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#define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #include "my_template.hpp" #include "random/base.hpp" #include "convex/minplus_convolution_of_triples.hpp" void test() { FOR(N, 0, 300) { vi A(N), B(N), C(N); FOR(i, N) A[i] = RNG(1, 1 << 30); FOR(i, N) B[i] = RNG(1, 1 << 30); FOR(i, N) C[i] = RNG(1, 1 << 30); // 愚直 vi dp(2 * N + 1, infty<ll>); dp[0] = 0; FOR(i, N) { ll a = A[i], b = B[i], c = C[i]; vi newdp(2 * N + 1, infty<ll>); FOR(i, len(dp)) { if (i + 0 <= 2 * N) chmin(newdp[i + 0], dp[i] + a); if (i + 1 <= 2 * N) chmin(newdp[i + 1], dp[i] + b); if (i + 2 <= 2 * N) chmin(newdp[i + 2], dp[i] + c); } swap(dp, newdp); } MinPlus_Convolution_of_Triples<ll> X; FOR(i, N) X.add(A[i], B[i], C[i]); X.solve(); FOR(K, 2 * N + 1) { ll val = X[K]; vc<int> x = X.restore(K); assert(SUM<int>(x) == K); ll sm = 0; FOR(i, N) { assert(0 <= x[i] && x[i] <= 2); if (x[i] == 0) sm += A[i]; if (x[i] == 1) sm += B[i]; if (x[i] == 2) sm += C[i]; } assert(sm == val && val == dp[K]); } } } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test(); solve(); return 0; }
#line 1 "test/1_mytest/minplus_conv_triple.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 3 "test/1_mytest/minplus_conv_triple.test.cpp" #line 2 "random/base.hpp" u64 RNG_64() { static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL; x_ ^= x_ << 7; return x_ ^= x_ >> 9; } u64 RNG(u64 lim) { return RNG_64() % lim; } ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); } #line 1 "convex/monotone_minima.hpp" // select(i,j,k) : (i,j) -> (i,k) を行うかどうか template <typename F> vc<int> monotone_minima(int H, int W, F select) { vc<int> min_col(H); auto dfs = [&](auto& dfs, int x1, int x2, int y1, int y2) -> void { if (x1 == x2) return; int x = (x1 + x2) / 2; int best_y = y1; for (int y = y1 + 1; y < y2; ++y) { if (select(x, best_y, y)) best_y = y; } min_col[x] = best_y; dfs(dfs, x1, x, y1, best_y + 1); dfs(dfs, x + 1, x2, best_y, y2); }; dfs(dfs, 0, H, 0, W); return min_col; } #line 2 "convex/minplus_convolution.hpp" template <typename T> vc<T> minplus_convolution_convex_convex(vc<T>& A, vc<T>& B) { int n = len(A), m = len(B); if (n == 0 && m == 0) return {}; vc<T> C(n + m - 1, infty<T>); while (n > 0 && A[n - 1] == infty<T>) --n; while (m > 0 && B[m - 1] == infty<T>) --m; if (n == 0 || m == 0) return C; int a = 0, b = 0; while (a < n && A[a] == infty<T>) ++a; while (b < m && B[b] == infty<T>) ++b; C[a + b] = A[a] + B[b]; for (int i = a + b + 1; i < n + m - 1; ++i) { if (b == m - 1 || (a != n - 1 && A[a + 1] + B[b] < A[a] + B[b + 1])) { chmin(C[i], A[++a] + B[b]); } else { chmin(C[i], A[a] + B[++b]); } } return C; } template <typename T> vc<T> minplus_convolution_arbitrary_convex(vc<T>& A, vc<T>& B) { int n = len(A), m = len(B); if (n == 0 && m == 0) return {}; vc<T> C(n + m - 1, infty<T>); while (m > 0 && B[m - 1] == infty<T>) --m; if (m == 0) return C; int b = 0; while (b < m && B[b] == infty<T>) ++b; auto select = [&](int i, int j, int k) -> bool { if (i < k) return false; if (i - j >= m - b) return true; return A[j] + B[b + i - j] >= A[k] + B[b + i - k]; }; vc<int> J = monotone_minima(n + m - b - 1, n, select); FOR(i, n + m - b - 1) { T x = A[J[i]], y = B[b + i - J[i]]; if (x < infty<T> && y < infty<T>) C[b + i] = x + y; } return C; } template <typename T, bool convA, bool convB> vc<T> minplus_convolution(vc<T>& A, vc<T>& B) { static_assert(convA || convB); if constexpr (convA && convB) return minplus_convolution_convex_convex(A, B); if constexpr (convA && !convB) return minplus_convolution_arbitrary_convex(B, A); if constexpr (convB && !convA) return minplus_convolution_arbitrary_convex(A, B); return {}; } #line 2 "convex/minplus_convolution_of_triples.hpp" // https://codeforces.com/contest/436/problem/E // 長さ 3 の数列 {a[i][0], a[i][1], a[i][2]} たちの畳み込み, O(NlogN) // 同種の問題:(a_i,b_i) があって、b_i は a_i を取ってからだけ取れる template <typename T> struct MinPlus_Convolution_of_Triples { int N = 0; T sm0 = 0; vc<array<T, 3>> dat; vc<T> dp1, dp2, dp; vc<int> I1, I2; bool solved = false; void add(T x0, T x1, T x2) { sm0 += x0, dat.eb(array<T, 3>{x0, x1, x2}); } void solve() { solved = true; N = dat.size(); FOR(i, N) { int a = dat[i][1] - dat[i][0], b = dat[i][2] - dat[i][1]; (a <= b ? I1 : I2).eb(i); }; sort(all(I2), [&](int i, int j) -> bool { return dat[i][2] - dat[i][0] < dat[j][2] - dat[j][0]; }); solve_1(); solve_2(); dp = minplus_convolution<T, true, false>(dp1, dp2); for (auto&& x: dp) x += sm0; } T operator[](int i) { return dp[i]; } vc<int> restore(int k) { assert(solved); int k1 = -1, k2 = -1; FOR(i, k + 1) { int j = k - i; if (0 <= i && i < len(dp1) && 0 <= j && j < len(dp2) && dp1[i] + dp2[j] + sm0 == dp[k]) { k1 = i, k2 = j; break; } } assert(k1 != -1 && k2 != -1); vc<int> x(N); vc<int> x1 = restore_1(k1); vc<int> x2 = restore_2(k2); for (int i = 0; i < N; ++i) x[i] = x1[i] + x2[i]; return x; } private: void solve_1() { dp1.reserve(len(I1)); for (int i: I1) { dp1.eb(dat[i][1] - dat[i][0]), dp1.eb(dat[i][2] - dat[i][1]); } sort(all(dp1)); dp1 = cumsum<T>(dp1); } vc<int> restore_1(int k) { vc<pair<T, int>> A; for (int i: I1) { A.eb(dat[i][1] - dat[i][0], i); A.eb(dat[i][2] - dat[i][1], i); } nth_element(A.begin(), A.begin() + k, A.end()); vc<int> x(N); FOR(i, k) x[A[i].se]++; return x; } void solve_2() { // B-A > C-B のケース // 解の構造を考えると、ほとんどすべてで x=0 or x=2 というとりかたになる // 既に C-A でソート済 auto& I = I2; int n = len(I); dp2.assign(2 * n + 1, infty<T>); // 偶数個 dp2[0] = 0; for (int i = 0; i < n; ++i) { dp2[2 * i + 2] = dp2[2 * i] + (dat[I[i]][2] - dat[I[i]][0]); } // 奇数個, prefix からひとつキャンセルする T ma = -infty<T>; for (int i = 0; i < n; ++i) { chmax(ma, dat[I[i]][2] - dat[I[i]][1]); chmin(dp2[2 * i + 1], dp2[2 * i + 2] - ma); } // 奇数個, suffix からひとつ追加する T mi = infty<T>; for (int i = n - 1; i >= 0; --i) { chmin(mi, dat[I[i]][1] - dat[I[i]][0]); chmin(dp2[2 * i + 1], dp2[2 * i] + mi); } return; } vc<int> restore_2(int k) { auto& I = I2; int n = len(I); vc<int> x(N); if (k % 2 == 0) { FOR(i, k / 2) x[I[i]] = 2; return x; } pair<T, int> ma = {-infty<T>, -1}; FOR(i, (k + 1) / 2) { if (chmax(ma.fi, dat[I[i]][2] - dat[I[i]][1])) ma.se = I[i]; } if (dp2[k] == dp2[k + 1] - ma.fi) { FOR(i, (k + 1) / 2) x[I[i]] = 2; x[ma.se]--; return x; } pair<T, int> mi = {infty<T>, -1}; for (int i = n - 1; i >= k / 2; --i) { if (chmin(mi.fi, dat[I[i]][1] - dat[I[i]][0])) mi.se = I[i]; } if (dp2[k] == dp2[k - 1] + mi.fi) { FOR(i, (k - 1) / 2) x[I[i]] = 2; x[mi.se] = 1; return x; } assert(0); return x; } }; #line 6 "test/1_mytest/minplus_conv_triple.test.cpp" void test() { FOR(N, 0, 300) { vi A(N), B(N), C(N); FOR(i, N) A[i] = RNG(1, 1 << 30); FOR(i, N) B[i] = RNG(1, 1 << 30); FOR(i, N) C[i] = RNG(1, 1 << 30); // 愚直 vi dp(2 * N + 1, infty<ll>); dp[0] = 0; FOR(i, N) { ll a = A[i], b = B[i], c = C[i]; vi newdp(2 * N + 1, infty<ll>); FOR(i, len(dp)) { if (i + 0 <= 2 * N) chmin(newdp[i + 0], dp[i] + a); if (i + 1 <= 2 * N) chmin(newdp[i + 1], dp[i] + b); if (i + 2 <= 2 * N) chmin(newdp[i + 2], dp[i] + c); } swap(dp, newdp); } MinPlus_Convolution_of_Triples<ll> X; FOR(i, N) X.add(A[i], B[i], C[i]); X.solve(); FOR(K, 2 * N + 1) { ll val = X[K]; vc<int> x = X.restore(K); assert(SUM<int>(x) == K); ll sm = 0; FOR(i, N) { assert(0 <= x[i] && x[i] <= 2); if (x[i] == 0) sm += A[i]; if (x[i] == 1) sm += B[i]; if (x[i] == 2) sm += C[i]; } assert(sm == val && val == dp[K]); } } } void solve() { int a, b; cin >> a >> b; cout << a + b << "\n"; } signed main() { test(); solve(); return 0; }