Ensure O(n) worst-case complexity.

diff --git a/ChangeLog b/ChangeLog
index 1e5cda365526b2f1da226a61d04591efce7dedb9..80bfad57e4937b60eed97d925b41e83591c4c5fb 100644 (file)
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,12 @@
 2007-02-11  Bruno Haible  <bruno@clisp.org>
 
+       Ensure O(n) worst-case complexity of c_strstr.
+       * lib/c-strstr.c: Include stdbool.h, string.h.
+       (knuth_morris_pratt): New function.
+       (c_strstr): Add some bookkeeping. Invoke knuth_morris_pratt when the
+       bookkeeping indicates that it's worth it.
+       * modules/c-strstr (Depends-on): Add stdbool, strnlen.
+
        * lib/c-strstr.c: Complete rewrite for maintainability.
 
        * modules/c-strstr-tests: New file.

diff --git a/lib/c-strstr.c b/lib/c-strstr.c
index a3623f650a45ff00d1535b360c3c36727410f32e..fe38f5321955150abbd597d85951179b3c1b9878 100644 (file)
--- a/lib/c-strstr.c
+++ b/lib/c-strstr.c
@@ -21,7 +21,97 @@
 /* Specification.  */
 #include "c-strstr.h"
 
-#include <stddef.h>
+#include <stdbool.h>
+#include <stdlib.h>
+#include <string.h>
+
+/* Knuth-Morris-Pratt algorithm.
+   See http://en.wikipedia.org/wiki/Knuth-Morris-Pratt_algorithm
+   Return a boolean indicating success.  */
+static bool
+knuth_morris_pratt (const char *haystack, const char *needle,
+                   const char **resultp)
+{
+  size_t m = strlen (needle);
+
+  /* Allocate the table.  */
+  size_t *table = (size_t *) malloc (m * sizeof (size_t));
+  if (table == NULL)
+    return false;
+  /* Fill the table.
+     For 0 < i < m:
+       0 < table[i] <= i is defined such that
+       rhaystack[0..i-1] == needle[0..i-1] and rhaystack[i] != needle[i]
+       implies
+       forall 0 <= x < table[i]: rhaystack[x..x+m-1] != needle[0..m-1],
+       and table[i] is as large as possible with this property.
+     table[0] remains uninitialized.  */
+  {
+    size_t i, j;
+
+    table[1] = 1;
+    j = 0;
+    for (i = 2; i < m; i++)
+      {
+       unsigned char b = (unsigned char) needle[i - 1];
+
+       for (;;)
+         {
+           if (b == (unsigned char) needle[j])
+             {
+               table[i] = i - ++j;
+               break;
+             }
+           if (j == 0)
+             {
+               table[i] = i;
+               break;
+             }
+           j = j - table[j];
+         }
+      }
+  }
+
+  /* Search, using the table to accelerate the processing.  */
+  {
+    size_t j;
+    const char *rhaystack;
+    const char *phaystack;
+
+    *resultp = NULL;
+    j = 0;
+    rhaystack = haystack;
+    phaystack = haystack;
+    /* Invariant: phaystack = rhaystack + j.  */
+    while (*phaystack != '\0')
+      if ((unsigned char) needle[j] == (unsigned char) *phaystack)
+       {
+         j++;
+         phaystack++;
+         if (j == m)
+           {
+             /* The entire needle has been found.  */
+             *resultp = rhaystack;
+             break;
+           }
+       }
+      else if (j > 0)
+       {
+         /* Found a match of needle[0..j-1], mismatch at needle[j].  */
+         rhaystack += table[j];
+         j -= table[j];
+       }
+      else
+       {
+         /* Found a mismatch at needle[0] already.  */
+         rhaystack++;
+         phaystack++;
+       }
+  }
+
+  free (table);
+  return true;
+}
 
 /* Find the first occurrence of NEEDLE in HAYSTACK.  */
 char *
@@ -34,6 +124,26 @@ c_strstr (const char *haystack, const char *needle)
          needle may be found in haystack.  */
   if (*needle != '\0')
     {
+      /* Minimizing the worst-case complexity:
+        Let n = strlen(haystack), m = strlen(needle).
+        The naïve algorithm is O(n*m) worst-case.
+        The Knuth-Morris-Pratt algorithm is O(n) worst-case but it needs a
+        memory allocation.
+        To achieve linear complexity and yet amortize the cost of the memory
+        allocation, we activate the Knuth-Morris-Pratt algorithm only once
+        the naïve algorithm has already run for some time; more precisely,
+        when
+          - the outer loop count is >= 10,
+          - the average number of comparisons per outer loop is >= 5,
+          - the total number of comparisons is >= m.
+        But we try it only once.  If the memory allocation attempt failed,
+        we don't retry it.  */
+      bool try_kmp = true;
+      size_t outer_loop_count = 0;
+      size_t comparison_count = 0;
+      size_t last_ccount = 0;                  /* last comparison count */
+      const char *needle_last_ccount = needle; /* = needle + last_ccount */
+
       /* Speed up the following searches of needle by caching its first
         character.  */
       unsigned char b = (unsigned char) *needle;
@@ -44,6 +154,37 @@ c_strstr (const char *haystack, const char *needle)
          if (*haystack == '\0')
            /* No match.  */
            return NULL;
+
+         /* See whether it's advisable to use an asymptotically faster
+            algorithm.  */
+         if (try_kmp
+             && outer_loop_count >= 10
+             && comparison_count >= 5 * outer_loop_count)
+           {
+             /* See if needle + comparison_count now reaches the end of
+                needle.  */
+             if (needle_last_ccount != NULL)
+               {
+                 needle_last_ccount +=
+                   strnlen (needle_last_ccount, comparison_count - last_ccount);
+                 if (*needle_last_ccount == '\0')
+                   needle_last_ccount = NULL;
+                 last_ccount = comparison_count;
+               }
+             if (needle_last_ccount == NULL)
+               {
+                 /* Try the Knuth-Morris-Pratt algorithm.  */
+                 const char *result;
+                 bool success =
+                   knuth_morris_pratt (haystack, needle - 1, &result);
+                 if (success)
+                   return (char *) result;
+                 try_kmp = false;
+               }
+           }
+
+         outer_loop_count++;
+         comparison_count++;
          if ((unsigned char) *haystack == b)
            /* The first character matches.  */
            {
@@ -58,6 +199,7 @@ c_strstr (const char *haystack, const char *needle)
                  if (*rhaystack == '\0')
                    /* No match.  */
                    return NULL;
+                 comparison_count++;
                  if ((unsigned char) *rhaystack != (unsigned char) *rneedle)
                    /* Nothing in this round.  */
                    break;

diff --git a/modules/c-strstr b/modules/c-strstr
index bcc7b77a16d89c567e9ed9193bf90e93185c5d6b..703d879a210ba33622311f0e4b9f2105182811c4 100644 (file)
--- a/modules/c-strstr
+++ b/modules/c-strstr
@@ -6,6 +6,8 @@ lib/c-strstr.h
 lib/c-strstr.c
 
 Depends-on:
+stdbool
+strnlen
 
 configure.ac: