eertree first (#173)

* eertree first * minor fix * Update Codigos/String/EertreE/README.md Co-authored-by: João Oliveira <[email protected]> * Update Codigos/String/EertreE/README.md Co-authored-by: João Oliveira <[email protected]> * Update Codigos/String/EertreE/README.md Co-authored-by: João Oliveira <[email protected]> * Update Codigos/String/EertreE/README.md Co-authored-by: João Oliveira <[email protected]> --------- Co-authored-by: João Oliveira <[email protected]>
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diff --git a/Codigos/String/EertreE/README.md b/Codigos/String/EertreE/README.md
@@ -0,0 +1,10 @@
+# [EertreE](eertree.cpp)
+
+Constrói a Palindromic Tree de uma string $S$ em $\mathcal{O}(|S|)$. Todo nodo da árvore representa exatamente uma substring palindrômica de $S$.
+
+- `len[u]` representa o tamanho do palíndromo representado pelo nodo `u`.
+- `lnk[u]` é o nodo que representa o maior sufixo palindrômico do nodo `u`.
+- `cnt[u]` é a frequência da substring representada pelo nodo `u`.
+- `first[u]` representa a primeira ocorrência da substring representada pelo nodo `u`, note que `first[u]` guarda o índice do último caractere dessa substring.
+- `number_of_palindromes()` retorna a quantidade de substrings palindrômicas de $S$, lembre-se de chamar a função `build_cnt()` antes dessa.
+- `number_of_distinct_palindromes()` retorna a quantidade de substrings palindrômicas distintas.
diff --git a/Codigos/String/EertreE/eertree.cpp b/Codigos/String/EertreE/eertree.cpp
@@ -0,0 +1,54 @@
+const int N = 6e6 + 15;
+const int ALF = 10;
+
+struct eertree {
+    int str[N], len[N], lnk[N], cnt[N], first[N], node_cnt, it, last;
+    ll palindrome_substring_sum;
+    const char norm = '0';
+    array<int, ALF> to[N];
+
+    inline int get(char c) { return c - norm; }
+
+    void set_string(const string &s) {
+        int n = (int)s.size();
+        memset(str, 0, sizeof(int) * (it + 1));
+        memset(len, 0, sizeof(int) * (it + 1));
+        memset(lnk, 0, sizeof(int) * (it + 1));
+        memset(cnt, 0, sizeof(int) * (it + 1));
+        for (int i = 0; i <= it; i++)
+            for (int j = 0; j < ALF; j++) to[i][j] = 0;
+        node_cnt = 2, it = 1, last = 0, str[0] = -1;
+        len[0] = 0, len[1] = -1, lnk[0] = 1, lnk[1] = 1;
+        for (int i = 0; i < n; i++) insert(s[i]);
+        build_cnt();
+    }
+
+    void insert(char ch) {
+        int c = get(ch);
+        str[it] = c;
+        while (str[it - 1 - len[last]] != c) last = lnk[last];
+        if (!to[last][c]) {
+            int prev = lnk[last];
+            while (str[it - 1 - len[prev]] != c) prev = lnk[prev];
+            lnk[node_cnt] = to[prev][c];
+            len[node_cnt] = len[last] + 2;
+            to[last][c] = node_cnt++;
+        }
+        last = to[last][c];
+        first[last] = it;
+        cnt[last]++;
+        it++;
+    }
+
+    void build_cnt() {
+        ll ans = 0;
+        for (int i = it; i > 1; i--) {
+            ans += cnt[i];
+            cnt[lnk[i]] += cnt[i];
+        }
+        palindrome_substring_sum = ans;
+    }
+
+    inline ll number_of_palindromes() { return palindrome_substring_sum; }
+    inline int number_of_distinct_palindromes() { return node_cnt - 2; }
+} et;