verify/library_checker/string/number_of_substrings.test.cpp

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• Last update: 2024-11-09 02:46:49+09:00
• Problem: https://judge.yosupo.jp/problem/number_of_substrings

Depends on

• RollingHash (src/string/rolling_hash.hpp)
• suffix_array (src/string/suffix_array.hpp)
• Modint_2_61m1 (src/template/modint_2_61m1.hpp)
• template (src/template/template.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/number_of_substrings"
#include "../../../src/template/template.hpp"
#include "../../../src/string/rolling_hash.hpp"
#include "../../../src/string/suffix_array.hpp"
int main(void) {
    string s;
    cin >> s;
    ll n = s.size();
    RollingHash rh(s);
    ll ans = n * (n + 1) / 2;
    vector<int> sa = suffix_array(s);
    rep(i, 0, n - 1) {
        ans -= rh.lcp(rh, rh, sa[i], sa[i + 1]);
    }
    cout << ans << '\n';
}

#line 1 "verify/library_checker/string/number_of_substrings.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/number_of_substrings"
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/template/modint_2_61m1.hpp"
struct Modint_2_61m1 {
    using mint = Modint_2_61m1;
    using u64 = uint64_t;
    using u128 = __uint128_t;
    static constexpr u64 mod() {
        return m;
    }
    static constexpr mint raw(const u64 v) {
        mint a;
        a._v = v;
        return a;
    }
    constexpr Modint_2_61m1()
        : _v(0) {}
    template <class T>
    constexpr Modint_2_61m1(const T& v) {
        static_assert(is_integral_v<T>);
        if constexpr(is_signed_v<T>) {
            int64_t x = int64_t(v % int64_t(m));
            if(x < 0) x += m;
            _v = u64(x);
        } else _v = u64(v % m);
    }
    constexpr u64 val() const {
        return _v;
    }
    constexpr mint& operator++() {
        return *this += 1;
    }
    constexpr mint& operator--() {
        return *this -= 1;
    }
    constexpr mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
    }
    constexpr mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
    }
    constexpr mint& operator+=(mint rhs) {
        if(_v >= m - rhs._v) _v -= m;
        _v += rhs._v;
        return *this;
    }
    constexpr mint& operator-=(mint rhs) {
        if(_v < rhs._v) _v += m;
        _v -= rhs._v;
        return *this;
    }
    constexpr mint& operator*=(mint rhs) {
        return *this = *this * rhs;
    }
    constexpr mint& operator/=(mint rhs) {
        return *this *= rhs.inv();
    }
    constexpr mint operator+() const {
        return *this;
    }
    constexpr mint operator-() const {
        return mint{} - *this;
    }
    constexpr mint pow(u64 n) const {
        if(n == 0) return 1;
        mint x = *this, r = 1;
        while(1) {
            if(n & 1) r *= x;
            n >>= 1;
            if(n == 0) return r;
            x *= x;
        }
    }
    constexpr mint inv() const {
        assert(_v);
        return pow(m - 2);
    }
    friend constexpr mint operator+(mint lhs, mint rhs) {
        return lhs += rhs;
    }
    friend constexpr mint operator-(mint lhs, mint rhs) {
        return lhs -= rhs;
    }
    friend constexpr mint operator*(mint lhs, mint rhs) {
        return raw(modulo(u128(lhs._v) * rhs._v));
    }
    friend constexpr mint operator/(mint lhs, mint rhs) {
        return lhs /= rhs;
    }
    friend constexpr bool operator==(mint lhs, mint rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(mint lhs, mint rhs) {
        return lhs._v != rhs._v;
    }
    friend istream& operator>>(istream& in, mint& x) {
        long long a;
        in >> a;
        x = a;
        return in;
    }
    friend ostream& operator<<(ostream& out, const mint& x) {
        return out << x.val();
    }

   private:
    static constexpr u64 m = (1ull << 61) - 1;
    u64 _v = 0;
    inline static constexpr u64 modulo(const u128& x) {
        const u64 val = (x >> 61) + (x & m);
        return val >= m ? val - m : val;
    }
};
#line 4 "src/string/rolling_hash.hpp"
struct RollingHash {
    using mint = Modint_2_61m1;
    RollingHash(const string& s, unsigned long long BASE = 0)
        : len((int)s.size()), pow(len + 1), hash(len + 1) {
        if(BASE == 0) {
            mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
            uniform_int_distribution<unsigned long long> dist(1ull << 10, 1ull << 60);
            BASE = dist(mt);
        }
        base = BASE;
        pow[0] = 1;
        for(int i = 0; i < len; ++i) {
            pow[i + 1] = pow[i] * base;
        }
        for(int i = 0; i < len; ++i) {
            hash[i + 1] = hash[i] * base + s[i];
        }
    }
    unsigned long long get(const int lower, const int upper) const {
        assert(0 <= lower and lower <= upper and upper <= len);
        return (hash[upper] - hash[lower] * pow[upper - lower]).val();
    }
    unsigned long long get_hash(const string& t) const {
        mint res = 0;
        for(int i = 0; i < (int)t.size(); ++i) {
            res = res * base + t[i];
        }
        return res.val();
    }
    int find(const string& t, const int lower = 0) const {
        if((int)t.size() > len) return -1;
        const unsigned long long ha = get_hash(t);
        for(int i = lower; i < len - (int)t.size() + 1; ++i) {
            if(ha == get(i, i + (int)t.size())) return i;
        }
        return -1;
    }
    int lcp(const RollingHash& a, const RollingHash& b, const int al, const int bl) const {
        int ok = 0, ng = min(a.len - al, b.len - bl) + 1;
        while(ok + 1 < ng) {
            const int med = (ok + ng) / 2;
            if(a.get(al, med + al) == b.get(bl, med + bl)) {
                ok = med;
            } else {
                ng = med;
            }
        }
        return ok;
    }

   private:
    int len;
    mint base;
    vector<mint> pow;
    vector<mint> hash;
};
#line 3 "src/string/suffix_array.hpp"
template <typename T>
vector<int> suffix_array(const vector<T>& s, const bool compress = true) {
    auto sa_is = [&](auto& sa_is, const vector<int>& s, const int upper) -> vector<int> {
        const 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};
        }
        vector<int> sa(n);
        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]);
        }
        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 vector<int>& lms) {
            fill(sa.begin(), sa.end(), -1);
            vector<int> buf(upper + 1);
            copy(sum_s.begin(), sum_s.end(), buf.begin());
            for(const int d : lms) {
                if(d == n) continue;
                sa[buf[s[d]]++] = d;
            }
            copy(sum_l.begin(), sum_l.end(), buf.begin());
            sa[buf[s[n - 1]]++] = n - 1;
            for(int i = 0; i < n; ++i) {
                const int v = sa[i];
                if(v >= 1 and !ls[v - 1]) {
                    sa[buf[s[v - 1]]++] = v - 1;
                }
            }
            copy(sum_l.begin(), sum_l.end(), buf.begin());
            for(int i = n - 1; i >= 0; --i) {
                const int v = sa[i];
                if(v >= 1 and ls[v - 1]) {
                    sa[--buf[s[v - 1] + 1]] = v - 1;
                }
            }
        };
        vector<int> lms_map(n + 1, -1);
        int m = 0;
        for(int i = 1; i < n; ++i) {
            if(!ls[i - 1] and ls[i]) {
                lms_map[i] = m++;
            }
        }
        vector<int> lms;
        lms.reserve(m);
        for(int i = 1; i < n; ++i) {
            if(!ls[i - 1] and ls[i]) {
                lms.push_back(i);
            }
        }
        induce(lms);
        if(m) {
            vector<int> sorted_lms;
            sorted_lms.reserve(m);
            for(const int v : sa) {
                if(lms_map[v] != -1) sorted_lms.push_back(v);
            }
            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];
                const int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
                const 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 or s[l] != s[r]) same = false;
                }
                if(!same) ++rec_upper;
                rec_s[lms_map[sorted_lms[i]]] = rec_upper;
            }
            const auto rec_sa = sa_is(sa_is, rec_s, rec_upper);
            for(int i = 0; i < m; ++i) {
                sorted_lms[i] = lms[rec_sa[i]];
            }
            induce(sorted_lms);
        }
        return sa;
    };
    if(compress) {
        const int n = (int)s.size();
        vector<int> idx(n);
        iota(idx.begin(), idx.end(), 0);
        sort(idx.begin(), idx.end(), [&](const int l, const int r) { return s[l] < s[r]; });
        vector<int> s2(n);
        int upper = 0;
        for(int i = 0; i < n; ++i) {
            if(i and s[idx[i - 1]] != s[idx[i]]) ++upper;
            s2[idx[i]] = upper;
        }
        return sa_is(sa_is, s2, upper);
    }
    return sa_is(sa_is, s, *max_element(s.begin(), s.end()));
}
vector<int> suffix_array(const string& s) {
    const int n = (int)s.size();
    vector<int> s2(n);
    for(int i = 0; i < n; ++i) {
        s2[i] = s[i];
    }
    return suffix_array(s2, false);
}
template <typename T>
vector<int> lcp_array(const vector<T>& s, const vector<int>& sa) {
    const int n = (int)s.size();
    assert(n >= 1);
    vector<int> rnk(n);
    for(int i = 0; i < n; ++i) {
        rnk[sa[i]] = i;
    }
    vector<int> lcp(n - 1);
    int h = 0;
    for(int i = 0; i < n; ++i) {
        if(h > 0) --h;
        if(rnk[i] == 0) continue;
        const int j = sa[rnk[i] - 1];
        for(; j + h < n and i + h < n; ++h) {
            if(s[j + h] != s[i + h]) break;
        }
        lcp[rnk[i] - 1] = h;
    }
    return lcp;
}
vector<int> lcp_array(const string& s, const vector<int>& sa) {
    const int n = (int)s.size();
    vector<int> s2(n);
    for(int i = 0; i < n; ++i) {
        s2[i] = s[i];
    }
    return lcp_array(s2, sa);
}
#line 5 "verify/library_checker/string/number_of_substrings.test.cpp"
int main(void) {
    string s;
    cin >> s;
    ll n = s.size();
    RollingHash rh(s);
    ll ans = n * (n + 1) / 2;
    vector<int> sa = suffix_array(s);
    rep(i, 0, n - 1) {
        ans -= rh.lcp(rh, rh, sa[i], sa[i + 1]);
    }
    cout << ans << '\n';
}

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