t n2 = (n + 1) / 2;
+	/* Note: n1 + n2 = n, n1 <= n2.  */
+	/* Sort src[n1..n-1], scratching tmp[0..n2-1].  */
+	merge_sort_inplace (src + n1, n2, tmp);
+	/* Sort src[0..n1-1] into tmp[0..n1-1], scratching tmp[n1..2*n1-1].  */
+	merge_sort_fromto (src, tmp, n1, tmp + n1);
+	/* Merge the two half results.  */
+	merge (tmp, n1, src + n1, n2, src);
+      }
+      break;
+    }
+}
+
+#undef ELEMENT
+#undef COMPARE
+#undef STATIC
new file mode 100644
--- /dev/null
+++ b/modules/array-mergesort
@@ -0,0 +1,21 @@
+Description:
+Merge-sort algorithm on arrays.
+
+Files:
+lib/array-mergesort.h
+
+Depends-on:
+
+configure.ac:
+
+Makefile.am:
+
+Include:
+"array-mergesort.h"
+
+License:
+LGPL
+
+Maintainer:
+Bruno Haible
+