[Courgette] Fix sorting in QSufSort's split().

courgette/third_party/qsufsort.h

Index: courgette/third_party/qsufsort.h
diff --git a/courgette/third_party/qsufsort.h b/courgette/third_party/qsufsort.h
index 399768c474ecf1e76e53a5d46861460fb24d192c..f1bad03cf701cfeb7c4be47a2c848d7e643efd71 100644
--- a/courgette/third_party/qsufsort.h
+++ b/courgette/third_party/qsufsort.h
@@ -13,10 +13,12 @@
   2010-05-26 - Use a paged array for V and I. The address space may be too
                fragmented for these big arrays to be contiguous.
                  --Stephen Adams <sra@chromium.org>
-  2015-08-03 - Extrat qsufsort to a separate file as template.
+  2015-08-03 - Extract qsufsort to a separate file as template.
                  --Samuel Huang <huangs@chromium.org>
   2015-08-19 - Optimize split() and search(), add comments.
                  --Samuel Huang <huangs@chromium.org>
+  2016-04-2? - Rewrite split() to use std::sort() with I, V, resolution.
+                 --Samuel Huang <huangs@chromium.org>
 */
 
 #include <algorithm>
@@ -33,88 +35,57 @@ namespace qsuf {
 // (2) indentation,
 // (3) using 'const',
 // (4) changing the V and I parameters from int* to template <typename T>.
-// (5) optimizing split() and search(); fix styles.
+// (5) optimizing search(); fix styles.
+// (6) rewriting split() to use std::sort(), followed by I, V resolution.
 //
 // The code appears to be a rewritten version of the suffix array algorithm
 // presented in "Faster Suffix Sorting" by N. Jesper Larsson and Kunihiko
 // Sadakane, special cased for bytes.
 
+// Before: V[I[start:end]] = end - 1.
+// After: V[I[start:end]] take values in [start, end), forming "groups" of
+// suffixes that are unresolved up to length |h|. But if a group has size 1,
+// i.e., V[I[i]] == i and is unique, then we reassign I[i] to be negative so on
+// the next iteration we'd skip it.
 template <typename T> static void split(T I, T V, int start, int end, int h) {
-  // For small interval, apply selection sort.
-  if (end - start < 6) {
-    for (int i = start; i < end; ) {
-      int skip = 1;
-      int best = V[I[i] + h];
-      for (int j = i + 1; j < end; j++) {
-        int cur = V[I[j] + h];
-        if (best > cur) {
-          best = cur;
-          int tmp = I[i];
-          I[i] = I[j];
-          I[j] = tmp;
-          skip = 1;
-        } else if (best == cur) {
-          int tmp = I[i + skip];
-          I[i + skip] = I[j];
-          I[j] = tmp;
-          ++skip;
-        }
-      }
-      if (skip == 1) {
-        V[I[i]] = i;
-        I[i] = -1;
-      } else {
-        for (int j = i, jend = i + skip; j < jend; j++)
-          V[I[j]] = jend - 1;
-      }
-      i += skip;
-    }
+  if (start >= end)
     return;
-  }
 
-  // Split [start, end) into 3 intervals:
-  //   [start, j) with secondary keys < pivot,
-  //   [j, k) with secondary keys == pivot,
-  //   [k, end) with secondary keys > pivot.
-  int pivot = V[I[(start + end) / 2] + h];
-  int j = start;
-  int k = end;
-  for (int i = start; i < k; ) {
-    int cur = V[I[i] + h];
-    if (cur < pivot) {
-      if (i != j) {
-        int tmp = I[i];
-        I[i] = I[j];
-        I[j] = tmp;
-      }
-      ++i;
-      ++j;
-    } else if (cur > pivot) {
-      --k;
-      int tmp = I[i];
-      I[i] = I[k];
-      I[k] = tmp;
-    } else {
-      ++i;
+  // Sort I[start:end] using V[I[start:end] + h] as key.
+  std::sort(I.begin() + start, I.begin() + end,
+            [&](int a, int b) { return V[a + h] < V[b + h]; });
+
+  // V[I[start:end] + h] is sorted. [start,end) can be split into distinct
+  // "groups" {[a,b)} that statisfy V[I[a:b] + h] = const. For each group [a,b),
+  // reassign V[I[a:b]] := b - 1. For size-1 groups (b - a == 1), reassign
+  // I[a] := -1 to indicate completion.
+  int group_last_member = end - 1;
+  int group_key = V[I[group_last_member] + h];
+
+  // Iterate backwards to assign V[I[a:b]] := b - 1 in one pass.
+  for (int i = end - 2; i >= start; --i) {
+    int cur_key = V[I[i] + h];
+
+    // We update V[I[a:b]], but this can trample V[I[i] + h]! Fortunately, since
+    // we're reassigning all V[] values of |end - 1| to value in [begin, end)
+    // (that never appear elsewhere), so if we find anything in [begin, end),
+    // we know it used to be |end - 1|, and can reinterpret accordingly.
+    if (cur_key >= start && cur_key < end)
+      cur_key = end - 1;
+
+    // Did we find new group?
+    if (group_key != cur_key) {
+      // If previous group found has 1 member, then mark completion.
+      if (group_last_member == i + 1)
+        I[i + 1] = -1;
+      group_last_member = i;
+      group_key = cur_key;
     }
+    V[I[i]] = group_last_member;
   }
 
-  // Recurse on the "< pivot" piece.
-  if (start < j)
-    split<T>(I, V, start, j, h);
-
-  // Update the "== pivot" piece.
-  if (j == k - 1) {
-    V[I[j]] = j;
-    I[j] = -1;
-  } else {
-    for (int i = j; i < k; ++i)
-      V[I[i]] = k - 1;
-  }
-
-  // Recurse on the "> pivot" piece.
-  if (k < end)
-    split<T>(I, V, k, end, h);
+  if (group_last_member == start)
+    I[start] = -1;
 }
 
 template <class T>