結果

問題 No.952 危険な火薬庫
ユーザー drken1215
提出日時 2025-05-15 16:23:10
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
MLE  
実行時間 -
コード長 8,404 bytes
コンパイル時間 4,131 ms
コンパイル使用メモリ 323,836 KB
実行使用メモリ 780,384 KB
最終ジャッジ日時 2025-05-15 16:23:26
合計ジャッジ時間 15,718 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 18 MLE * 5
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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) {
        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;
    vector<i128> A(N), S(N+1, 0);
    REP(i, N) {
        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, vector(2, INF)));  // 0: 白で終わる, 1: 黒で終わる
    vector mdp(N+2, vector(N+1, INF));

    auto push = [&](int i, int j) -> void {
        // auto func = [i, j, &S, &dp](ll x) -> ll {
        //     return dp[i][j][0] + S[i-j]*S[i-j]
        // };
        chts[i-j].insert(-S[i]*2, S[i]*S[i] + dp[i][j][0]);

        chmin(mdp[i+1][j], min(mdp[i][j], dp[i][j][1]));
    };

    dp[0][0][0] = 0, dp[0][0][1] = 0;
    push(0, 0);

    REP2(i, 1, N+1) {
        //COUT(i);
        REP(j, i+1) {
            // 0 -> 1
            // REP2(k, 0, j) {
            //     chmin(dp[i][j][1], dp[i-j+k][k][0] + (S[i] - S[i-j+k]) * (S[i] - S[i-j+k]));
            // }
            // (dp[i-j][0][0] + S[i]² - 2S[i]S[i-j] + S[i-j]²
            // dp[i-j+1][1][0] + S[i]² - 2S[i]S[i-j+1] + S[i-j+1]²
            // ...
            // dp[i-1][j-1][0] + S[i]² - 2S[i]S[i-1] + S[i-1]²
            chmin(dp[i][j][1], chts[i-j].query_monotone(S[i]) + S[i] * S[i]);

            // 1 -> 0
            // REP(k, i) {
            //     chmin(dp[i][j][0], dp[k][j][1]);
            // }
            chmin(dp[i][j][0], mdp[i][j]);

            //cout << i << ", " << j << ": " << make_pair(dp[i][j][0], dp[i][j][1]) << endl;

            push(i, j);
        }
    }

    REP2(k, 1, N+1) {
        cout << min(dp[N][k][0], dp[N][k][1]) << endl;
    }
}
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