Added manacher algo

content/kactl.tex

@@ -21,6 +21,7 @@
 	\kactlchapter{contest}
 	\kactlchapter{data-structures}
 	\kactlchapter{graph}
+	\kactlchapter{string}
 	\kactlchapter{number-theory}
 	\kactlchapter{geometry}
 	\kactlchapter{math}

content/string/chapter.tex

@@ -0,0 +1,3 @@
+\chapter{String}
+
+\kactlimport{manacher.cpp}

content/string/manacher.cpp

@@ -0,0 +1,52 @@
+/**
+ * Author: me
+ * Description: Find longest palindrome centered at each index.
+ * Initialise with original 0-indexed string. QUERYING IS 1-INDEXED.
+ * Time: $O(N)$
+ */
+
+struct Manacher {
+	string s;
+	vector<int> pl;
+
+	void calc() {
+		int n = s.length() - 1;
+		int l = 0, r = 0;
+
+		for (int i = 1; i <= n; i += 1) {
+			if (i < r) pl[i] = min(r-i, pl[l+r-i]);
+			while (s[i-pl[i]-1] == s[i+pl[i]+1]) pl[i] += 1;
+			if (i + pl[i] > r) {
+				l = i - pl[i];
+				r = i + pl[i];
+			}
+		}
+	}
+
+	Manacher() {}
+	void init(string _s, char f='~') {
+		s = "@"; s += f;
+		for (char c: _s)
+		{s += c; s += f;} s += '|';
+		pl.resize(s.length(), 0);
+		calc();
+	}
+
+	// Query for substring [l, r]
+	// on original string with 1-indexed
+	bool is_palindrome(int l, int r) {
+		l <<= 1; r <<= 1;
+		int mid = (l+r) >> 1;
+		return mid + pl[mid] >= r;
+	}
+};
+/*
+Manacher mana;
+
+void example() {
+	string s;
+	cin >> s;
+	mana.init(s);
+	int l, r; cin >> l >> r;
+	cout << mana.is_palindrome(l, r);
+}*/

lab/code.cpp

@@ -0,0 +1,59 @@
+/**
+ * Author: me
+ * Description: Find longest palindrome centered at each index.
+ * Initialise with original 0-indexed string. QUERYING IS 1-INDEXED.
+ * Time: $O(N)$
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+struct Manacher {
+	string s;
+	vector<int> pl;
+
+	void calc() {
+		int n = s.length() - 1;
+		int l = 0, r = 0;
+
+		for (int i = 1; i <= n; i += 1) {
+			if (i < r) pl[i] = min(r-i, pl[l+r-i]);
+			while (s[i-pl[i]-1] == s[i+pl[i]+1]) pl[i] += 1;
+			if (i + pl[i] > r) {
+				l = i - pl[i];
+				r = i + pl[i];
+			}
+		}
+	}
+
+	Manacher() {}
+	void init(string _s, char f='~') {
+		s = "@"; s += f;
+		for (char c: _s)
+		{s += c; s += f;} s += '|';
+		pl.resize(s.length(), 0);
+		calc();
+	}
+
+	// Query for substring [l, r]
+	// on original string with 1-indexed
+	bool is_palindrome(int l, int r) {
+		l <<= 1; r <<= 1;
+		int mid = (l+r) >> 1;
+		return mid + pl[mid] >= r;
+	}
+};
+
+Manacher mana;
+
+void example() {
+	string s;
+	cin >> s;
+	mana.init(s);
+	int l, r; cin >> l >> r;
+	cout << mana.is_palindrome(l, r);
+}
+
+int main() {
+	example();
+}