This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub maspypy/library
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #include "my_template.hpp" #include "game/solve_partizan_game.hpp" void test_push() { // LESSONS IN PLAY p.113 vc<string> states = {"LR", ".RL", ".R", "RRL"}; auto get_options = [&](string s) -> pair<vc<string>, vc<string>> { vc<string> left_ops, right_ops; FOR(i, len(s)) { if (s[i] == '.') continue; string t = s; char x = '.'; int p = i; while (p >= 0) { swap(x, t[p--]); if (x == '.') break; } if (s[i] == 'L') left_ops.eb(t); if (s[i] == 'R') right_ops.eb(t); } return {left_ops, right_ops}; }; auto MP = solve_partizan_game<string, ll>(states, get_options); // for (auto&& [s, x]: MP) { print(s, x.to_string()); } assert(MP["LR"].to_string() == "-3/2"); assert(MP[".RL"].to_string() == "7/4"); assert(MP[".R"].to_string() == "-2/1"); assert(MP["RRL"].to_string() == "13/8"); } void test_problem_5_2() { // switch になるので解けない int LIM = 10; vc<int> states(LIM); iota(all(states), 0); auto get_options = [&](int s) -> pair<vc<int>, vc<int>> { vc<int> left_ops, right_ops; if (s % 3 == 0 && s >= 1) left_ops.eb(s - 1), right_ops.eb(s - 1); if (s % 3 == 0 && s >= 2) left_ops.eb(s - 2), right_ops.eb(s - 2); if (s % 3 == 1 && s >= 1) left_ops.eb(s - 1); if (s % 3 == 1 && s >= 2) left_ops.eb(s - 2); if (s % 3 == 2 && s >= 1) right_ops.eb(s - 1); if (s % 3 == 2 && s >= 2) right_ops.eb(s - 2); return {left_ops, right_ops}; }; auto MP = solve_partizan_game<int, ll>(states, get_options); assert(MP.empty()); } void test_problem_5_3() { int LIM = 10; vc<int> states(LIM); iota(all(states), 0); auto get_options = [&](int s) -> pair<vc<int>, vc<int>> { vc<int> left_ops, right_ops; if (s % 2 == 0 && s >= 2) left_ops.eb(s - 2); if (s % 2 == 0 && s >= 1) right_ops.eb(s - 1); if (s % 2 == 1 && s >= 1) left_ops.eb(s - 1); if (s % 2 == 1 && s >= 2) right_ops.eb(s - 2); return {left_ops, right_ops}; }; auto MP = solve_partizan_game<int, ll>(states, get_options); assert(MP[0].to_string() == "0/1"); assert(MP[1].to_string() == "1/1"); assert(MP[2].to_string() == "1/2"); assert(MP[3].to_string() == "3/4"); assert(MP[4].to_string() == "5/8"); assert(MP[5].to_string() == "11/16"); } int solve_cherries(string s) { // LR cherries を O(N) で解く auto eval = [&](char c) -> int { if (c == 'L') return 1; if (c == 'R') return -1; return 0; }; int n = len(s); if (n == 0) return 0; int res = 0; FOR(2) { reverse(all(s)); while (n >= 2 && s[n - 1] == s[n - 2]) { res += eval(s[n - 1]); s.pop_back(); n = len(s); } } char a = '.', b = '.'; FOR_R(i, n - 1) if (s[i] == s[i + 1]) a = s[i]; FOR(i, n - 1) if (s[i] == s[i + 1]) b = s[i]; int x = eval(s[0]) + eval(a) + eval(b) + eval(s[n - 1]); return res + x / 2; }; void test_cherries() { int MAX_LEN = 20; vc<string> states; states.eb(""); int p = 0, q = 1; FOR(MAX_LEN) { FOR(i, p, q) { states.eb(states[i] + "L"); states.eb(states[i] + "R"); } p = q; q = len(states); } auto get_options = [&](string s) -> pair<vc<string>, vc<string>> { vc<string> left, right; int n = len(s); if (n && s[0] == 'L') left.eb(s.substr(1, n - 1)); if (n && s[0] == 'R') right.eb(s.substr(1, n - 1)); if (n && s[n - 1] == 'L') left.eb(s.substr(0, n - 1)); if (n && s[n - 1] == 'R') right.eb(s.substr(0, n - 1)); return {left, right}; }; auto MP = solve_partizan_game<string, ll>(states, get_options); for (auto&& [s, x]: MP) { int my_ans = solve_cherries(s); assert(x == Dyadic_Rational<ll>(my_ans, 1)); } } void test() { test_push(); test_problem_5_2(); test_problem_5_3(); test_cherries(); } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test(); solve(); return 0; }
#line 1 "test/1_mytest/partizan.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 "game/dyadic_rational.hpp" // a+b/2^M の形で持つ template <typename INTEGER> struct Dyadic_Rational { using X = Dyadic_Rational; INTEGER a, b; static constexpr int M = std::numeric_limits<INTEGER>::digits - 2; Dyadic_Rational(INTEGER a = 0) : a(a), b(0) {} // x + y / z Dyadic_Rational(INTEGER x, INTEGER y, INTEGER z) : a(x), b(y) { auto [q, r] = divmod(b, z); a += q; b = r; b *= (INTEGER(1) << M) / z; } // x/y Dyadic_Rational(INTEGER x, INTEGER y) : Dyadic_Rational(0, x, y) {} static X from_ab(INTEGER a, INTEGER b) { X x(a); x.b = b; return x; } // 比較 bool operator==(X const& rhs) const { return (a == rhs.a && b == rhs.b); } bool operator!=(X const& rhs) const { return !(*this == rhs); } bool operator<(X const& rhs) const { return (a < rhs.a) || (a == rhs.a && b < rhs.b); } bool operator<=(X const& rhs) const { return (a < rhs.a) || (a == rhs.a && b <= rhs.b); } bool operator>(X const& rhs) const { return (a > rhs.a) || (a == rhs.a && b > rhs.b); } bool operator>=(X const& rhs) const { return (a > rhs.a) || (a == rhs.a && b >= rhs.b); } // 加法 friend X operator+(const X& x, const X& y) { INTEGER a = x.a + y.a, b = x.b + y.b; while (b >= INTEGER(1) << M) { ++a; b -= INTEGER(1) << M; } return from_ab(a, b); } friend X operator-(const X& x, const X& y) { INTEGER a = x.a - y.a, b = x.b - y.b; while (b < 0) { --a; b += INTEGER(1) << M; } return from_ab(a, b); } friend X operator-(const X& x) { INTEGER a = -x.a, b = -x.b; while (b < 0) { --a; b += INTEGER(1) << M; } return from_ab(a, b); } X& operator+=(const X& x) { return (*this) = (*this) + x; } X& operator-=(const X& x) { return (*this) = (*this) - x; } static X simplest(const X& x, const X& y) { assert(x < y); if (y.a < 0) return -simplest(-y, -x); { INTEGER l = x.a + 1; INTEGER r = (y.b == 0 ? y.a - 1 : y.a); if (l <= 0 && 0 <= r) return X(0); if (l <= r && 0 <= l) return X(l); if (l <= r && r <= 0) return X(r); } INTEGER l = x.b + 1; INTEGER r = (y.b == 0 ? (INTEGER(1) << M) - 1 : y.b - 1); if (l == r) return from_ab(x.a, l); int k = topbit(l ^ r); r &= ~((INTEGER(1) << k) - 1); return from_ab(x.a, r); } static constexpr X infinity() { return from_ab(INTEGER(1) << M, 0); } string to_string() { ll x = a, y = b, z = INTEGER(1) << M; while (y % 2 == 0 && z % 2 == 0) { y /= 2, z /= 2; } y += x * z; return std::to_string(y) + "/" + std::to_string(z); } }; #line 2 "game/solve_partizan_game.hpp" // 全部 dyadic rational number になるときだけ解ける // 失敗したときは、empty map が返る // ・states:興味のある state 全体 // ・get_options:pair<vc<STATE>, vc<STATE>>(STATE), left ops / right ops template <typename STATE, typename INTEGER, typename F> unordered_map<STATE, Dyadic_Rational<INTEGER>> solve_partizan_game( const vector<STATE>& states, F get_options) { using X = Dyadic_Rational<INTEGER>; unordered_map<STATE, X> MP; bool success = 1; auto dfs = [&](auto& dfs, const STATE& s) -> X { if (!success) return X(); if (MP.count(s)) return MP[s]; vc<X> left, right; X xl = -X::infinity(), xr = X::infinity(); auto [left_ops, right_ops] = get_options(s); for (auto&& t: left_ops) chmax(xl, dfs(dfs, t)); for (auto&& t: right_ops) chmin(xr, dfs(dfs, t)); if (xl >= xr) { // switch success = 0; MP.clear(); return X(); } return (MP[s] = X::simplest(xl, xr)); }; for (auto&& s: states) dfs(dfs, s); return MP; } #line 5 "test/1_mytest/partizan.test.cpp" void test_push() { // LESSONS IN PLAY p.113 vc<string> states = {"LR", ".RL", ".R", "RRL"}; auto get_options = [&](string s) -> pair<vc<string>, vc<string>> { vc<string> left_ops, right_ops; FOR(i, len(s)) { if (s[i] == '.') continue; string t = s; char x = '.'; int p = i; while (p >= 0) { swap(x, t[p--]); if (x == '.') break; } if (s[i] == 'L') left_ops.eb(t); if (s[i] == 'R') right_ops.eb(t); } return {left_ops, right_ops}; }; auto MP = solve_partizan_game<string, ll>(states, get_options); // for (auto&& [s, x]: MP) { print(s, x.to_string()); } assert(MP["LR"].to_string() == "-3/2"); assert(MP[".RL"].to_string() == "7/4"); assert(MP[".R"].to_string() == "-2/1"); assert(MP["RRL"].to_string() == "13/8"); } void test_problem_5_2() { // switch になるので解けない int LIM = 10; vc<int> states(LIM); iota(all(states), 0); auto get_options = [&](int s) -> pair<vc<int>, vc<int>> { vc<int> left_ops, right_ops; if (s % 3 == 0 && s >= 1) left_ops.eb(s - 1), right_ops.eb(s - 1); if (s % 3 == 0 && s >= 2) left_ops.eb(s - 2), right_ops.eb(s - 2); if (s % 3 == 1 && s >= 1) left_ops.eb(s - 1); if (s % 3 == 1 && s >= 2) left_ops.eb(s - 2); if (s % 3 == 2 && s >= 1) right_ops.eb(s - 1); if (s % 3 == 2 && s >= 2) right_ops.eb(s - 2); return {left_ops, right_ops}; }; auto MP = solve_partizan_game<int, ll>(states, get_options); assert(MP.empty()); } void test_problem_5_3() { int LIM = 10; vc<int> states(LIM); iota(all(states), 0); auto get_options = [&](int s) -> pair<vc<int>, vc<int>> { vc<int> left_ops, right_ops; if (s % 2 == 0 && s >= 2) left_ops.eb(s - 2); if (s % 2 == 0 && s >= 1) right_ops.eb(s - 1); if (s % 2 == 1 && s >= 1) left_ops.eb(s - 1); if (s % 2 == 1 && s >= 2) right_ops.eb(s - 2); return {left_ops, right_ops}; }; auto MP = solve_partizan_game<int, ll>(states, get_options); assert(MP[0].to_string() == "0/1"); assert(MP[1].to_string() == "1/1"); assert(MP[2].to_string() == "1/2"); assert(MP[3].to_string() == "3/4"); assert(MP[4].to_string() == "5/8"); assert(MP[5].to_string() == "11/16"); } int solve_cherries(string s) { // LR cherries を O(N) で解く auto eval = [&](char c) -> int { if (c == 'L') return 1; if (c == 'R') return -1; return 0; }; int n = len(s); if (n == 0) return 0; int res = 0; FOR(2) { reverse(all(s)); while (n >= 2 && s[n - 1] == s[n - 2]) { res += eval(s[n - 1]); s.pop_back(); n = len(s); } } char a = '.', b = '.'; FOR_R(i, n - 1) if (s[i] == s[i + 1]) a = s[i]; FOR(i, n - 1) if (s[i] == s[i + 1]) b = s[i]; int x = eval(s[0]) + eval(a) + eval(b) + eval(s[n - 1]); return res + x / 2; }; void test_cherries() { int MAX_LEN = 20; vc<string> states; states.eb(""); int p = 0, q = 1; FOR(MAX_LEN) { FOR(i, p, q) { states.eb(states[i] + "L"); states.eb(states[i] + "R"); } p = q; q = len(states); } auto get_options = [&](string s) -> pair<vc<string>, vc<string>> { vc<string> left, right; int n = len(s); if (n && s[0] == 'L') left.eb(s.substr(1, n - 1)); if (n && s[0] == 'R') right.eb(s.substr(1, n - 1)); if (n && s[n - 1] == 'L') left.eb(s.substr(0, n - 1)); if (n && s[n - 1] == 'R') right.eb(s.substr(0, n - 1)); return {left, right}; }; auto MP = solve_partizan_game<string, ll>(states, get_options); for (auto&& [s, x]: MP) { int my_ans = solve_cherries(s); assert(x == Dyadic_Rational<ll>(my_ans, 1)); } } void test() { test_push(); test_problem_5_2(); test_problem_5_3(); test_cherries(); } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test(); solve(); return 0; }