From 4c12f8c3a3ea66c8ab9988a5b6f650f6d313d1d7 Mon Sep 17 00:00:00 2001
From: Ahmed Dardery <Megadardery@yahoo.com>
Date: Sat, 23 Oct 2021 13:56:46 +0200
Subject: [PATCH 1/2] new: Palindromic Tree

---
 content/strings/PalindromicTree.h        | 58 ++++++++++++++++++++++++
 content/strings/chapter.tex              |  1 +
 stress-tests/strings/PalindromicTree.cpp | 32 +++++++++++++
 3 files changed, 91 insertions(+)
 create mode 100644 content/strings/PalindromicTree.h
 create mode 100644 stress-tests/strings/PalindromicTree.cpp

diff --git a/content/strings/PalindromicTree.h b/content/strings/PalindromicTree.h
new file mode 100644
index 000000000..34497244b
--- /dev/null
+++ b/content/strings/PalindromicTree.h
@@ -0,0 +1,58 @@
+/**
+ * Author: Ahmed Dardery
+ * Date: 2020-12-24
+ * License: CC0
+ * Source: https://codeforces.com/blog/entry/13959
+ * Description: Builds a palindromic tree over a string
+ * 0 is the imaginary string, 1 is the empty string
+ * [2, n) are the palindromes, s.substr(pos[i], len[i]), occurs freq[i]
+ * fail[i] is the longest suffix palindrome of ith palindrome
+ * Time: O(n)
+ * Status: stress-tested
+ */
+#pragma once
+
+struct PalinTree {
+  const int A = 128;
+  string str;
+  vi fail, len, pos, lz, freq;
+  vector<vi> nxt;
+  int n, cur;
+ 
+  PalinTree(const string &s) : str(s) {
+    fail = len = pos = lz = freq = vi(sz(s) + 2);
+    nxt.resize(sz(s) + 2);
+    n = cur = fail[0] = fail[1] = 0;
+    addNode(-1, -1), addNode(0, 0);
+    for(int i = 0; i < sz(s); ++i) addChar(i, s[i]);
+    propagate();
+  }
+ 
+  void addChar(int i, int c) {
+    int u = getFailure(cur, i);
+    int &ch = nxt[u][c];
+    if (~ch) return (void) ++lz[cur = ch];
+    int v = cur = ch = addNode(len[u] + 2, i - len[u] - 1);
+    fail[v] = len[v] == 1 ? 1 : nxt[getFailure(fail[u], i)][c];
+  }
+ 
+  int addNode(int l, int p) {
+    nxt[n].assign(A, -1);
+    len[n] = l, pos[n] = p, lz[n] = 1, freq[n] = 0;
+    return n++;
+  }
+ 
+  void propagate() {
+    for (int i = n - 1; ~i; --i) {
+      freq[i] += lz[i];
+      lz[fail[i]] += lz[i];
+      lz[i] = 0;
+    }
+  }
+ 
+  int getFailure(int u, int i) {
+    while (i <= len[u] || str[i] != str[i - len[u] - 1]) u = fail[u];
+    return u;
+  }
+};
+ 
\ No newline at end of file
diff --git a/content/strings/chapter.tex b/content/strings/chapter.tex
index 7db9b774e..7fa02e708 100644
--- a/content/strings/chapter.tex
+++ b/content/strings/chapter.tex
@@ -8,3 +8,4 @@ \chapter{Strings}
 \kactlimport{SuffixTree.h}
 \kactlimport{Hashing.h}
 \kactlimport{AhoCorasick.h}
+\kactlimport{PalindromicTree.h}
diff --git a/stress-tests/strings/PalindromicTree.cpp b/stress-tests/strings/PalindromicTree.cpp
new file mode 100644
index 000000000..e61a351ba
--- /dev/null
+++ b/stress-tests/strings/PalindromicTree.cpp
@@ -0,0 +1,32 @@
+#include "../utilities/template.h"
+#include "../../content/strings/PalindromicTree.h"
+
+
+int main() {
+  rep(alpha, 2, 27) {
+    rep(t, 0, 10000) {
+      int n = 1 + rand() % 30;
+      string s(n, 0);
+      rep(i, 0, n) {
+        s[i] = char(rand() % alpha);
+      }
+      PalinTree tree(s);
+      map<string, int> mp;
+      vector<vi> dp(n+1, vi(n+1));
+      rep(i, 0, n+1) dp[0][i] = 1;
+      rep(l, 1, n + 1) rep(i, 0, n - l + 1) {
+        dp[l][i] = l<= 1 || (dp[l-2][i + 1] && s[i] == s[i + l - 1]);
+        if (dp[l][i])
+          ++mp[s.substr(i, l)];
+      }
+      rep(i, 2, tree.n) {
+        string sub = s.substr(tree.pos[i], tree.len[i]);
+        int cnt = mp.find(sub)->second;
+        assert(cnt == tree.freq[i]);
+        mp.erase(sub);
+      }
+      assert(mp.empty());
+    }
+  }
+  cout << "Test passed!\n";
+}

From ac039dd0af7bdb1ff4714d59da708feaf9d568fa Mon Sep 17 00:00:00 2001
From: Ahmed Dardery <Megadardery@yahoo.com>
Date: Sat, 23 Oct 2021 14:02:54 +0200
Subject: [PATCH 2/2] use rep instead of for loop

---
 content/strings/PalindromicTree.h | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/content/strings/PalindromicTree.h b/content/strings/PalindromicTree.h
index 34497244b..dc90aaac7 100644
--- a/content/strings/PalindromicTree.h
+++ b/content/strings/PalindromicTree.h
@@ -24,7 +24,7 @@ struct PalinTree {
     nxt.resize(sz(s) + 2);
     n = cur = fail[0] = fail[1] = 0;
     addNode(-1, -1), addNode(0, 0);
-    for(int i = 0; i < sz(s); ++i) addChar(i, s[i]);
+    rep(i, 0, sz(s)) addChar(i, s[i]);
     propagate();
   }
  
@@ -55,4 +55,4 @@ struct PalinTree {
     return u;
   }
 };
- 
\ No newline at end of file
+