結果
| 問題 |
No.409 ダイエット
|
| コンテスト | |
| ユーザー |
 ningenMe
|
| 提出日時 | 2021-05-03 04:42:02 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,089 ms / 2,000 ms |
| コード長 | 11,706 bytes |
| コンパイル時間 | 2,493 ms |
| コンパイル使用メモリ | 215,412 KB |
| 最終ジャッジ日時 | 2025-01-21 06:12:37 |
|
ジャッジサーバーID （参考情報） |
judge4 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 92 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
#define REP(i,n) for(long long i = 0; i < (n); i++)
#define FOR(i, m, n) for(long long i = (m);i < (n); ++i)
#define ALL(obj) (obj).begin(),(obj).end()
#define SPEED cin.tie(0);ios::sync_with_stdio(false);
template<class T> using V = vector<T>;
template<class T, class U> using P = pair<T, U>;
template<class T> using PQ = priority_queue<T>;
template<class T> using PQR = priority_queue<T,vector<T>,greater<T>>;
constexpr long long MOD = (long long)1e9 + 7;
constexpr long long MOD2 = 998244353;
constexpr long long HIGHINF = (long long)1e18;
constexpr long long LOWINF = (long long)1e15;
constexpr long double PI = 3.1415926535897932384626433;
template <class T> vector<T> multivector(size_t N,T init){return vector<T>(N,init);}
template <class... T> auto multivector(size_t N,T... t){return vector<decltype(multivector(t...))>(N,multivector(t...));}
template <class T> void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}}
template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;}
template <class T>ostream &operator<<(ostream &o, const set<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const multiset<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;}
template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;}
template <template <class tmp> class T, class U> ostream &operator<<(ostream &o, const T<U> &obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr)o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
void print(void) {cout << endl;}
template <class Head> void print(Head&& head) {cout << head;print();}
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward<Tail>(tail)...);}
template <class T> void chmax(T& a, const T b){a=max(a,b);}
template <class T> void chmin(T& a, const T b){a=min(a,b);}
void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;}
void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;}
void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;}
/*
* @title RandomizedBinarySearchTree - 平衡二分探索木
* @docs md/data-structure/binary-search-tree/RandomizedBinarySearchTree.md
*/
template<class Monoid> class RandomizedBinarySearchTree {
using TypeNode = typename Monoid::TypeNode;
unsigned int x = 123456789, y = 362436069, z = 521288629, w = 88675123;
unsigned int xor_shift() {
unsigned int t = (x ^ (x << 11)); x = y; y = z; z = w;
return (w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)));
}
struct Node {
private:
void build() {left = right = nullptr;size = 1;}
public:
Node *left, *right;
TypeNode value, range_value;
int size;
Node() : value(Monoid::unit_node), range_value(Monoid::unit_node) {build();}
Node(TypeNode v) : value(v), range_value(v) {build();}
friend ostream &operator<<(ostream &os, const Node* node) {return os << "{" << node->value << ", " << node->range_value << ", " << node->size << "}";}
};
Node* root;
inline int size(Node *node) {return node==nullptr ? 0 : node->size;}
inline TypeNode range_value(Node *node) {return node==nullptr ? Monoid::unit_node : node->range_value;}
inline TypeNode get(Node *node, size_t k) {
if (node==nullptr) return Monoid::unit_node;
if (k == size(node->left)) return node->value;
if (k < size(node->left)) return get(node->left, k);
else return get(node->right, k-1 - size(node->left));
}
inline Node* update(Node *node) {
node->size = size(node->left) + size(node->right) + 1;
node->range_value = Monoid::func_fold(Monoid::func_fold(range_value(node->left),node->value),range_value(node->right));
return node;
}
inline Node* merge_impl(Node *left, Node *right) {
if (left==nullptr) return right;
if (right==nullptr) return left;
if (xor_shift() % (left->size + right->size) < left->size) {
left->right = merge_impl(left->right, right);
return update(left);
}
else {
right->left = merge_impl(left, right->left);
return update(right);
}
}
inline pair<Node*, Node*> split_impl(Node* node, int k) {
if (node==nullptr) return make_pair(nullptr, nullptr);
if (k <= size(node->left)) {
pair<Node*, Node*> sub = split_impl(node->left, k);
node->left = sub.second;
return make_pair(sub.first, update(node));
}
else {
pair<Node*, Node*> sub = split_impl(node->right, k - 1 - size(node->left));
node->right = sub.first;
return make_pair(update(node), sub.second);
}
}
inline TypeNode fold_impl(Node *node, int l, int r) {
if (l < 0 || size(node) <= l || r<=0 || r-l <= 0) return Monoid::unit_node;
if (l == 0 && r == size(node)) return range_value(node);
TypeNode value = Monoid::unit_node;
int sl = size(node->left);
if(sl > l) value = Monoid::func_fold(value,fold_impl(node->left,l,min(sl,r)));
l = max(l-sl,0), r -= sl;
if(l == 0 && r > 0) value = Monoid::func_fold(value,node->value);
l = max(l-1,0), r -= 1;
if(l >= 0 && r > l) value = Monoid::func_fold(value,fold_impl(node->right,l,r));
return value;
}
inline int lower_bound(Node *node, TypeNode value) {
if (node==nullptr) return 0;
if (value <= node->value) return lower_bound(node->left, value);
else return size(node->left) + lower_bound(node->right, value) + 1;
}
inline int upper_bound(Node *node, TypeNode value) {
if (node==nullptr) return 0;
if (value < node->value) return upper_bound(node->left, value);
else return size(node->left) + upper_bound(node->right, value) + 1;
}
inline void insert_impl(const TypeNode value) {
pair<Node*, Node*> sub = split_impl(this->root, lower_bound(this->root,value));
this->root = this->merge_impl(this->merge_impl(sub.first, new Node(value)), sub.second);
}
inline void erase_impl(const TypeNode value) {
int k1 = lower_bound(value), k2 = upper_bound(value);
if(k1==k2) return;
auto sub = split_impl(this->root,k1);
this->root = merge_impl(sub.first, split_impl(sub.second, 1).second);
}
public:
RandomizedBinarySearchTree() : root(nullptr) {}
inline int size() {return size(this->root);}
inline int empty(void) {return bool(size()==0);}
inline Node* merge(Node *left, Node *right) {return merge_impl(left,right);}
inline pair<Node*, Node*> split(int k) {return split_impl(this->root,k);}
inline void insert(const TypeNode value) {insert_impl(value);}
inline void erase(const TypeNode value) {erase_impl(value);}
inline TypeNode get(size_t k) {return get(this->root, k);}
inline TypeNode fold(int l, int r) {return fold_impl(this->root,l,r);}
inline int lower_bound(TypeNode value) {return lower_bound(this->root,value);}
inline int upper_bound(TypeNode value) {return upper_bound(this->root,value);}
inline int count(TypeNode value) {return upper_bound(value) - lower_bound(value);}
void print() {int m = size(this->root); for(int i=0;i<m;++i) cout << get(i) << " \n"[i==m-1];}
};
//最大値クエリ
template<class T> struct ValueMax {
using TypeValue = T;
inline static constexpr TypeValue unit_value = -3e18;
inline static constexpr bool func_compare(TypeValue l,TypeValue r){return l>r;}
};
/*
* @title ConvexHullTrick - 非単調CHT
* @docs md/data-structure/convex-hull-trick/ConvexHullTrick.md
*/
template<class Operator> class ConvexHullTrick {
private:
using TypeValue = typename Operator::TypeValue;
using Line = pair<TypeValue,TypeValue>;
struct Monoid {
using TypeNode = Line;
inline static constexpr TypeNode unit_node = {0,0};
inline static constexpr TypeNode func_fold(TypeNode l,TypeNode r){return {0,0};}
};
RandomizedBinarySearchTree<Monoid> lines;
//3直線に関してline2が必要か確認 (このとき a1 < a2 < a3が必要=rbstの順そのまま)
inline int is_required(const Line& line1, const Line& line2, const Line& line3) {
return Operator::func_compare((line2.second-line3.second)*(line2.first-line1.first),(line1.second-line2.second)*(line3.first-line2.first));
}
//y=ax+bの値
inline TypeValue y(const Line line, TypeValue x) {
return line.first * x + line.second;
}
public:
ConvexHullTrick() {
// do nothing
}
//ax+bを追加
void insert(const TypeValue a, const TypeValue b) {
insert({a,b});
}
//ax+bを追加 armortized O(log(N))
void insert(const Line line) {
int k=lines.lower_bound(line), flg=1;
Line l,r;
if(0 <= k-1) {
l = lines.get(k-1);
//lと傾きが同じなら、どちらかをerase
if(l.first==line.first) {
if(Operator::func_compare(l.second,line.second)) return;
else lines.erase(l);
}
}
if(k < lines.size()) {
r = lines.get(k);
//rと傾きが同じなら、どちらかをerase
if(r.first==line.first) {
if(Operator::func_compare(r.second,line.second)) return;
else lines.erase(r);
}
}
//自身が必要か判定
if(0 <= k-1 && k < lines.size() && !is_required(l,line,r)) return;
//傾きが小さい側の不必要な直線を取り除く
for(k=lines.lower_bound(line);k>=2&&!is_required(lines.get(k-2), lines.get(k-1), line);k=lines.lower_bound(line)) lines.erase(lines.get(k-1));
//傾きが大きい側の不必要な直線を取り除く
for(k=lines.lower_bound(line);k+1<lines.size()&&!is_required(line,lines.get(k),lines.get(k+1));k=lines.lower_bound(line)) lines.erase(lines.get(k));
lines.insert(line);
}
//O(log(N)^2)
TypeValue get(TypeValue x) {
int ng = -1, ok = (int)lines.size()-1, md;
while (ok - ng > 1) {
md = (ok + ng) >> 1;
( Operator::func_compare(y(lines.get(md),x),y(lines.get(md+1),x)) ?ok:ng)=md;
}
return y(lines.get(ok),x);
}
//O(log(N)^2)
Line get_line(TypeValue x) {
int ng = -1, ok = (int)lines.size()-1, md;
while (ok - ng > 1) {
md = (ok + ng) >> 1;
( Operator::func_compare(y(lines.get(md),x),y(lines.get(md+1),x)) ?ok:ng)=md;
}
return lines.get(ok);
}
void print() {
lines.print();
}
};
int main() {
ll N,A,B,W; cin >> N >> A >> B >> W;
vector<ll> D(N+2,0);
for(int i = 1; i <= N; ++i) cin >> D[i];
// dp[i]=min{j:[0,i)} -> dp[j]+B*k*(k+1)/2-k*A+D[i] (k=i-j-1)
// -> dp[j]+B*(i-j-1)*(i-j)/2-(i-j-1)*A+D[i]
// -> dp[j]+B/2*(i*i-2*i*j+j*j-i+j)-A*(i-j-1)+D[i]
// -> (-B*j)*i + dp[j]+B/2*(j*j+j)+A*j + B/2*(i*i-i)-A*(i-1)+D[i]
// dp[i]=-max{j:[0,i)}-> (B*j)*i + -{dp[j]+B/2*(j*j+j)+A*j}
// ->
vector<ll> dp(N+2,1e15);
dp[0]=W;
ConvexHullTrick<ValueMax<ll>> cht;
cht.insert(0,-dp[0]);
for(ll i=1;i<=N+1;++i){
dp[i]=-cht.get(i) + B*(i*i-i)/2-A*(i-1)+D[i];
cht.insert(B*i,-(dp[i]+B*(i*i+i)/2+A*i));
}
cout << dp[N+1] << endl;
return 0;
}