suffix_array.cpp

/*
 * sa[i] is the starting index of the suffix which
 * is $i$'th in the sorted suffix array. 
 * The returned vector is of size $n+1$, and \texttt{sa[0] = n}.
 * The \texttt{lcp} array contains longest common prefixes for
 * neighbouring strings in the suffix array:
 * \texttt{lcp[i] = lcp(sa[i], sa[i-1])}, \texttt{lcp[0] = 0}.
 * The input string must not contain any zero bytes.
 * Time: O(n \log n)
 */

struct SuffixArray {
  vector<int> sa, lcp;
  SuffixArray(string &s, int lim = 256) { // or basic_string<int>
    int n = s.size() + 1, k = 0, a, b;
    vector<int> x(s.begin(), s.end() + 1), y(n), ws(max(n, lim)), rank(n);
    sa = lcp = y, iota(sa.begin(), sa.end(), 0);
    for (int j = 0, p = 0; p < n; j = max(1, j * 2), lim = p) {
      p = j, iota(y.begin(), y.end(), n - j);
      for (int i = 0; i < n; i++)
        if (sa[i] >= j)
          y[p++] = sa[i] - j;
      fill(ws.begin(), ws.end(), 0);
      for (int i = 0; i < n; i++)
        ws[x[i]]++;
      for (int i = 1; i < lim; i++)
        ws[i] += ws[i - 1];
      for (int i = n; i--;)
        sa[--ws[x[y[i]]]] = y[i];
      swap(x, y), p = 1, x[sa[0]] = 0;
      for (int i = 1; i < n; i++)
        a = sa[i - 1], b = sa[i],
        x[b] = (y[a] == y[b] && y[a + j] == y[b + j]) ? p - 1 : p++;
    }
    for (int i = 1; i < n; i++)
      rank[sa[i]] = i;
    for (int i = 0, j; i < n - 1; lcp[rank[i++]] = k)
      for (k &&k--, j = sa[rank[i] - 1]; s[i + k] == s[j + k]; k++)
        ;
  }
};