Longest palindromic substring enumeration (Manacher's algorithm) （回文長配列構築）
(string/manacher.hpp)

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• Last update: 2022-01-08 20:23:44+09:00
• Include: #include "string/manacher.hpp"
• Link: https://snuke.hatenablog.com/entry/2014/12/02/235837

文字列・数列などの列に対して Manacher’s algorithm を適用．長さ $N$ の入力に対し時間計算量 $O(N)$．

使用方法

string S = "sakanakanandaka";
vector<int> v = manacher(S); // Manacher's algorithm を適用（奇数長の回文だけならこれでOK）．
vector<pair<int, int>> palindromes = enumerate_palindromes(S);
for (auto [l, r] : palindromes) {
    cout << r - l << ' '; // S[l, r) は最長回文連続部分列（[1, 1) のような空文字列も含む）．
}

文献

• [1] G. Manacher, “A new linear-time “on-line” algorithm for finding the smallest initial palindrome of a string”, Journal of the ACM, 22 (3), 346-351, 1975.

Verified with

• graph/test/shortest_path_dial.yuki1695.test.cpp
• graph/test/zero_one_bfs.yuki1695.test.cpp
• string/test/manacher.test.cpp
• string/test/manacher_mp.test.cpp

Code

#pragma once
#include <string>
#include <utility>
#include <vector>

// CUT begin
// Manacher's Algorithm: radius of palindromes
// Input: std::string or std::vector<T> of length N
// Output: std::vector<int> of size N
// Complexity: O(N)
// Sample:
// - `sakanakanandaka` -> [1, 1, 2, 1, 4, 1, 4, 1, 2, 2, 1, 1, 1, 2, 1]
// Reference: https://snuke.hatenablog.com/entry/2014/12/02/235837
template <typename T> std::vector<int> manacher(const std::vector<T> &S) {
    std::vector<int> res(S.size());
    int i = 0, j = 0;
    while (i < int(S.size())) {
        while (i - j >= 0 and i + j < int(S.size()) and S[i - j] == S[i + j]) j++;
        res[i] = j;
        int k = 1;
        while (i - k >= 0 and i + k < int(S.size()) and k + res[i - k] < j)
            res[i + k] = res[i - k], k++;
        i += k, j -= k;
    }
    return res;
}
std::vector<int> manacher(const std::string &S) {
    std::vector<char> v(S.size());
    for (int i = 0; i < int(S.size()); i++) v[i] = S[i];
    return manacher(v);
}

template <typename T>
std::vector<std::pair<int, int>> enumerate_palindromes(const std::vector<T> &vec) {
    std::vector<T> v;
    const int N = vec.size();
    for (int i = 0; i < N - 1; i++) {
        v.push_back(vec[i]);
        v.push_back(-1);
    }
    v.push_back(vec.back());
    const auto man = manacher(v);
    std::vector<std::pair<int, int>> ret;
    for (int i = 0; i < N * 2 - 1; i++) {
        if (i & 1) {
            int w = man[i] / 2;
            ret.emplace_back((i + 1) / 2 - w, (i + 1) / 2 + w);
        } else {
            int w = (man[i] - 1) / 2;
            ret.emplace_back(i / 2 - w, i / 2 + w + 1);
        }
    }
    return ret;
}

std::vector<std::pair<int, int>> enumerate_palindromes(const std::string &S) {
    std::vector<char> v(S.size());
    for (int i = 0; i < int(S.size()); i++) v[i] = S[i];
    return enumerate_palindromes<char>(v);
}

#line 2 "string/manacher.hpp"
#include <string>
#include <utility>
#include <vector>

// CUT begin
// Manacher's Algorithm: radius of palindromes
// Input: std::string or std::vector<T> of length N
// Output: std::vector<int> of size N
// Complexity: O(N)
// Sample:
// - `sakanakanandaka` -> [1, 1, 2, 1, 4, 1, 4, 1, 2, 2, 1, 1, 1, 2, 1]
// Reference: https://snuke.hatenablog.com/entry/2014/12/02/235837
template <typename T> std::vector<int> manacher(const std::vector<T> &S) {
    std::vector<int> res(S.size());
    int i = 0, j = 0;
    while (i < int(S.size())) {
        while (i - j >= 0 and i + j < int(S.size()) and S[i - j] == S[i + j]) j++;
        res[i] = j;
        int k = 1;
        while (i - k >= 0 and i + k < int(S.size()) and k + res[i - k] < j)
            res[i + k] = res[i - k], k++;
        i += k, j -= k;
    }
    return res;
}
std::vector<int> manacher(const std::string &S) {
    std::vector<char> v(S.size());
    for (int i = 0; i < int(S.size()); i++) v[i] = S[i];
    return manacher(v);
}

template <typename T>
std::vector<std::pair<int, int>> enumerate_palindromes(const std::vector<T> &vec) {
    std::vector<T> v;
    const int N = vec.size();
    for (int i = 0; i < N - 1; i++) {
        v.push_back(vec[i]);
        v.push_back(-1);
    }
    v.push_back(vec.back());
    const auto man = manacher(v);
    std::vector<std::pair<int, int>> ret;
    for (int i = 0; i < N * 2 - 1; i++) {
        if (i & 1) {
            int w = man[i] / 2;
            ret.emplace_back((i + 1) / 2 - w, (i + 1) / 2 + w);
        } else {
            int w = (man[i] - 1) / 2;
            ret.emplace_back(i / 2 - w, i / 2 + w + 1);
        }
    }
    return ret;
}

std::vector<std::pair<int, int>> enumerate_palindromes(const std::string &S) {
    std::vector<char> v(S.size());
    for (int i = 0; i < int(S.size()); i++) v[i] = S[i];
    return enumerate_palindromes<char>(v);
}

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