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:heavy_check_mark: test/mytest/substring_abundant.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#include "my_template.hpp"
#include "string/substring_abundant_string.hpp"

void test() {
  auto check = [&](ll N) -> bool {
    string S = substring_abundant_string(N);
    assert(len(S) == N);
    ll ub = 1;
    FOR(k, 1, N + 1) {
      ub = min(ub * 2, N);
      ll n = min(ub, N - k + 1);
      set<string> ss;
      FOR(i, N - k + 1) { ss.insert(S.substr(i, k)); }
      if (len(ss) != n) return 0;
    }
    return 1;
  };
  FOR(n, 1, 100) { assert(check(n)); }
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

signed main() {
  test();
  solve();
  return 0;
}
#line 1 "test/mytest/substring_abundant.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) \
  for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}
#endif
#line 1 "string/run_length.hpp"
template <typename STRING = string, typename CHAR = char>
vc<pair<CHAR, int>> run_length(STRING& S) {
  vc<pair<CHAR, int>> res;
  for (auto&& x: S) {
    if (res.empty() || res.back().fi != x) { res.emplace_back(x, 0); }
    res.back().se++;
  }
  return res;
}
#line 2 "string/substring_abundant_string.hpp"

// 部分文字列の種類数が最大であるような 01 文字列の構成
// https://qoj.ac/contest/1096/problem/5434?v=1
// https://oeis.org/A094913
// https://www.mimuw.edu.pl/~rytter/MYPAPERS/paper.pdf
string substring_abundant_string(ll N) {
  ll N0 = N;
  N = 1;
  while ((1 << N) + (N - 1) < N0) ++N;

  string S = [&]() -> string {
    if (N == 1) return "01";
    if (N == 2) return "00110";

    auto SHIFT = [&](string x, string y) -> string {
      int n = len(x);
      x += x;
      FOR(i, n, n + n) {
        if (x.substr(i - len(y), len(y)) == y) { return x.substr(i - n, n); }
      }
      return "";
    };
    auto oplus = [&](string x, string y) -> string {
      int n = topbit(len(y));
      assert(len(x) == (1 << n) && len(y) == (1 << n));
      return x + SHIFT(y, x.substr(len(x) - n, n));
    };
    auto NOT = [&](string x) -> string {
      string y;
      for (auto&& s: x) y += (s == '0' ? '1' : '0');
      return y;
    };
    auto PSI = [&](string x) -> string {
      int a = 0;
      FOR(i, len(x)) {
        a ^= (x[i] - '0');
        x[i] = ('0' + a);
      }
      return x;
    };

    auto NEXT = [&](string x) -> string {
      x = PSI(x);
      return oplus(x, NOT(x));
    };

    auto otimes = [&](string x, string y) -> string {
      string t;
      FOR(topbit(len(x))) t += '0';
      x = SHIFT(x, t);
      y = SHIFT(y, t);
      rotate(x.begin(), x.end() - len(t), x.end());
      rotate(y.begin(), y.end() - len(t), y.end());

      int n = len(x);
      int x0 = 0, x1 = 0, y0 = 0, y1 = 1;
      for (auto&& [k, v]: run_length(x)) {
        if (k == '0') chmax(x0, v);
        if (k == '1') chmax(x1, v);
      }
      for (auto&& [k, v]: run_length(y)) {
        if (k == '0') chmax(y0, v);
        if (k == '1') chmax(y1, v);
      }
      string X, Y;
      for (auto&& [k, v]: run_length(x)) {
        if (k == '0' && v < x0) { X += string(v, k); }
        if (k == '0' && v == x0) { X += string(v - 1, k); }
        if (k == '1' && v < x1) { X += string(v, k); }
        if (k == '1' && v == x1) { X += string(v + 1, k); }
      }
      for (auto&& [k, v]: run_length(y)) {
        if (k == '0' && v < y0) { Y += string(v, k); }
        if (k == '0' && v == y0) { Y += string(v + 1, k); }
        if (k == '1' && v < y1) { Y += string(v, k); }
        if (k == '1' && v == y1) { Y += string(v - 1, k); }
      }
      return X + Y;
    };

    string x = "0011", y = "0011";
    FOR(i, 2, N - 1) {
      string t;
      FOR(i) t += '1';
      x = SHIFT(x, t);
      x = NEXT(x);
      y = SHIFT(y, t);
      y = NOT(NEXT(y));
    }
    x = otimes(x, y);
    FOR(i, N - 1) x += x[i];
    return x;
  }();
  return S.substr(0, N0);
}
#line 4 "test/mytest/substring_abundant.test.cpp"

void test() {
  auto check = [&](ll N) -> bool {
    string S = substring_abundant_string(N);
    assert(len(S) == N);
    ll ub = 1;
    FOR(k, 1, N + 1) {
      ub = min(ub * 2, N);
      ll n = min(ub, N - k + 1);
      set<string> ss;
      FOR(i, N - k + 1) { ss.insert(S.substr(i, k)); }
      if (len(ss) != n) return 0;
    }
    return 1;
  };
  FOR(n, 1, 100) { assert(check(n)); }
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

signed main() {
  test();
  solve();
  return 0;
}
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