algo(problems): spoj longcs lcs multiple strings

Author: mateusvrs

algorithms/problems/lcs-ks-strings.cpp

@@ -0,0 +1,30 @@
+int lcs_ks_strings(vector<string>& sts, int k) {
+  vi fml;
+  string t;
+  for (int i = 0; i < k; i++) {
+    t += sts[i];
+    for (int j = 0; j < sts[i].size(); j++) fml.push_back(i);
+  }
+
+  vi p = suffix_array(t);
+  deque<int> lcp = lcp_suffix_array(t, p);
+  lcp.push_front(0);
+
+  int l = 0, r = 0, cnt = 0, lcs = 0, n = p.size();
+  vector<int> fr(k + 1);
+  multiset<int> mst;
+  while (l < n) {
+    while (r < n and cnt < k) {
+      mst.insert(lcp[r]);
+      if (!fr[fml[p[r]]]++) cnt++;
+      r++;
+    }
+    mst.erase(mst.find(lcp[l]));
+    if (mst.size() and cnt == k) lcs = max(lcs, *mst.begin());
+    fr[fml[p[l]]]--;
+    if (!fr[fml[p[l]]]) cnt--;
+    l++;
+  }
+
+  return lcs;
+}

algorithms/problems/lcs-ks-strings.tex

@@ -0,0 +1,3 @@
+\subsection{Longest Common Substring (LONGCS - SPOJ)}
+
+Time: $N = \sum_{i = 1}^k |S_i|$; Suffix Array + LCP with Suffix Array + $O(N \cdot \log N)$