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test/3_yukicoder/705.test.cpp
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- Last update: 2024-12-26 06:32:57+09:00
- Problem: https://yukicoder.me/problems/no/705
Depends on
- convex/larsch.hpp
- convex/monge.hpp
- convex/smawk.hpp
my_template.hpp
- other/fibonacci_search.hpp
- other/io.hpp
Code
#define PROBLEM "https://yukicoder.me/problems/no/705"
#include "my_template.hpp"
#include "other/io.hpp"
#include "convex/monge.hpp"
void solve() {
LL(N);
VEC(ll, A, N);
VEC(ll, X, N);
VEC(ll, Y, N);
auto f = [&](ll i, ll j) -> ll {
ll a = A[j - 1];
ll x = X[i], y = Y[i];
ll dx = abs(a - x);
ll dy = abs(y);
return dx * dx * dx + dy * dy * dy;
};
print(monge_shortest_path<ll>(N, f).back());
}
signed main() {
solve();
return 0;
}#line 1 "test/3_yukicoder/705.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/705"
#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 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_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (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 kth_bit(int k) {
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
return x >> k & 1;
}
template <typename UINT>
struct all_bit {
struct iter {
UINT s;
iter(UINT s) : s(s) {}
int operator*() const { return lowbit(s); }
iter &operator++() {
s &= s - 1;
return *this;
}
bool operator!=(const iter) const { return s != 0; }
};
UINT s;
all_bit(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
template <typename UINT>
struct all_subset {
static_assert(is_unsigned<UINT>::value);
struct iter {
UINT s, t;
bool ed;
iter(UINT s) : s(s), t(s), ed(0) {}
int operator*() const { return s ^ t; }
iter &operator++() {
(t == 0 ? ed = 1 : t = (t - 1) & s);
return *this;
}
bool operator!=(const iter) const { return !ed; }
};
UINT s;
all_subset(UINT s) : s(s) {}
iter begin() const { return iter(s); }
iter end() const { return iter(0); }
};
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 "other/io.hpp"
#define FASTIO
#include <unistd.h>
// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }
template <class T, class U>
void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
for (auto &d: x) rd(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c: s) wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }
template <class T, class U>
void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt(' '); }
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
template <class T>
void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
void YA(bool t = 1) { print(t ? "YA" : "TIDAK"); }
void TIDAK(bool t = 1) { YES(!t); }
#line 2 "convex/larsch.hpp"
// https://noshi91.github.io/Library/algorithm/larsch.cpp.html
template <class T>
class LARSCH {
struct reduce_row;
struct reduce_col;
struct reduce_row {
int n;
std::function<T(int, int)> f;
int cur_row;
int state;
std::unique_ptr<reduce_col> rec;
reduce_row(int n_) : n(n_), f(), cur_row(0), state(0), rec() {
const int m = n / 2;
if (m != 0) { rec = std::make_unique<reduce_col>(m); }
}
void set_f(std::function<T(int, int)> f_) {
f = f_;
if (rec) {
rec->set_f([&](int i, int j) -> T { return f(2 * i + 1, j); });
}
}
int get_argmin() {
const int cur_row_ = cur_row;
cur_row += 1;
if (cur_row_ % 2 == 0) {
const int prev_argmin = state;
const int next_argmin = [&]() {
if (cur_row_ + 1 == n) {
return n - 1;
} else {
return rec->get_argmin();
}
}();
state = next_argmin;
int ret = prev_argmin;
for (int j = prev_argmin + 1; j <= next_argmin; j += 1) {
if (f(cur_row_, ret) > f(cur_row_, j)) { ret = j; }
}
return ret;
} else {
if (f(cur_row_, state) <= f(cur_row_, cur_row_)) {
return state;
} else {
return cur_row_;
}
}
}
};
struct reduce_col {
int n;
std::function<T(int, int)> f;
int cur_row;
std::vector<int> cols;
reduce_row rec;
reduce_col(int n_) : n(n_), f(), cur_row(0), cols(), rec(n) {}
void set_f(std::function<T(int, int)> f_) {
f = f_;
rec.set_f([&](int i, int j) -> T { return f(i, cols[j]); });
}
int get_argmin() {
const int cur_row_ = cur_row;
cur_row += 1;
const auto cs = [&]() -> std::vector<int> {
if (cur_row_ == 0) {
return {{0}};
} else {
return {{2 * cur_row_ - 1, 2 * cur_row_}};
}
}();
for (const int j: cs) {
while ([&]() {
const int size = cols.size();
return size != cur_row_ && f(size - 1, cols.back()) > f(size - 1, j);
}()) {
cols.pop_back();
}
if (int(cols.size()) != n) { cols.push_back(j); }
}
return cols[rec.get_argmin()];
}
};
std::unique_ptr<reduce_row> base;
public:
LARSCH(int n, std::function<T(int, int)> f)
: base(std::make_unique<reduce_row>(n)) {
base->set_f(f);
}
int get_argmin() { return base->get_argmin(); }
};
#line 2 "convex/smawk.hpp"
// select(i,j,k) は (i,j) -> (i,k) を行うかどうか
// 残念ながら monotone minima より高速な場合が存在しない説がある
// https://codeforces.com/contest/1423/problem/M
template <typename F>
vc<int> smawk(int H, int W, F select) {
auto dfs = [&](auto& dfs, vc<int> X, vc<int> Y) -> vc<int> {
int N = len(X);
if (N == 0) return {};
vc<int> YY;
for (auto&& y: Y) {
while (len(YY)) {
int py = YY.back(), x = X[len(YY) - 1];
if (!select(x, py, y)) break;
YY.pop_back();
}
if (len(YY) < len(X)) YY.eb(y);
}
vc<int> XX;
FOR(i, 1, len(X), 2) XX.eb(X[i]);
vc<int> II = dfs(dfs, XX, YY);
vc<int> I(N);
FOR(i, len(II)) I[i + i + 1] = II[i];
int p = 0;
FOR(i, 0, N, 2) {
int LIM = (i + 1 == N ? Y.back() : I[i + 1]);
int best = Y[p];
while (Y[p] < LIM) {
++p;
if (select(X[i], best, Y[p])) best = Y[p];
}
I[i] = best;
}
return I;
};
vc<int> X(H), Y(W);
iota(all(X), 0), iota(all(Y), 0);
return dfs(dfs, X, Y);
}
#line 1 "other/fibonacci_search.hpp"
// returns: {fx, x}
// [L, R) での極小値をひとつ求める、単峰は不要
template <typename T, bool MINIMIZE, typename F>
pair<T, ll> fibonacci_search(F f, ll L, ll R) {
assert(L < R);
--R;
ll a = L, b = L + 1, c = L + 2, d = L + 3;
int n = 0;
while (d < R) { b = c, c = d, d = b + c - a, ++n; }
auto get = [&](ll x) -> T {
if (R < x) return infty<T>;
return (MINIMIZE ? f(x) : -f(x));
};
T ya = get(a), yb = get(b), yc = get(c), yd = get(d);
// この中で極小ならば全体でも極小、を維持する
FOR(n) {
if (yb <= yc) {
d = c, c = b, b = a + d - c;
yd = yc, yc = yb, yb = get(b);
} else {
a = b, b = c, c = a + d - b;
ya = yb, yb = yc, yc = get(c);
}
}
ll x = a;
T y = ya;
if (chmin(y, yb)) x = b;
if (chmin(y, yc)) x = c;
if (chmin(y, yd)) x = d;
if (MINIMIZE) return {y, x};
return {-y, x};
}
#line 4 "convex/monge.hpp"
// 定義域 [0, N] の範囲で f の monge 性を確認
template <typename T, typename F>
bool check_monge(int N, F f) {
FOR(l, N + 1) FOR(k, l) FOR(j, k) FOR(i, j) {
T lhs = f(i, l) + f(j, k);
T rhs = f(i, k) + f(j, l);
if (lhs < rhs) {
print("monge ng");
print(i, j, k, l, f(i, k), f(i, l), f(j, k), f(j, l), lhs, rhs);
return false;
}
}
print("monge ok");
return true;
}
// newdp[j] = min (dp[i] + f(i,j))
template <typename T, typename F>
vc<T> monge_dp_update(int N, vc<T>& dp, F f) {
assert(len(dp) == N + 1);
auto select = [&](int i, int j, int k) -> int {
if (i <= k) return j;
return (dp[j] + f(j, i) > dp[k] + f(k, i) ? k : j);
};
vc<int> I = SMAWK(N + 1, N + 1, select);
vc<T> newdp(N + 1, infty<T>);
FOR(j, N + 1) {
int i = I[j];
chmin(newdp[j], dp[i] + f(i, j));
}
return newdp;
}
// 遷移回数を問わない場合
template <typename T, typename F>
vc<T> monge_shortest_path(int N, F f) {
vc<T> dp(N + 1, infty<T>);
dp[0] = 0;
LARSCH<T> larsch(N, [&](int i, int j) -> T {
++i;
if (i <= j) return infty<T>;
return dp[j] + f(j, i);
});
FOR(r, 1, N + 1) {
int l = larsch.get_argmin();
dp[r] = dp[l] + f(l, r);
}
return dp;
}
// https://noshi91.github.io/algorithm-encyclopedia/d-edge-shortest-path-monge
// |f| の上限 f_lim も渡す
// ・larsch が結構重いので、自前で dp できるならその方がよい
// ・複数の d で計算するとき：同じ lambda
// に対する計算をメモ化しておくと定数倍高速？ ・ABC305
template <typename T, typename F>
T monge_shortest_path_d_edge(int N, int d, T f_lim, F f) {
assert(d <= N);
auto calc_L = [&](T lambda) -> T {
auto cost = [&](int frm, int to) -> T { return f(frm, to) + lambda; };
vc<T> dp = monge_shortest_path<T>(N, cost);
return dp[N] - lambda * d;
};
auto [x, fx] = fibonacci_search<T, false>(calc_L, -3 * f_lim, 3 * f_lim + 1);
return fx;
}
// https://topcoder-g-hatena-ne-jp.jag-icpc.org/spaghetti_source/20120915/1347668163.html
// Prop 1
// 上三角 monge A, B
// C[i][j] = min_k (A[i][k] + B[k][j])
template <typename T, typename F1, typename F2>
vvc<T> monge_matrix_product(int N, F1 A, F2 B) {
vv(T, C, N + 1, N + 1, infty<T>);
vc<int> K(N + 1);
FOR(i, N + 1) C[i][i] = A(i, i) + B(i, i), K[i] = i;
FOR(s, 1, N + 1) {
vc<int> newK(N + 1 - s);
FOR(i, N + 1 - s) {
int j = i + s;
int p = K[i], q = K[i + 1];
FOR(k, p, q + 1) if (chmin(C[i][j], A(i, k) + B(k, j))) newK[i] = k;
}
swap(K, newK);
}
return C;
}
#line 5 "test/3_yukicoder/705.test.cpp"
void solve() {
LL(N);
VEC(ll, A, N);
VEC(ll, X, N);
VEC(ll, Y, N);
auto f = [&](ll i, ll j) -> ll {
ll a = A[j - 1];
ll x = X[i], y = Y[i];
ll dx = abs(a - x);
ll dy = abs(y);
return dx * dx * dx + dy * dy * dy;
};
print(monge_shortest_path<ll>(N, f).back());
}
signed main() {
solve();
return 0;
}