Suffix Array (lib/string/suffix_array.hpp)

• View this file on GitHub
• Last update: 2025-05-14 10:33:39+09:00
• Include: #include "lib/string/suffix_array.hpp"

Verified with

• test/aoj/alds1/suffix_array.test.cpp
• test/aoj/course/ALDS1_14_D.test.cpp
• test/yosupo/string/longest_common_substring.test.cpp
• test/yosupo/string/number_of_substring.test.cpp
• test/yosupo/string/suffix_array.test.cpp

Code

#pragma once
#include <algorithm>
#include <cassert>
#include <numeric>
#include <string>
#include <utility>
#include <vector>

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.emplace_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.emplace_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

/// @brief Suffix Array
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;
}

/// @brief Suffix Array
template <class T>
std::vector<int> suffix_array(const std::vector<T> &s) {
    int n = int(s.size());
    std::vector<int> idx(n);
    std::iota(idx.begin(), idx.end(), 0);
    std::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);
}

/// @brief Suffix Array
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) {
    assert(s.size() == sa.size());
    int n = int(s.size());
    assert(n >= 1);
    std::vector<int> rnk(n);
    for (int i = 0; i < n; ++i) {
        assert(0 <= sa[i] && sa[i] < n);
        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);
}

#line 2 "lib/string/suffix_array.hpp"
#include <algorithm>
#include <cassert>
#include <numeric>
#include <string>
#include <utility>
#include <vector>

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.emplace_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.emplace_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

/// @brief Suffix Array
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;
}

/// @brief Suffix Array
template <class T>
std::vector<int> suffix_array(const std::vector<T> &s) {
    int n = int(s.size());
    std::vector<int> idx(n);
    std::iota(idx.begin(), idx.end(), 0);
    std::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);
}

/// @brief Suffix Array
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) {
    assert(s.size() == sa.size());
    int n = int(s.size());
    assert(n >= 1);
    std::vector<int> rnk(n);
    for (int i = 0; i < n; ++i) {
        assert(0 <= sa[i] && sa[i] < n);
        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);
}

Back to top page