結果
| 問題 |
No.704 ゴミ拾い Medium
|
| コンテスト | |
| ユーザー |
 はまやんはまやん
|
| 提出日時 | 2018-06-16 08:16:24 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 6,440 bytes |
| コンパイル時間 | 1,585 ms |
| コンパイル使用メモリ | 171,488 KB |
| 実行使用メモリ | 19,592 KB |
| 最終ジャッジ日時 | 2024-06-30 16:07:48 |
| 合計ジャッジ時間 | 5,755 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 20 TLE * 1 -- * 23 |
ソースコード
#include<bits/stdc++.h>
#define rep(i,a,b) for(int i=a;i<b;i++)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define fore(i,a) for(auto &i:a)
#define all(x) (x).begin(),(x).end()
#pragma GCC optimize ("-O3")
using namespace std; void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); }
typedef long long ll; const int inf = INT_MAX / 2; const ll infl = 1LL << 60;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a = b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a = b; return 1; } return 0; }
//---------------------------------------------------------------------------------------------------
class ConvexHullDynamic
{
typedef long long coef_t;
typedef long long coord_t;
typedef long long val_t;
/*
* Line 'y=a*x+b' represented by 2 coefficients 'a' and 'b'
* and 'xLeft' which is intersection with previous line in hull(first line has -INF)
*/
private:
struct Line
{
coef_t a, b;
double xLeft;
enum Type
{
line, maxQuery, minQuery
} type;
coord_t val;
explicit Line(coef_t aa = 0, coef_t bb = 0) : a(aa), b(bb), xLeft(-INFINITY), type(Type::line), val(0) {}
val_t valueAt(coord_t x) const { return a * x + b; }
friend bool areParallel(const Line &l1, const Line &l2) { return l1.a == l2.a; }
friend double intersectX(const Line &l1, const Line &l2) { return areParallel(l1, l2) ? INFINITY : 1.0 * (l2.b - l1.b) / (l1.a - l2.a); }
bool operator<(const Line &l2) const
{
if (l2.type == line)
return this->a < l2.a;
if (l2.type == maxQuery)
return this->xLeft < l2.val;
if (l2.type == minQuery)
return this->xLeft > l2.val;
}
};
bool isMax; //whether or not saved envelope is top(search of max value)
public:
std::set< Line > hull; //envelope itself
private:
/*
* INFO: Check position in hull by iterator
* COMPLEXITY: O(1)
*/
bool hasPrev(std::set< Line >::iterator it) { return it != hull.begin(); }
bool hasNext(std::set< Line >::iterator it) { return it != hull.end() && std::next(it) != hull.end(); }
/*
* INFO: Check whether line l2 is irrelevant
* NOTE: Following positioning in hull must be true
* l1 is next left to l2
* l2 is right between l1 and l3
* l3 is next right to l2
* COMPLEXITY: O(1)
*/
bool irrelevant(const Line &l1, const Line &l2, const Line &l3) { return intersectX(l1, l3) <= intersectX(l1, l2); }
bool irrelevant(std::set< Line >::iterator it)
{
return hasPrev(it) && hasNext(it)
&& (isMax && irrelevant(*std::prev(it), *it, *std::next(it))
|| !isMax && irrelevant(*std::next(it), *it, *std::prev(it)));
}
/*
* INFO: Updates 'xValue' of line pointed by iterator 'it'
* COMPLEXITY: O(1)
*/
std::set< Line >::iterator updateLeftBorder(std::set< Line >::iterator it)
{
if (isMax && !hasPrev(it) || !isMax && !hasNext(it))
return it;
double val = intersectX(*it, isMax ? *std::prev(it) : *std::next(it));
Line buf(*it);
it = hull.erase(it);
buf.xLeft = val;
it = hull.insert(it, buf);
return it;
}
public:
explicit ConvexHullDynamic(bool isMax = false) : isMax(isMax) {}
/*
* INFO: Adding line to the envelope
* Line is of type 'y=a*x+b' represented by 2 coefficients 'a' and 'b'
* COMPLEXITY: Adding N lines(N calls of function) takes O(N*log N) time
*/
void addLine(coef_t a, coef_t b)
{
//find the place where line will be inserted in set
Line l3 = Line(a, b);
auto it = hull.lower_bound(l3);
//if parallel line is already in set, one of them becomes irrelevant
if (it != hull.end() && areParallel(*it, l3)) {
if (isMax && it->b < b || !isMax && it->b > b)
it = hull.erase(it);
else
return;
}
//try to insert
it = hull.insert(it, l3);
if (irrelevant(it)) {
hull.erase(it);
return;
}
//remove lines which became irrelevant after inserting line
while (hasPrev(it) && irrelevant(std::prev(it))) hull.erase(std::prev(it));
while (hasNext(it) && irrelevant(std::next(it))) hull.erase(std::next(it));
//refresh 'xLine'
it = updateLeftBorder(it);
if (hasPrev(it))
updateLeftBorder(std::prev(it));
if (hasNext(it))
updateLeftBorder(std::next(it));
}
val_t getBest(coord_t x) const
{
Line q;
q.val = x;
q.type = isMax ? Line::Type::maxQuery : Line::Type::minQuery;
auto bestLine = hull.lower_bound(q);
if (isMax) --bestLine;
return bestLine->valueAt(x);
}
};
/*---------------------------------------------------------------------------------------------------
∧＿∧
∧＿∧ （´<_｀ ） Welcome to My Coding Space!
（ ´_ゝ`） / ⌒i
／ ＼ | |
/ /￣￣￣￣/ |
＿_(__ﾆつ/ ＿/ .| .|＿＿＿＿
＼/＿＿＿＿/ （u ⊃
---------------------------------------------------------------------------------------------------*/
int N;
ll A[301010], X[301010], Y[301010];
ll dp[301010];
ConvexHullDynamic ch;
//---------------------------------------------------------------------------------------------------
void _main() {
cin >> N;
rep(i, 1, N + 1) cin >> A[i];
rep(i, 1, N + 1) cin >> X[i];
rep(i, 1, N + 1) cin >> Y[i];
rep(i, 0, N + 1) dp[i] = infl;
dp[0] = 0;
/* O(N^2)
rep(i, 1, N + 1) {
rep(j, 0, i) {
ll dx = abs(A[i] - X[j + 1]);
ll dy = Y[j + 1];
ll z = dp[j] + dx + dy;
chmin(dp[i], z);
}
}*/
rep(i, 1, N + 1) {
rep(j, 0, i) if (A[i] < X[j + 1]) chmin(dp[i], dp[j] + X[j + 1] - A[i] + Y[j + 1]);
rep(j, 0, i) if (A[i] >= X[j + 1]) chmin(dp[i], dp[j] + A[i] - X[j + 1] + Y[j + 1]);
}
cout << dp[N] << endl;
}