結果
| 問題 | No.2654 [Cherry 6th Tune] Re: start! (Black Sheep) |
| ユーザー |
 hashiryo
|
| 提出日時 | 2024-08-16 18:41:12 |
| 言語 | C++17(clang) (17.0.6 + boost 1.83.0) |
| 結果 |
MLE
|
| 実行時間 | - |
| コード長 | 19,795 bytes |
| コンパイル時間 | 3,662 ms |
| コンパイル使用メモリ | 169,344 KB |
| 実行使用メモリ | 548,776 KB |
| 最終ジャッジ日時 | 2024-08-16 18:41:27 |
| 合計ジャッジ時間 | 14,689 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 130 ms
494,948 KB |
| testcase_01 | AC | 127 ms
494,836 KB |
| testcase_02 | AC | 129 ms
494,888 KB |
| testcase_03 | MLE | - |
| testcase_04 | -- | - |
| testcase_05 | -- | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
| testcase_17 | -- | - |
| testcase_18 | -- | - |
| testcase_19 | -- | - |
| testcase_20 | -- | - |
| testcase_21 | -- | - |
| testcase_22 | -- | - |
| testcase_23 | -- | - |
| testcase_24 | -- | - |
| testcase_25 | -- | - |
| testcase_26 | -- | - |
| testcase_27 | -- | - |
| testcase_28 | -- | - |
| testcase_29 | -- | - |
| testcase_30 | -- | - |
| testcase_31 | -- | - |
| testcase_32 | -- | - |
| testcase_33 | -- | - |
| testcase_34 | -- | - |
| testcase_35 | -- | - |
| testcase_36 | -- | - |
| testcase_37 | -- | - |
| testcase_38 | -- | - |
| testcase_39 | -- | - |
ソースコード
// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
// clang-format off
std::ostream&operator<<(std::ostream&os,std::int8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,std::uint8_t x){return os<<(int)x;}
std::ostream&operator<<(std::ostream&os,const __int128_t &u){if(!u)os<<"0";__int128_t tmp=u<0?(os<<"-",-u):u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
std::ostream&operator<<(std::ostream&os,const __uint128_t &u){if(!u)os<<"0";__uint128_t tmp=u;std::string s;while(tmp)s+='0'+(tmp%10),tmp/=10;return std::reverse(s.begin(),s.end()),os<<s;}
#define checkpoint() (void(0))
#define debug(...) (void(0))
#define debugArray(x,n) (void(0))
#define debugMatrix(x,h,w) (void(0))
// clang-format on
// clang-format off
template<class T>struct make_long{using type= T;};
template<>struct make_long<int8_t>{using type= int16_t;};
template<>struct make_long<uint8_t>{using type= uint16_t;};
template<>struct make_long<int16_t>{using type= int32_t;};
template<>struct make_long<uint16_t>{using type= uint32_t;};
template<>struct make_long<int32_t>{using type= int64_t;};
template<>struct make_long<uint32_t>{using type= uint64_t;};
template<>struct make_long<int64_t>{using type= __int128_t;};
template<>struct make_long<uint64_t>{using type= __uint128_t;};
template<>struct make_long<float>{using type= double;};
template<>struct make_long<double>{using type= long double;};
template<class T> using make_long_t= typename make_long<T>::type;
// clang-format on
template <class T, bool persistent= false, size_t NODE_SIZE= 1 << 22> class PiecewiseLinearConvex {
using D= make_long_t<T>;
struct Node {
int ch[2];
T z, x, d, a;
D s;
size_t sz;
friend std::ostream &operator<<(std::ostream &os, const Node &t) { return os << "{z:" << t.z << ",x:" << t.x << ",d:" << t.d << ",a:" << t.a << ",s:" << t.s << ",sz:" << t.sz << ",ch:(" << t.ch[0] << "," << t.ch[1] << ")}"; }
};
static inline size_t ni= 1;
static inline Node *n= new Node[NODE_SIZE]{Node{}};
static inline void info(int t, int d, std::stringstream &ss) {
if (!t) return;
info(n[t].ch[0], d + 1, ss);
for (int i= 0; i < d; ++i) ss << " ";
ss << " ■ " << n[t] << '\n', info(n[t].ch[1], d + 1, ss);
}
static inline void dump_xs(int t, std::vector<T> &xs) {
if (t) push(t), dump_xs(n[t].ch[0], xs), xs.push_back(n[t].x), dump_xs(n[t].ch[1], xs);
}
static inline void dump_slopes_l(int t, T ofs, std::vector<T> &as) {
if (t) push(t), dump_slopes_l(n[t].ch[1], ofs, as), ofs+= n[n[t].ch[1]].a + n[t].d, as.push_back(-ofs), dump_slopes_l(n[t].ch[0], ofs, as);
}
static inline void dump_slopes_r(int t, T ofs, std::vector<T> &as) {
if (t) push(t), dump_slopes_r(n[t].ch[0], ofs, as), ofs+= n[n[t].ch[0]].a + n[t].d, as.push_back(ofs), dump_slopes_r(n[t].ch[1], ofs, as);
}
static inline int create(T d, T x) { return n[ni].d= d, n[ni].x= x, n[ni].z= 0, ni++; }
template <class Iter> static inline int build(Iter bg, Iter ed) {
if (bg == ed) return 0;
auto md= bg + (ed - bg) / 2;
int t= create(md->first, md->second);
return n[t].ch[0]= build(bg, md), n[t].ch[1]= build(md + 1, ed), update(t), t;
}
template <class Iter> static inline void dump(Iter itr, int t) {
if (!t) return;
push(t);
size_t sz= n[n[t].ch[0]].sz;
dump(itr, n[t].ch[0]), *(itr + sz)= {n[t].d, n[t].x}, dump(itr + sz + 1, n[t].ch[1]);
}
static inline void update(int t) {
int l= n[t].ch[0], r= n[t].ch[1];
n[t].sz= 1 + n[l].sz + n[r].sz, n[t].a= n[t].d + n[l].a + n[r].a, n[t].s= D(n[t].x) * n[t].d + n[l].s + n[r].s;
}
template <bool b= 1> static inline void prop(int &t, T v) {
if constexpr (persistent && b) {
if (!t) return;
n[ni]= n[t], t= ni++;
}
n[t].z+= v, n[t].s+= D(v) * n[t].a, n[t].x+= v;
}
static inline void push(int t) {
if (n[t].z != 0) prop(n[t].ch[0], n[t].z), prop(n[t].ch[1], n[t].z), n[t].z= 0;
}
template <bool r> static inline int join_(int t, int a, int b) {
push(a);
if constexpr (r) b= join<0>(b, t, n[a].ch[0]);
else b= join<0>(n[a].ch[1], t, b);
if constexpr (persistent) n[ni]= n[a], a= ni++;
if (n[n[a].ch[r]].sz * 4 >= n[b].sz) return n[a].ch[!r]= b, update(a), a;
return n[a].ch[!r]= n[b].ch[r], update(a), n[b].ch[r]= a, update(b), b;
}
template <bool b= 1> static inline int join(int l, int t, int r) {
if constexpr (persistent && b) n[ni]= n[t], t= ni++;
if (n[l].sz > n[r].sz * 4) return join_<0>(t, l, r);
if (n[r].sz > n[l].sz * 4) return join_<1>(t, r, l);
return n[t].ch[0]= l, n[t].ch[1]= r, update(t), t;
}
static inline std::array<int, 3> split(int t, T x) {
if (!t) return {0, 0, 0};
push(t);
if (n[t].x < x) {
auto [a, b, c]= split(n[t].ch[1], x);
return {join(n[t].ch[0], t, a), b, c};
} else if (x < n[t].x) {
auto [a, b, c]= split(n[t].ch[0], x);
return {a, b, join(c, t, n[t].ch[1])};
}
return {n[t].ch[0], t, n[t].ch[1]};
}
static inline int unite(int l, int r) {
if (!l) return r;
if (!r) return l;
push(l);
if constexpr (persistent) n[ni]= n[l], l= ni++;
auto [a, b, c]= split(r, n[l].x);
return n[l].d+= n[b].d, join<0>(unite(a, n[l].ch[0]), l, unite(n[l].ch[1], c));
}
static inline int insert(int t, T x, T d) {
if (!t) return n[ni]= Node{{0, 0}, 0, x, d, d, D(x) * d, 1}, ni++;
push(t);
if constexpr (persistent) n[ni]= n[t], t= ni++;
if (n[t].x == x) return n[t].d+= d, update(t), t;
return x < n[t].x ? join<0>(insert(n[t].ch[0], x, d), t, n[t].ch[1]) : join<0>(n[t].ch[0], t, insert(n[t].ch[1], x, d));
}
template <bool r> static inline std::pair<int, int> pop(int t) {
if (push(t); !n[t].ch[r]) return {n[t].ch[!r], t};
auto [a, s]= pop<r>(n[t].ch[r]);
if constexpr (r) return {join(n[t].ch[!r], t, a), s};
else return {join(a, t, n[t].ch[!r]), s};
}
template <bool r> static inline bool lt(T a, T b) {
if constexpr (r) return b < a;
else return a < b;
}
template <bool r> static inline int cut(int t, T x) {
if (!t) return t;
if (push(t); n[t].x == x) return n[t].ch[!r];
if (lt<r>(n[t].x, x)) return cut<r>(n[t].ch[!r], x);
if constexpr (r) return join(n[t].ch[0], t, cut<1>(n[t].ch[1], x));
else return join(cut<0>(n[t].ch[0], x), t, n[t].ch[1]);
}
template <bool r> static inline D calc_y(int t, T x, T ol, D ou) {
for (; t;) {
if (push(t); lt<r>(n[t].x, x)) t= n[t].ch[!r];
else {
if (ol+= n[n[t].ch[!r]].a, ou+= n[n[t].ch[!r]].s; n[t].x == x) break;
ol+= n[t].d, ou+= D(n[t].x) * n[t].d, t= n[t].ch[r];
}
}
return D(x) * ol - ou;
}
template <bool r> static inline std::array<int, 3> split(int t, T p, T &ol, D &ou) {
push(t);
T s= ol + n[n[t].ch[!r]].a;
if (p < s) {
auto [a, b, c]= split<r>(n[t].ch[!r], p, ol, ou);
if constexpr (r) return {a, b, join(c, t, n[t].ch[r])};
else return {join(n[t].ch[r], t, a), b, c};
}
ol= s + n[t].d;
if (ol < p) {
ou+= n[n[t].ch[!r]].s + D(n[t].x) * n[t].d;
auto [a, b, c]= split<r>(n[t].ch[r], p, ol, ou);
if constexpr (r) return {join(n[t].ch[!r], t, a), b, c};
else return {a, b, join(c, t, n[t].ch[!r])};
}
ou+= n[n[t].ch[!r]].s;
return {n[t].ch[0], t, n[t].ch[1]};
}
template <bool l> static inline bool lte(T a, T b) {
if constexpr (l) return a < b;
else return a <= b;
}
template <bool l, bool r> static inline std::pair<int, int> split_cum(int t, T p, T &ol, D &ou) {
push(t);
T s= ol + n[n[t].ch[!r]].a;
if (lte<l>(p, s)) {
auto [c, b]= split_cum<l, r>(n[t].ch[!r], p, ol, ou);
if constexpr (l) {
if constexpr (r) return {join(c, t, n[t].ch[r]), b};
else return {join(n[t].ch[r], t, c), b};
} else return {c, b};
}
ol= s + n[t].d;
if (lte<!l>(ol, p)) {
ou+= n[n[t].ch[!r]].s + D(n[t].x) * n[t].d;
auto [a, b]= split_cum<l, r>(n[t].ch[r], p, ol, ou);
if constexpr (l) return {a, b};
else {
if constexpr (r) return {join(n[t].ch[!r], t, a), b};
else return {join(a, t, n[t].ch[!r]), b};
}
}
ou+= n[n[t].ch[!r]].s;
return {n[t].ch[!r ^ l], t};
}
int mn, lr[2];
bool bf[2];
T o[2], rem, bx[2];
D y;
inline D calc_y(T x) {
if (!mn) return 0;
if (n[mn].x == x) return 0;
return x < n[mn].x ? -calc_y<0>(lr[0], x, o[0], D(n[mn].x) * o[0]) : calc_y<1>(lr[1], x, o[1], D(n[mn].x) * o[1]);
}
inline void slope_eval(bool neg) {
T p= neg ? -rem : rem, ol= o[neg];
if (p <= ol) o[neg]-= p, o[!neg]+= p, y+= D(n[mn].x) * rem;
else {
D ou= D(n[mn].x) * ol;
auto [a, b, c]= neg ? split<1>(lr[neg], p, ol, ou) : split<0>(lr[neg], p, ol, ou);
o[neg]= ol - p, ol-= n[b].d, ou+= D(n[b].x) * (o[!neg]= p - ol);
if (neg) y-= ou, lr[!neg]= join(lr[!neg], mn, a), lr[neg]= c;
else y+= ou, lr[!neg]= join(c, mn, lr[!neg]), lr[neg]= a;
mn= b;
}
rem= 0;
}
template <bool l, bool neg> inline void slope_eval_cum() {
T p= neg ? -rem : rem, ol= o[neg];
if (lte<l>(p, ol)) o[neg]-= p, o[!neg]+= p, y+= D(n[mn].x) * rem;
else {
D ou= D(n[mn].x) * ol;
auto [a, b]= split_cum<l, neg>(lr[neg], p, ol, ou);
o[neg]= ol - p, ol-= n[b].d, ou+= D(n[b].x) * (o[!neg]= p - ol);
if constexpr (l) lr[neg]= a;
else {
if constexpr (neg) lr[!neg]= join(lr[!neg], mn, a);
else lr[!neg]= join(a, mn, lr[!neg]);
}
if constexpr (neg) y-= ou;
else y+= ou;
mn= b;
}
rem= 0;
}
template <bool r> void add_inf(T x0) {
if (bf[r] && !lt<r>(bx[r], x0)) return;
if (assert(!bf[!r] || !lt<r>(bx[!r], x0)), bf[r]= true, bx[r]= x0; !mn) return;
if (lt<r>(x0, n[mn].x)) return lr[r]= cut<r>(lr[r], x0), void();
D q= n[lr[!r]].s + D(n[mn].x) * o[!r];
T v= o[!r] + n[lr[!r]].a;
lr[!r]= cut<r>(lr[!r], x0);
if (!r) y-= q, rem+= v;
else y+= q, rem-= v;
if (lr[!r]) std::tie(lr[r], mn)= pop<!r>(lr[!r]), lr[!r]= 0;
else mn= lr[r]= 0;
o[r]= n[mn].d, o[!r]= 0;
}
inline void prop(T x) {
if constexpr (persistent) mn= create(n[mn].d, n[mn].x);
n[mn].x+= x;
}
public:
// f(x) := 0
PiecewiseLinearConvex(): mn(0), lr{0, 0}, bf{0, 0}, o{0, 0}, rem(0), bx{0, 0}, y(0) {}
// f(x) := sum max(0, a(x-x0))
PiecewiseLinearConvex(const std::vector<std::pair<T, T>> &ramps): PiecewiseLinearConvex() {
int m= ramps.size();
if (!m) return;
std::vector<std::pair<T, T>> w(m);
int s= 0, t= 0;
for (auto [d, x]: ramps) {
if (d == 0) continue;
if (d < 0) y-= D(d) * x, rem+= d, d= -d;
w[s++]= {d, x};
}
std::sort(w.begin(), w.begin() + s, [](auto a, auto b) { return a.second < b.second; });
for (int i= 0; i < s; ++i) {
if (t && w[t - 1].second == w[i].second) w[t - 1].first+= w[i].first;
else w[t++]= w[i];
}
mn= create(w[0].first, w[0].second), o[1]= n[mn].d, lr[1]= build(w.begin() + 1, w.begin() + t);
}
std::string info() {
std::stringstream ss;
if (ss << "\n rem:" << rem << ", y:" << y << ", mn:" << mn << ", lr:{" << lr[0] << ", " << lr[1] << "}\n bf[0]:" << bf[0] << ", bf[1]:" << bf[1] << ", bx[0]:" << bx[0] << ", bx[1]:" << bx[1] << "\n " << "o[0]:" << o[0] << ", o[1]:" << o[1] << "\n"; mn) {
if (lr[0]) info(lr[0], 1, ss);
ss << " ■ " << n[mn] << '\n';
if (lr[1]) info(lr[1], 1, ss);
}
return ss.str();
}
template <class... Args> static inline void rebuild(Args &...plc) {
static_assert(std::conjunction_v<std::is_same<PiecewiseLinearConvex, Args>...>);
constexpr size_t m= sizeof...(Args);
std::array<std::vector<std::pair<T, T>>, m> ls, rs;
std::array<std::pair<T, T>, m> mns;
int i= 0;
(void)(int[]){(mns[i]= {n[plc.mn].d, n[plc.mn].x}, ls[i].resize(n[plc.lr[0]].sz), rs[i].resize(n[plc.lr[1]].sz), dump(ls[i].begin(), plc.lr[0]), dump(rs[i].begin(), plc.lr[1]), ++i)...};
ni= 1, i= 0;
(void)(int[]){((plc.mn ? (plc.mn= create(mns[i].first, mns[i].second)) : 0), plc.lr[0]= build(ls[i].begin(), ls[i].end()), plc.lr[1]= build(rs[i].begin(), rs[i].end()), ++i)...};
}
static inline void rebuild(std::vector<PiecewiseLinearConvex> &plcs) {
size_t m= plcs.size();
std::vector<std::vector<std::pair<T, T>>> ls(m), rs(m);
std::vector<std::pair<T, T>> mns(m);
for (int i= m; i--;) mns[i]= {n[plcs[i].mn].d, n[plcs[i].mn].x}, ls[i].resize(n[plcs[i].lr[0]].sz), rs[i].resize(n[plcs[i].lr[1]].sz), dump(ls[i].begin(), plcs[i].lr[0]), dump(rs[i].begin(), plcs[i].lr[1]);
ni= 1;
for (int i= m; i--;) (plcs[i].mn ? (plcs[i].mn= create(mns[i].first, mns[i].second)) : 0), plcs[i].lr[0]= build(ls[i].begin(), ls[i].end()), plcs[i].lr[1]= build(rs[i].begin(), rs[i].end());
}
static void reset() { ni= 1; }
static bool pool_empty() {
if constexpr (persistent) return ni >= NODE_SIZE * 0.8;
else return ni + 1000 >= NODE_SIZE;
}
// f(x) += c
void add_const(D c) { y+= c; }
// f(x) += ax, /
void add_linear(T a) { rem+= a; }
// f(x) += max(a(x-x0),b(x-x0)), (a < b)
void add_max(T a, T b, T x0) {
assert(a < b);
if (bf[0] && x0 <= bx[0]) y-= D(b) * x0, rem+= b;
else if (bf[1] && bx[1] <= x0) y-= D(a) * x0, rem+= a;
else if (T c= b - a; mn) {
if (n[mn].x == x0) {
if constexpr (persistent) mn= create(n[mn].d, n[mn].x);
n[mn].d+= c, o[1]+= c, y-= D(a) * x0, rem+= a;
} else {
if (n[mn].x < x0) lr[1]= insert(lr[1], x0, c), y-= D(a) * x0, rem+= a;
else lr[0]= insert(lr[0], x0, c), y-= D(b) * x0, rem+= b;
}
} else mn= create(c, x0), y-= D(a) * x0, rem+= a, o[0]= 0, o[1]= c;
}
// f(x) += max(0, a(x-x0))
void add_ramp(T a, T x0) {
if (a != 0) a > 0 ? add_max(0, a, x0) : add_max(a, 0, x0);
}
// f(x) += a|x-x0|, \/
void add_abs(T a, T x0) {
if (assert(a >= 0); a != 0) add_max(-a, a, x0);
}
// right=false : f(x) += inf (x < x_0), right=true: f(x) += inf (x_0 < x)
void add_inf(bool right= false, T x0= 0) { return right ? add_inf<1>(x0) : add_inf<0>(x0); }
// f(x) <- f(x-x0)
void shift(T x0) {
if (bx[0]+= x0, bx[1]+= x0, y-= D(rem) * x0; mn) prop(x0), prop(lr[0], x0), prop(lr[1], x0);
}
// rev=false: f(x) <- min_{y<=x} f(y), rev=true : f(x) <- min_{x<=y} f(y)
void chmin_cum(bool rev= false) {
if (bf[0] && bf[1] && bx[0] == bx[1]) y+= D(rem) * bx[0], rem= 0;
else if (rem != 0) {
bool r= rem < 0;
T u= (r ? -rem : rem) - o[r] - n[lr[r]].a;
if (0 <= u) {
if (r ^ rev) {
if (u > 0 && bf[r]) {
D q= n[lr[r]].s + D(n[mn].x) * o[r] + D(u) * bx[r];
if (r ? y-= q : y+= q; mn) lr[!r]= join(lr[0], mn, lr[1]);
o[!r]= u, rem= 0, mn= create(u, bx[r]), lr[r]= 0, o[r]= 0;
}
} else {
assert(bf[r]);
D q= n[lr[r]].s + D(n[mn].x) * o[r] + D(u) * bx[r];
(r ? y-= q : y+= q), rem= 0, mn= lr[r]= 0, o[r]= 0;
}
bf[!rev]= false;
return;
}
if ((r ^ rev)) r ? slope_eval_cum<0, 1>() : slope_eval_cum<0, 0>();
else r ? slope_eval_cum<1, 1>() : slope_eval_cum<1, 0>();
if constexpr (persistent) mn= create(o[rev], n[mn].x);
else n[mn].d= o[rev];
} else if (mn) {
if (o[rev] == 0) {
if (lr[rev]) std::tie(lr[rev], mn)= rev ? pop<0>(lr[rev]) : pop<1>(lr[rev]), o[rev]= n[mn].d;
else mn= 0;
} else {
if constexpr (persistent) mn= create(o[rev], n[mn].x);
else n[mn].d= o[rev];
}
}
bf[!rev]= false, lr[!rev]= 0, o[!rev]= 0;
}
// f(x) <- min_{lb<=y<=ub} f(x-y). (lb <= ub), \_/ -> \__/
void chmin_slide_win(T lb, T ub) {
assert(lb <= ub);
if (bf[0] && bf[1] && bx[0] == bx[1]) y+= D(rem) * bx[0], rem= 0;
else {
if (rem != 0) {
bool r= rem < 0;
T u= (r ? -rem : rem) - o[r] - n[lr[r]].a;
if (0 < u) {
T b[2]= {lb, ub};
if (bf[r]) {
D q= n[lr[r]].s + D(n[mn].x) * o[r] + D(u) * bx[r];
if (r ? y-= q : y+= q; mn) lr[!r]= join(lr[0], mn, lr[1]), prop<0>(lr[!r], b[!r]);
lr[r]= 0, rem= 0, o[!r]= u, o[r]= 0, mn= create(u, bx[r] + b[!r]);
} else {
y-= D(rem) * b[!r];
if (mn) prop(b[!r]), prop(lr[0], b[!r]), prop(lr[1], b[!r]);
}
bx[0]+= lb, bx[1]+= ub;
return;
}
slope_eval(r);
}
if (mn) {
if (o[0] == 0) prop(ub);
else if (o[1] == 0) prop(lb);
else lr[1]= join<0>(0, create(o[1], n[mn].x), lr[1]), prop(lb), n[mn].d= o[0], o[1]= 0;
prop(lr[0], lb), prop(lr[1], ub);
}
}
bx[0]+= lb, bx[1]+= ub;
}
D operator()(T x) { return assert(!bf[0] || bx[0] <= x), assert(!bf[1] || x <= bx[1]), calc_y(x) + D(rem) * x + y; }
D min() {
if (rem == 0) return y;
bool r= rem < 0;
T u= (r ? -rem : rem) - o[r] - n[lr[r]].a;
if (0 < u) {
assert(bf[r]);
D q= n[lr[r]].s + D(n[mn].x) * o[r] + D(u) * bx[r];
return r ? y - q : y + q;
}
return slope_eval(r), y;
}
std::array<T, 2> argmin() {
if (rem != 0) {
bool r= rem < 0;
if (o[r] + n[lr[r]].a < (r ? -rem : rem)) {
assert(bf[r]);
return {bx[r], bx[r]};
}
slope_eval(r);
}
std::array<T, 2> ret= {bx[0], bx[1]};
int t= mn;
if (!t) return ret;
bool r= o[0] == 0;
if (!r && o[1] != 0) ret[0]= ret[1]= n[t].x;
else if (ret[r]= n[t].x, t= lr[!r]; t) {
for (; push(t), n[t].ch[r];) t= n[t].ch[r];
ret[!r]= n[t].x;
} else assert(bf[!r]);
return ret;
}
size_t size() { return n[lr[0]].sz + n[lr[1]].sz + !!mn; }
PiecewiseLinearConvex &operator+=(const PiecewiseLinearConvex &g) { return *this= *this + g; }
PiecewiseLinearConvex operator+(PiecewiseLinearConvex g) const {
PiecewiseLinearConvex ret= *this;
if (g.bf[0]) ret.add_inf(false, g.bx[0]);
if (g.bf[1]) ret.add_inf(true, g.bx[1]);
if (bf[0]) g.add_inf(false, bx[0]);
if (bf[1]) g.add_inf(true, bx[1]);
ret.y+= g.y, ret.rem+= g.rem;
if (!g.mn) return ret;
if (!ret.mn) return ret.mn= g.mn, ret.lr[0]= g.lr[0], ret.lr[1]= g.lr[1], ret.o[0]= g.o[0], ret.o[1]= g.o[1], ret;
ret.y+= n[ret.lr[0]].s + D(n[ret.mn].x) * ret.o[0] + n[g.lr[0]].s + D(n[g.mn].x) * g.o[0], ret.rem-= ret.o[0] + n[ret.lr[0]].a + g.o[0] + n[g.lr[0]].a;
int t= unite(join(ret.lr[0], ret.mn, ret.lr[1]), join(g.lr[0], g.mn, g.lr[1]));
return std::tie(ret.lr[1], ret.mn)= pop<0>(t), ret.lr[0]= 0, ret.o[0]= 0, ret.o[1]= n[ret.mn].d, ret;
}
std::vector<T> dump_xs() {
std::vector<T> xs;
if (bf[0]) xs.push_back(bx[0]);
dump_xs(lr[0], xs);
if (mn) xs.push_back(n[mn].x);
dump_xs(lr[1], xs);
if (bf[1]) xs.push_back(bx[1]);
return xs;
}
std::vector<std::pair<T, D>> dump_xys() {
auto xs= dump_xs();
std::vector<std::pair<T, D>> xys(xs.size());
for (int i= xs.size(); i--;) xys[i]= {xs[i], operator()(xs[i])};
return xys;
}
std::vector<T> dump_slopes() {
std::vector<T> as;
if (mn) as.push_back(-o[0]), dump_slopes_l(lr[0], o[0], as), std::reverse(as.begin(), as.end()), as.push_back(o[1]), dump_slopes_r(lr[1], o[1], as);
else as.push_back(0);
for (auto &a: as) a+= rem;
return as;
}
};
using namespace std;
signed main() {
cin.tie(0);
ios::sync_with_stdio(0);
int N;
cin >> N;
vector<int> A(N + 1);
for (int i= 0; i <= N; ++i) cin >> A[i];
vector<vector<int>> tree(N + 1);
for (int i= 0; i < N; ++i) {
int u, v;
cin >> u >> v;
tree[u].push_back(v);
tree[v].push_back(u);
}
using PLC= PiecewiseLinearConvex<int, true, 3 << 22>;
vector<PLC> fs(N + 1);
vector<int> mn(N + 1), mx(N + 1);
vector<long long> ans(N + 1);
auto dfs= [&](auto &&dfs, int v, int p, int d) -> void {
if (d < 2) {
ans[v]= -1;
} else if (mn[v] == mx[v]) {
ans[v]= 1;
} else {
PLC f= fs[v], g= fs[v];
f.add_linear(-mn[v]);
f.chmin_slide_win(-1, 1);
f.add_linear(mn[v]);
g.add_linear(-mx[v]);
g.chmin_slide_win(-1, 1);
g.add_linear(mx[v]);
ans[v]= min(-f(0), -g(0));
}
for (int u: tree[v]) {
if (u == p) continue;
mn[u]= mn[v], mx[u]= mx[v], fs[u]= fs[v];
if (A[u] < mn[u]) swap(mn[u], A[u]);
else if (mx[u] < A[u]) swap(mx[u], A[u]);
fs[u].add_linear(-A[u]);
fs[u].chmin_slide_win(-1, 1);
fs[u].add_linear(A[u]);
if (PLC::pool_empty()) PLC::rebuild(fs);
dfs(dfs, u, v, d + 1);
}
if (PLC::pool_empty()) PLC::rebuild(fs);
};
for (int u: tree[0]) {
tie(mn[u], mx[u])= minmax(A[0], A[u]);
fs[u].add_inf(), fs[u].add_inf(true);
dfs(dfs, u, 0, 1);
}
for (int i= 1; i <= N; ++i) cout << ans[i] << "\n";
return 0;
}