結果
| 問題 |
No.952 危険な火薬庫
|
| ユーザー |
 drken1215
|
| 提出日時 | 2025-05-15 23:10:40 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,568 ms / 2,000 ms |
| コード長 | 7,993 bytes |
| コンパイル時間 | 3,941 ms |
| コンパイル使用メモリ | 320,720 KB |
| 実行使用メモリ | 295,652 KB |
| 最終ジャッジ日時 | 2025-05-15 23:11:03 |
| 合計ジャッジ時間 | 15,701 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 23 |
ソースコード
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
template<class S, class T> inline bool chmax(S &a, T b) { return (a < b ? a = b, 1 : 0); }
template<class S, class T> inline bool chmin(S &a, T b) { return (a > b ? a = b, 1 : 0); }
using pint = pair<int, int>;
using pll = pair<long long, long long>;
using tint = array<int, 3>;
using tll = array<long long, 3>;
using fint = array<int, 4>;
using fll = array<long long, 4>;
using vint = vector<int>;
using vll = vector<long long>;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
template <class T>
using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;
#define REP(i, a) for (long long i = 0; i < (long long)(a); i++)
#define REP2(i, a, b) for (long long i = a; i < (long long)(b); i++)
#define RREP(i, a) for (long long i = (a)-1; i >= (long long)(0); --i)
#define RREP2(i, a, b) for (long long i = (b)-1; i >= (long long)(a); --i)
#define EB emplace_back
#define PB push_back
#define MP make_pair
#define MT make_tuple
#define FI first
#define SE second
#define ALL(x) x.begin(), x.end()
#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl
// debug stream
template<class T1, class T2> ostream& operator << (ostream &s, pair<T1,T2> P)
{ return s << '<' << P.first << ", " << P.second << '>'; }
template<class T> ostream& operator << (ostream &s, vector<T> P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, deque<T> P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, vector<vector<T> > P)
{ for (int i = 0; i < P.size(); ++i) { s << endl << P[i]; } return s << endl; }
template<class T> ostream& operator << (ostream &s, set<T> P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class T> ostream& operator << (ostream &s, multiset<T> P)
{ for (auto it : P) { s << "<" << it << "> "; } return s; }
template<class T1, class T2> ostream& operator << (ostream &s, map<T1,T2> P)
{ for (auto it : P) { s << "<" << it.first << "->" << it.second << "> "; } return s; }
/*///////////////////////////////////////////////////////*/
// Utility
/*///////////////////////////////////////////////////////*/
// 4-neighbor
const vector<int> dx = {1, 0, -1, 0};
const vector<int> dy = {0, 1, 0, -1};
// 8-neighbor
const vector<int> dx8 = {1, 0, -1, 0, 1, -1, 1, -1};
const vector<int> dy8 = {0, 1, 0, -1, 1, 1, -1, -1};
// bit
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); }
// xor128による乱数生成、周期は2^128-1
unsigned int randInt() {
static unsigned int tx = 123456789, ty=362436069, tz=521288629, tw=88675123;
unsigned int tt = (tx^(tx<<11));
tx = ty; ty = tz; tz = tw;
return ( tw=(tw^(tw>>19))^(tt^(tt>>8)) );
}
int randInt(int minv, int maxv) {
return randInt() % (maxv - minv + 1) + minv;
}
ll randll(ll minv, ll maxv) {
ll a = randInt(), b = randInt();
return (a * (1LL<<29) + b) % (maxv - minv + 1) + minv;
}
template<class T> void shuffle(vector<T>& vec) {
int n = vec.size();
for (int i = n - 1; i > 0; --i) {
int k = randInt() % (i + 1);
swap(vec[i], vec[k]);
}
}
// floor, ceil
template<class T> T floor(T a, T b) {
if (a % b == 0 || a >= 0) return a / b;
else return -((-a) / b) - 1;
}
template<class T> T ceil(T x, T y) {
return floor(x + y - 1, y);
}
// kth root
// N < 2^64, K <= 64
uint64_t kth_root(uint64_t N, uint64_t K) {
assert(K >= 1);
if (N <= 1 || K == 1) return N;
if (K >= 64) return 1;
if (N == uint64_t(-1)) --N;
auto mul = [&](uint64_t x, uint64_t y) -> uint64_t {
if (x < UINT_MAX && y < UINT_MAX) return x * y;
if (x == uint64_t(-1) || y == uint64_t(-1)) return uint64_t(-1);
return (x <= uint64_t(-1) / y ? x * y : uint64_t(-1));
};
auto power = [&](uint64_t x, uint64_t k) -> uint64_t {
if (k == 0) return 1ULL;
uint64_t res = 1ULL;
while (k) {
if (k & 1) res = mul(res, x);
x = mul(x, x);
k >>= 1;
}
return res;
};
uint64_t res;
if (K == 2) res = sqrtl(N) - 1;
else if (K == 3) res = cbrt(N) - 1;
else res = pow(N, nextafter(1 / double(K), 0));
while (power(res + 1, K) <= N) ++res;
return res;
}
// int 128
using i128 = __int128;
constexpr i128 to_integer(const string &s) {
i128 res = 0;
for (auto c : s) {
if (isdigit(c)) res = res * 10 + (c - '0');
}
if (s[0] == '-') res *= -1;
return res;
}
istream& operator >> (istream &is, i128 &x) {
string s;
is >> s;
x = to_integer(s);
return is;
}
ostream& operator << (ostream &os, const i128 &x) {
i128 ax = (x >= 0 ? x : -x);
char buffer[128];
char *d = end(buffer);
do {
--d;
*d = "0123456789"[ax % 10];
ax /= 10;
} while (ax != 0);
if (x < 0) {
--d;
*d = '-';
}
int len = end(buffer) - d;
if (os.rdbuf()->sputn(d, len) != len) {
os.setstate(ios_base::badbit);
}
return os;
}
// Convex Hull Trick
/*
追加クエリの直線の傾きが単調減少の場合
- insert (a, b): add y = ax + b
- query (x): min_i{a[i]*x + b}
*/
template<class T> struct CHT {
using Line = pair<T, T>;
deque<Line> lines;
inline bool check(const Line &a, const Line &b, const Line &c) {
return (b.first - a.first) * (c.second - b.second)
>= (b.second - a.second) * (c.first - b.first);
}
inline T get(int k, T x) {
if (lines.empty() || k >= lines.size()) return i128(1) << 66;
assert(k >= 0 && k < lines.size());
return lines[k].first * x + lines[k].second;
}
void insert(T a, T b) {
Line l(a, b);
while (lines.size() >= 2
&& check(lines[(int)lines.size()-2], lines[(int)lines.size()-1], l)) {
lines.pop_back();
}
lines.push_back(l);
}
T query(T x) {
int low = -1, high = (int)lines.size();
while (high - low > 1) {
int mid = (low + high) / 2;
if (get(mid, x) >= get(mid + 1, x)) low = mid;
else high = mid;
}
return get(high, x);
}
// クエリの単調性も成り立つ場合 (x が単調増加)
T query_monotone(T x) {
while (lines.size() >= 2 && get(0, x) >= get(1, x)) lines.pop_front();
if (lines.empty()) return i128(1) << 66;
return lines[0].first * x + lines[0].second;
}
};
int main() {
int N;
cin >> N;
N++;
vector<i128> A(N, 0), S(N+1, 0);
REP(i, N) {
if (i) cin >> A[i];
S[i+1] = S[i] + A[i];
}
vector chts(N+1, CHT<i128>());
i128 INF = i128(1)<<100;
vector dp(N+1, vector(N+1, INF));
auto push = [&](int i, int j) -> void {
if (i-1 >= 0) chts[i-j].insert(-S[i]*2, S[i]*S[i] + dp[i-1][j]);
};
dp[0][0] = 0;
push(0, 0);
REP2(i, 1, N+1) {
REP(j, i) {
chmin(dp[i][j], dp[i-1][j]);
/*
chmin(dp[i][j], dp[i-j-1][0] + S[i]² - 2S[i-j]S[i] + S[i-j]²)
chmin(dp[i][j], dp[i-j][1] + S[i]² - 2S[i-j-1]S[i] + S[i-j-1]²)
...
chmin(dp[i][j], dp[i-2][j-1] + S[i]² - 2S[i-1]S[i] + S[i-1]²)
*/
// REP(k, j) {
// chmin(dp[i][j], dp[i-j-1+k][k] + (S[i] - S[i-j+k]) * (S[i] - S[i-j+k]));
// }
chmin(dp[i][j], chts[i-j].query(S[i]) + S[i] * S[i]);
push(i, j);
}
}
REP2(k, 1, N) {
cout << dp[N][k] << endl;
}
}