noya2_Library

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:warning: string/suffix_array_search.hpp

Depends on

Code

#pragma once

#include "suffix_array.hpp"

namespace noya2 {

struct suffix_array_search {
    int n;
    std::string s;
    std::vector<int> sa;
    suffix_array_search (const std::string &_s) : n(_s.size()), s(_s){
        sa = suffix_array(s);
    }
    std::pair<int,int> lower_upper_bound(const std::string &t){
        int l = 0, r = n;
        for (int i = 0; auto c : t){
            int nl = lower_bound(i, l, r, c);
            int nr = upper_bound(i, l, r, c);
            l = nl;
            r = nr;
            i++;
        }
        return {l, r};
    }
    // max i, s.t. t[0,i) is contained in s as substring
    int max_match(const std::string &t){
        int l = 0, r = n;
        int i = 0;
        for (auto c : t){
            int nl = lower_bound(i, l, r, c);
            int nr = upper_bound(i, l, r, c);
            if (nl == nr) break;
            l = nl;
            r = nr;
            i++;
        }
        return i;
    }
    // sum[i=0,1,...,n-1] lcp(s[i,n), t)
    long long sum_of_lcp(const std::string &t){
        int l = 0, r = n;
        long long ans = 0;
        for (int i = 0; auto c : t){
            int nl = lower_bound(i, l, r, c);
            int nr = upper_bound(i, l, r, c);
            ans += nr - nl;
            l = nl;
            r = nr;
            i++;
        }
        return ans;
    }
    int lower_bound(int i, int l, int r, char c){
        if (l == r) return l;
        if (is_lteq(c, sa[l] + i)) return l;
        while (r - l > 1){
            int m = (l + r) / 2;
            if (is_lteq(c, sa[m] + i)){
                r = m;
            }
            else {
                l = m;
            }
        }
        return r;
    }
    int upper_bound(int i, int l, int r, char c){
        if (l == r) return l;
        if (is_lt(c, sa[l] + i)) return l;
        while (r - l > 1){
            int m = (l + r) / 2;
            if (is_lt(c, sa[m] + i)){
                r = m;
            }
            else {
                l = m;
            }
        }
        return r;
    }
  private:
    bool is_lt(char compare, int pos){
        if (pos >= n) return false;
        return compare < s[pos];
    }
    bool is_lteq(char compare, int pos){
        if (pos >= n) return false;
        return compare <= s[pos];
    }
};

} // namespace noya2
#line 2 "string/suffix_array_search.hpp"

#line 2 "string/suffix_array.hpp"

#include <algorithm>
#include <cassert>
#include <numeric>
#include <string>
#include <vector>

// atcoder/string

namespace noya2 {

namespace internal {

std::vector<int> sa_naive(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n);
    std::iota(sa.begin(), sa.end(), 0);
    std::sort(sa.begin(), sa.end(), [&](int l, int r) {
        if (l == r) return false;
        while (l < n && r < n) {
            if (s[l] != s[r]) return s[l] < s[r];
            l++;
            r++;
        }
        return l == n;
    });
    return sa;
}

std::vector<int> sa_doubling(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n), rnk = s, tmp(n);
    std::iota(sa.begin(), sa.end(), 0);
    for (int k = 1; k < n; k *= 2) {
        auto cmp = [&](int x, int y) {
            if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
            int rx = x + k < n ? rnk[x + k] : -1;
            int ry = y + k < n ? rnk[y + k] : -1;
            return rx < ry;
        };
        std::sort(sa.begin(), sa.end(), cmp);
        tmp[sa[0]] = 0;
        for (int i = 1; i < n; i++) {
            tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
        }
        std::swap(tmp, rnk);
    }
    return sa;
}

// SA-IS, linear-time suffix array construction
// Reference:
// G. Nong, S. Zhang, and W. H. Chan,
// Two Efficient Algorithms for Linear Time Suffix Array Construction
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int>& s, int upper) {
    int n = int(s.size());
    if (n == 0) return {};
    if (n == 1) return {0};
    if (n == 2) {
        if (s[0] < s[1]) {
            return {0, 1};
        } else {
            return {1, 0};
        }
    }
    if (n < THRESHOLD_NAIVE) {
        return sa_naive(s);
    }
    if (n < THRESHOLD_DOUBLING) {
        return sa_doubling(s);
    }

    std::vector<int> sa(n);
    std::vector<bool> ls(n);
    for (int i = n - 2; i >= 0; i--) {
        ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
    }
    std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
    for (int i = 0; i < n; i++) {
        if (!ls[i]) {
            sum_s[s[i]]++;
        } else {
            sum_l[s[i] + 1]++;
        }
    }
    for (int i = 0; i <= upper; i++) {
        sum_s[i] += sum_l[i];
        if (i < upper) sum_l[i + 1] += sum_s[i];
    }

    auto induce = [&](const std::vector<int>& lms) {
        std::fill(sa.begin(), sa.end(), -1);
        std::vector<int> buf(upper + 1);
        std::copy(sum_s.begin(), sum_s.end(), buf.begin());
        for (auto d : lms) {
            if (d == n) continue;
            sa[buf[s[d]]++] = d;
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        sa[buf[s[n - 1]]++] = n - 1;
        for (int i = 0; i < n; i++) {
            int v = sa[i];
            if (v >= 1 && !ls[v - 1]) {
                sa[buf[s[v - 1]]++] = v - 1;
            }
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        for (int i = n - 1; i >= 0; i--) {
            int v = sa[i];
            if (v >= 1 && ls[v - 1]) {
                sa[--buf[s[v - 1] + 1]] = v - 1;
            }
        }
    };

    std::vector<int> lms_map(n + 1, -1);
    int m = 0;
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) {
            lms_map[i] = m++;
        }
    }
    std::vector<int> lms;
    lms.reserve(m);
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) {
            lms.push_back(i);
        }
    }

    induce(lms);

    if (m) {
        std::vector<int> sorted_lms;
        sorted_lms.reserve(m);
        for (int v : sa) {
            if (lms_map[v] != -1) sorted_lms.push_back(v);
        }
        std::vector<int> rec_s(m);
        int rec_upper = 0;
        rec_s[lms_map[sorted_lms[0]]] = 0;
        for (int i = 1; i < m; i++) {
            int l = sorted_lms[i - 1], r = sorted_lms[i];
            int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
            int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
            bool same = true;
            if (end_l - l != end_r - r) {
                same = false;
            } else {
                while (l < end_l) {
                    if (s[l] != s[r]) {
                        break;
                    }
                    l++;
                    r++;
                }
                if (l == n || s[l] != s[r]) same = false;
            }
            if (!same) rec_upper++;
            rec_s[lms_map[sorted_lms[i]]] = rec_upper;
        }

        auto rec_sa =
            sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);

        for (int i = 0; i < m; i++) {
            sorted_lms[i] = lms[rec_sa[i]];
        }
        induce(sorted_lms);
    }
    return sa;
}

}  // namespace internal

std::vector<int> suffix_array(const std::vector<int>& s, int upper) {
    assert(0 <= upper);
    for (int d : s) {
        assert(0 <= d && d <= upper);
    }
    auto sa = internal::sa_is(s, upper);
    return sa;
}

template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {
    int n = int(s.size());
    std::vector<int> idx(n);
    iota(idx.begin(), idx.end(), 0);
    sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
    std::vector<int> s2(n);
    int now = 0;
    for (int i = 0; i < n; i++) {
        if (i && s[idx[i - 1]] != s[idx[i]]) now++;
        s2[idx[i]] = now;
    }
    return internal::sa_is(s2, now);
}

std::vector<int> suffix_array(const std::string& s) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return internal::sa_is(s2, 255);
}

// Reference:
// T. Kasai, G. Lee, H. Arimura, S. Arikawa, and K. Park,
// Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its
// Applications
template <class T>
std::vector<int> lcp_array(const std::vector<T>& s,
                           const std::vector<int>& sa) {
    int n = int(s.size());
    assert(n >= 1);
    std::vector<int> rnk(n);
    for (int i = 0; i < n; i++) {
        rnk[sa[i]] = i;
    }
    std::vector<int> lcp(n - 1);
    int h = 0;
    for (int i = 0; i < n; i++) {
        if (h > 0) h--;
        if (rnk[i] == 0) continue;
        int j = sa[rnk[i] - 1];
        for (; j + h < n && i + h < n; h++) {
            if (s[j + h] != s[i + h]) break;
        }
        lcp[rnk[i] - 1] = h;
    }
    return lcp;
}

std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return lcp_array(s2, sa);
}

}  // namespace noya2
#line 4 "string/suffix_array_search.hpp"

namespace noya2 {

struct suffix_array_search {
    int n;
    std::string s;
    std::vector<int> sa;
    suffix_array_search (const std::string &_s) : n(_s.size()), s(_s){
        sa = suffix_array(s);
    }
    std::pair<int,int> lower_upper_bound(const std::string &t){
        int l = 0, r = n;
        for (int i = 0; auto c : t){
            int nl = lower_bound(i, l, r, c);
            int nr = upper_bound(i, l, r, c);
            l = nl;
            r = nr;
            i++;
        }
        return {l, r};
    }
    // max i, s.t. t[0,i) is contained in s as substring
    int max_match(const std::string &t){
        int l = 0, r = n;
        int i = 0;
        for (auto c : t){
            int nl = lower_bound(i, l, r, c);
            int nr = upper_bound(i, l, r, c);
            if (nl == nr) break;
            l = nl;
            r = nr;
            i++;
        }
        return i;
    }
    // sum[i=0,1,...,n-1] lcp(s[i,n), t)
    long long sum_of_lcp(const std::string &t){
        int l = 0, r = n;
        long long ans = 0;
        for (int i = 0; auto c : t){
            int nl = lower_bound(i, l, r, c);
            int nr = upper_bound(i, l, r, c);
            ans += nr - nl;
            l = nl;
            r = nr;
            i++;
        }
        return ans;
    }
    int lower_bound(int i, int l, int r, char c){
        if (l == r) return l;
        if (is_lteq(c, sa[l] + i)) return l;
        while (r - l > 1){
            int m = (l + r) / 2;
            if (is_lteq(c, sa[m] + i)){
                r = m;
            }
            else {
                l = m;
            }
        }
        return r;
    }
    int upper_bound(int i, int l, int r, char c){
        if (l == r) return l;
        if (is_lt(c, sa[l] + i)) return l;
        while (r - l > 1){
            int m = (l + r) / 2;
            if (is_lt(c, sa[m] + i)){
                r = m;
            }
            else {
                l = m;
            }
        }
        return r;
    }
  private:
    bool is_lt(char compare, int pos){
        if (pos >= n) return false;
        return compare < s[pos];
    }
    bool is_lteq(char compare, int pos){
        if (pos >= n) return false;
        return compare <= s[pos];
    }
};

} // namespace noya2
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