#include #include using namespace std; #define rep(i,n) for(long long i = 0; i < (long long)(n); i++) #define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++) #define pb push_back #define all(x) (x).begin(), (x).end() #define fi first #define se second #define mt make_tuple #define mp make_pair #define ZERO(a) memset(a,0,sizeof(a)) template bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); } template bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } #define exists find_if #define forall all_of using ll = long long; using vll = vector; /*using vvll = vector;*/ using P = pair; using ld = long double; using vld = vector; using vi = vector; using vvi = vector; vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; } using vvll = vector>; static const double EPS = 1e-14; static const long long INF = 1e18; static const long long mo = 1e9+7; #define ldout fixed << setprecision(40) inline void input(int &v){ v=0;char c=0;int p=1; while(c<'0' || c>'9'){if(c=='-')p=-1;c=getchar();} while(c>='0' && c<='9'){v=(v<<3)+(v<<1)+c-'0';c=getchar();} v*=p; } template ostream &operator<<(ostream &o, const pair &v) { o << "(" << v.first << ", " << v.second << ")"; return o; } template struct seq{}; template struct gen_seq : gen_seq{}; template struct gen_seq<0, Is...> : seq{}; template void print_tuple(basic_ostream& os, Tuple const& t, seq){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get(t)), 0)...}; } template auto operator<<(basic_ostream& os, tuple const& t) -> basic_ostream& { os << "("; print_tuple(os, t, gen_seq()); return os << ")"; } template ostream &operator<<(ostream &o, const vector &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const set &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const unordered_set &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const map &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template ostream &operator<<(ostream &o, const unordered_map &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]"; return o; } vector range(const int x, const int y) { vector v(y - x + 1); iota(v.begin(), v.end(), x); return v; } template istream& operator>>(istream& i, vector& o) { rep(j, o.size()) i >> o[j]; return i;} string bits_to_string(ll input, ll n=64) { string s; rep(i, n) s += '0' + !!(input & (1ll << i)); reverse(all(s)); return s; } template ostream &operator<<(ostream &o, const priority_queue &v) { auto tmp = v; while (tmp.size()) { auto x = tmp.top(); tmp.pop(); o << x << " ";} o << endl; return o; } template unordered_map counter(vector vec){unordered_map ret; for (auto&& x : vec) ret[x]++; return ret;}; string substr(string s, P x) {return s.substr(x.fi, x.se - x.fi); } size_t random_seed; namespace std { using argument_type = P; template<> struct hash { size_t operator()(argument_type const& x) const { size_t seed = random_seed; seed ^= hash{}(x.fi); seed ^= (hash{}(x.se) << 1); return seed; } }; }; // hash for various class namespace myhash{ const int Bsizes[]={3,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81}; const int xor_nums[]={0x100007d1,0x5ff049c9,0x14560859,0x07087fef,0x3e277d49,0x4dba1f17,0x709c5988,0x05904258,0x1aa71872,0x238819b3,0x7b002bb7,0x1cf91302,0x0012290a,0x1083576b,0x76473e49,0x3d86295b,0x20536814,0x08634f4d,0x115405e8,0x0e6359f2}; const int hash_key=xor_nums[rand()%20]; const int mod_key=xor_nums[rand()%20]; template struct myhash{ std::size_t operator()(const T& val) const { return (hash{}(val)%mod_key)^hash_key; } }; }; template class uset:public std::unordered_set> { using SET=std::unordered_set>; public: uset():SET(){SET::rehash(myhash::Bsizes[rand()%20]);} }; uint32_t randxor() { static uint32_t x=1+(uint32_t)random_seed,y=362436069,z=521288629,w=88675123; uint32_t t; t=(x^(x<<11));x=y;y=z;z=w; return( w=(w^(w>>19))^(t^(t>>8)) ); } struct timeval start; double sec() { struct timeval tv; gettimeofday(&tv, NULL); return (tv.tv_sec - start.tv_sec) + (tv.tv_usec - start.tv_usec) * 1e-6; } struct init_{init_(){ gettimeofday(&start, NULL); ios::sync_with_stdio(false); cin.tie(0); struct timeval myTime; struct tm *time_st; gettimeofday(&myTime, NULL); time_st = localtime(&myTime.tv_sec); srand(myTime.tv_usec); random_seed = RAND_MAX / 2 + rand() / 2; }} init__; #define rand randxor ll n; vector a, x, y; // 状態1<=j<=nの確定のときに、状態0<=k; bool isQuadrangleInequality(func_t w) { repi(i, 1, n+1) repi(j, 1, n+1) rep(k, n) repi(l, k, n) if (i < l && j < k && i < k && j < l && i <= j && j <= k && k <= l) { if (w(i, l) + w(j, k) >= w(i, k) + w(j, l)) { } else { cout << i << " " << j << " " << k << " " << l << " " << "HIT" << endl; return 0; } } return 1; } ll solveBrutal(ll dp0, func_t w) { vector dp(n+1, INF); dp[0] = dp0; repi(i, 1, n+1) { rep(j, i) { chmin(dp[i], dp[j] + w(j, i)); } } // cout << dp <<"Brutal"<< endl; return dp[n]; } // Zvi Galil; Raffaele Giancarlo, "Speeding up dynamic programming with applications to molecular biology", 1987 // D. Eppstein, Z. Galil, and R. Giancalco: "Speeding up Dynamic Programming", 29th IEEE Symposium on Foundations of Computer Science, White Plains, New York, pp. 488-496, 1988. // // dp[j] = min_{0 <= k < j} (dp[k] + w(k, j)) (0 <= j <= n) // wが逆Quadrangle Inequalityを満たす場合のO(n log n)あるいはO(n)解法 // // given: // dp[0] // // given: // wは0-indexed monge n*n行列 (逆Quadrangle Ineqalityを満たす) // // 一般にO(n log n) // Closest Zero Propertyが満たされていて、hをO(1)自前実装するならばO(n) ll solveQuadrangleInequality(ll dp0, func_t w) { vector dp(n+1); dp[0] = dp0; // 状態rの確定のために、遷移kをしようとした時の候補 // k in [0, n), r in [1, n] auto C = [&](ll k, ll r) { assert(0<=k&&k 1) { ll mid = (ok + ng) / 2; if (w(l, mid) - w(k, mid) <= dp[k] - dp[l]) ok = mid; else ng = mid; } return ok; // Brutal /* ll ret = -1; repi(hc, l+1, n+1) { if (w(l, hc) - w(k, hc) <= dp[k] - dp[l]) { ret = hc; break; } } if (ret < 0) ret = n + 1; assert(ret == ok); return ret; */ }; deque

Q = {P(0, 1)}; repi(j, 1, n+1) { ll l = Q.back().fi; // 最小のつもり if (C(j-1, j) <= C(l, j)) { dp[j] = C(j-1, j); Q.clear(); Q.push_back(P(j-1, j+1)); } else { dp[j] = C(l, j); while (C(j-1, Q[0].se) <= C(Q[0].fi, Q[0].se)) Q.pop_front(); ll hc = h(j-1, Q[0].fi); if (hc != n + 1) Q.push_front(P(j-1, hc)); if (Q.size() >= 2 && j + 1 == Q[Q.size()-2].se) Q.pop_back(); else Q.back().se++; } } // cout << dp << "Eppstein" << endl; return dp[n]; } void compareMin(void) { function w = w_QuadrangleInequality; ll ret_m = solveQuadrangleInequality(0, w); #if 1 ll ret_b = solveBrutal(0, w); if (ret_b != ret_m) { cout << "Not Match" << endl; cout << "Jury : " << ret_b << ", Participant : " << ret_m<> n; a.resize(n); x.resize(n); y.resize(n); cin >> a; cin >> x; cin >> y; assert(1<=n&&n<=3e5); rep(i, n) { assert(0<=a[i]&&a[i]<=1e5); assert(0<=x[i]&&x[i]<=1e5); assert(0<=y[i]&&y[i]<=1e5); } rep(i, n-1) { assert(a[i]<=a[i+1]); assert(x[i]<=x[i+1]); } compareMin(); // compareMax(); return 0; }