1 files changed, 254 insertions, 0 deletions
diff --git a/base/suffix_array.cpp b/base/suffix_array.cpp
new file mode 100644
index 0000000000..7e5f5355ea
--- /dev/null
+++ b/base/suffix_array.cpp
@@ -0,0 +1,254 @@
+#include "base/suffix_array.hpp"
+
+#include "base/assert.hpp"
+
+#include <limits>
+
+using namespace std;
+
+namespace
+{
+bool LEQ(size_t a1, size_t a2, size_t b1, size_t b2)
+{
+  if (a1 != b1)
+    return a1 < b1;
+  return a2 <= b2;
+}
+
+bool LEQ(size_t a1, size_t a2, size_t a3, size_t b1, size_t b2, size_t b3)
+{
+  if (a1 != b1)
+    return a1 < b1;
+  return LEQ(a2, a3, b2, b3);
+}
+
+// Actually this is a counting sort, but the name RadixSort is used
+// here to keep the correspondence with the article about Skew|DC3.
+template <typename Values>
+void RadixSort(size_t numKeys, size_t const * keys, size_t numValues, Values const & values,
+               size_t * resultKeys)
+{
+  vector<size_t> count(numValues, 0);
+  for (size_t i = 0; i < numKeys; ++i)
+  {
+    auto const value = values[keys[i]];
+    ASSERT_LESS(value, count.size(), ());
+    ++count[values[keys[i]]];
+  }
+  for (size_t i = 1; i < numValues; ++i)
+    count[i] += count[i - 1];
+  for (size_t i = numKeys - 1; i < numKeys; --i)
+    resultKeys[--count[values[keys[i]]]] = keys[i];
+}
+
+bool InLeftHalf(size_t middle, size_t pos) { return pos < middle; }
+
+size_t RestoreIndex(size_t middle, size_t pos)
+{
+  return InLeftHalf(middle, pos) ? pos * 3 + 1 : (pos - middle) * 3 + 2;
+}
+
+struct SkewWrapper
+{
+  SkewWrapper(size_t n, uint8_t const * s) : m_n(n), m_s(s) {}
+
+  size_t operator[](size_t i) const
+  {
+    if (i < m_n)
+      return static_cast<size_t>(m_s[i]) + 1;
+    ASSERT_LESS(i, m_n + 3, ());
+    return 0;
+  }
+
+  size_t const m_n;
+  uint8_t const * const m_s;
+};
+
+template <typename Container>
+struct Slice
+{
+  Slice(Container const & c, size_t offset) : m_c(c), m_offset(offset) {}
+
+  size_t operator[](size_t i) const { return m_c[i + m_offset]; }
+
+  Container const & m_c;
+  size_t const m_offset;
+};
+
+template <typename Container>
+Slice<Container> MakeSlice(Container const & c, size_t offset)
+{
+  return Slice<Container>(c, offset);
+}
+
+// Builds suffix array over the string s, where for all i < n: 0 < s[i] <= k.
+//
+// Result is written to the array |SA|, where SA[i] is the offset of
+// the i-th ranked suffix.
+//
+// For implementation simplicity, it's assumed that s[n] = s[n + 1] = s[n + 2] =
+// 0.
+//
+// Idea and implementation was inspired by "Simple Linear Work Suffix
+// Array Construction" by Juha K¨arkk¨ainen and Peter Sanders.
+template <typename S>
+void RawSkew(size_t n, size_t maxValue, S const & s, size_t * sa)
+{
+  size_t const kInvalidId = numeric_limits<size_t>::max();
+
+  if (n == 0)
+    return;
+
+  if (n == 1)
+  {
+    sa[0] = 0;
+    return;
+  }
+
+  size_t const n0 = (n + 2) / 3;  // Number of =0 (mod 3) suffixes.
+  size_t const n1 = (n + 1) / 3;  // Number of =1 (mod 3) suffixes.
+  size_t const n2 = n / 3;        // Number of =2 (mod 3) suffixes.
+
+  size_t const n02 = n0 + n2;
+
+  size_t const fake1 = n0 != n1 ? 1 : 0;
+
+  // The total number of =1 (mod 3) suffixes (including the fake one)
+  // is the same as the number of =0 (mod 3) suffixes.
+  ASSERT_EQUAL(n1 + fake1, n0, ());
+  ASSERT_EQUAL(fake1, static_cast<uint32_t>(n % 3 == 1), ());
+
+  // Generate positions of =(1|2) (mod 3) suffixes.
+  vector<size_t> s12(n02 + 3);
+  vector<size_t> sa12(n02 + 3);
+
+  // (n0 - n1) is needed in case when n == 0 (mod 3).  We need a fake
+  // =1 (mod 3) suffix for proper sorting of =0 (mod 3) suffixes.
+  // Therefore we force here that the number of =1 (mod 3) suffixes
+  // should be the same as the number of =0 (mod 3) suffixes. That's
+  // why we need that s[n] = s[n + 1] = s[n + 2] = 0.
+  for (size_t i = 0, j = 0; i < n + fake1; ++i)
+  {
+    if (i % 3 != 0)
+      s12[j++] = i;
+  }
+
+  // Following three lines perform a stable sorting of all triples
+  // <s[i], s[i + 1], s[i + 2]> where i =(1|2) (mod 3), including
+  // possible fake1 suffix. Final order of these triples is written to
+  // |sa12|.
+  RadixSort(n02, s12.data(), maxValue + 1, MakeSlice(s, 2), sa12.data());
+  RadixSort(n02, sa12.data(), maxValue + 1, MakeSlice(s, 1), s12.data());
+  RadixSort(n02, s12.data(), maxValue + 1, s, sa12.data());
+
+  // Generate lexicographic names for all =(1|2) (mod 3) triples.
+  size_t name = 0;
+  size_t c0 = kInvalidId;
+  size_t c1 = kInvalidId;
+  size_t c2 = kInvalidId;
+  for (size_t i = 0; i < n02; ++i)
+  {
+    auto const pos = sa12[i];
+    if (s[pos] != c0 || s[pos + 1] != c1 || s[pos + 2] != c2)
+    {
+      c0 = s[pos];
+      c1 = s[pos + 1];
+      c2 = s[pos + 2];
+      ++name;
+    }
+
+    // Puts all =1 (mod 3) suffixes to the left part of s12, puts all
+    // =2 (mod 3) suffixes to the right part.
+    if (pos % 3 == 1)
+      s12[pos / 3] = name;
+    else
+      s12[pos / 3 + n0] = name;
+  }
+
+  if (name < n02)
+  {
+    // When not all triples unique, we need to build a suffix array
+    // for them.
+    RawSkew(n02 /* n */, name /* maxValue */, s12, sa12.data());
+    for (size_t i = 0; i < n02; ++i)
+      s12[sa12[i]] = i + 1;
+  }
+  else
+  {
+    // When all triples are unique, it's easy to build a suffix array.
+    for (size_t i = 0; i < n02; ++i)
+      sa12[s12[i] - 1] = i;
+  }
+
+  // SA12 is the suffix array for the string s12 now, and all symbols
+  // in s12 are unique.
+
+  // Need to do a stable sort for all =0 (mod 3) suffixes.
+  vector<size_t> s0(n0);
+  vector<size_t> sa0(n0);
+  for (size_t i = 0, j = 0; i < n02; ++i)
+  {
+    if (sa12[i] < n0)
+      s0[j++] = 3 * sa12[i];
+  }
+
+  // s0 is pre-sorted now in accordance with their tails (=1 (mod 3)
+  // suffixes). For full sorting we need to do a stable sort =0 (mod
+  // 3) suffixes in accordance with their first characters.
+  RadixSort(n0, s0.data(), maxValue + 1, s, sa0.data());
+
+  // SA0 is the suffix array for the string s0 now, and all symbols in
+  // s0 are unique.
+
+  // Okay, need to merge sorted =0 (mod 3) suffixes and =(1|2) (mod 3)
+  // suffixes.
+  size_t i0 = 0;
+  size_t i12 = fake1;
+  size_t k = 0;
+  while (i12 != n02 && i0 != n0)
+  {
+    size_t const p0 = sa0[i0];
+    size_t const p12 = RestoreIndex(n0, sa12[i12]);
+    ASSERT_LESS(p12 / 3, n0, ());
+
+    bool const isLEQ =
+        InLeftHalf(n0, sa12[i12])
+            ? LEQ(s[p12], s12[sa12[i12] + n0], s[p0], s12[p0 / 3])
+            : LEQ(s[p12], s[p12 + 1], s12[sa12[i12] - n0 + 1], s[p0], s[p0 + 1], s12[p0 / 3 + n0]);
+
+    if (isLEQ)
+    {
+      // Suffix =(1|2) (mod 3) is smaller.
+      sa[k++] = p12;
+      ++i12;
+    }
+    else
+    {
+      sa[k++] = p0;
+      ++i0;
+    }
+  }
+
+  for (; i12 != n02; ++k, ++i12)
+    sa[k] = RestoreIndex(n0, sa12[i12]);
+  for (; i0 != n0; ++k, ++i0)
+    sa[k] = sa0[i0];
+  ASSERT_EQUAL(k, n, ());
+}
+}  // namespace
+
+namespace base
+{
+void Skew(size_t n, uint8_t const * s, size_t * sa)
+{
+  auto const maxValue = static_cast<size_t>(numeric_limits<uint8_t>::max());
+  RawSkew(n, maxValue, SkewWrapper(n, s), sa);
+}
+
+void Skew(string const & s, vector<size_t> & sa)
+{
+  auto const n = s.size();
+  sa.assign(n, 0);
+  Skew(n, reinterpret_cast<uint8_t const *>(s.data()), sa.data());
+}
+}  // namespace base