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#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/1_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") // いまの CF だとこれ入れると動かない? // #pragma GCC target("avx2,popcnt") #include <bits/stdc++.h> using namespace std; using ll = long long; using u8 = uint8_t; using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template <class T> constexpr T infty = 0; template <> constexpr int infty<int> = 1'010'000'000; template <> constexpr ll infty<ll> = 2'020'000'000'000'000'000; template <> constexpr u32 infty<u32> = infty<int>; template <> constexpr u64 infty<u64> = infty<ll>; template <> constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000; 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; } template <typename T, typename... Vectors> void concat(vc<T> &first, const Vectors &... others) { vc<T> &res = first; (res.insert(res.end(), others.begin(), others.end()), ...); } #endif #line 1 "string/run_length.hpp" template <typename STRING = string> vc<pair<typename STRING::value_type, ll>> run_length(STRING& S) { vc<pair<typename STRING::value_type, ll>> 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/1_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; }