結果

問題 No.913 木の燃やし方
ユーザー square1001
提出日時 2020-02-13 22:31:58
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 312 ms / 3,000 ms
コード長 2,681 bytes
コンパイル時間 1,110 ms
コンパイル使用メモリ 87,940 KB
実行使用メモリ 18,040 KB
最終ジャッジ日時 2024-10-06 06:33:50
合計ジャッジ時間 13,261 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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 * 34
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 #
プレゼンテーションモードにする

#include <set>
#include <deque>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
const long long inf = 1LL << 62;
vector<long long> subsolve(int N, vector<long long> A) {
    A.insert(A.begin(), 0);
    for (int i = 0; i < N; ++i) {
        A[i + 1] += A[i];
    }
    // minimize (A[i] - A[j]) + (i - j)^2 = (A[i] + i * i) + (-A[j] + j * j) - 2 * j * i for each i
    vector<long long> intercept(N + 1), slope(N + 1);
    for (int i = 0; i <= N; ++i) {
        intercept[i] = -A[i] + 1LL * i * i;
        slope[i] = -2 * i;
    }
    int mid = N / 2 + 1;
    vector<long long> seq(N, inf);
    deque<int> que;
    for (int i = 0; i < mid; ++i) {
        while (que.size() >= 2) {
            int pa = que[que.size() - 2];
            int pb = que[que.size() - 1];
            __int128 cra = __int128(intercept[pa] - intercept[i]) * (i - pb);
            __int128 crb = __int128(intercept[pb] - intercept[i]) * (i - pa);
            if (cra < crb) que.pop_back();
            else break;
        }
        que.push_back(i);
        while (que.size() >= 2) {
            int pa = que[0];
            int pb = que[1];
            long long va = 1LL * slope[pa] * (i + 1) + intercept[pa];
            long long vb = 1LL * slope[pb] * (i + 1) + intercept[pb];
            if (va > vb) que.pop_front();
            else break;
        }
    }
    for (int i = mid; i <= N; ++i) {
        seq[i - 1] = que[0];
        while (que.size() >= 2) {
            int pa = que[0];
            int pb = que[1];
            long long va = 1LL * slope[pa] * (i + 1) + intercept[pa];
            long long vb = 1LL * slope[pb] * (i + 1) + intercept[pb];
            if (va > vb) que.pop_front();
            else break;
        }
    }
    for (int i = 0; i < N; ++i) {
        if (seq[i] != inf) {
            seq[i] = A[i + 1] - A[seq[i]] + 1LL * (i + 1 - seq[i]) * (i + 1 - seq[i]);
        }
    }
    for (int i = N - 2; i >= mid - 1; --i) {
        seq[i] = min(seq[i], seq[i + 1]);
    }
    return seq;
}
vector<long long> solve(int N, vector<long long> A) {
    if (N == 1) return vector<long long>({ A[0] + 1 });
    int mid = N / 2;
    vector<long long> res1 = subsolve(N, A);
    reverse(A.begin(), A.end());
    vector<long long> res2 = subsolve(N, A);
    reverse(res2.begin(), res2.end());
    for (int i = 0; i < N; ++i) {
        res1[i] = min(res1[i], res2[i]);
    }
    reverse(A.begin(), A.end());
    vector<long long> res3 = solve(mid, vector<long long>(A.begin(), A.begin() + mid));
    vector<long long> res4 = solve(N - mid, vector<long long>(A.begin() + mid, A.end()));
    for (int i = 0; i < mid; ++i) {
        res1[i] = min(res1[i], res3[i]);
    }
    for (int i = mid; i < N; ++i) {
        res1[i] = min(res1[i], res4[i - mid]);
    }
    return res1;
}
int main() {
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    int N;
    cin >> N;
    vector<long long> A(N);
    for (int i = 0; i < N; ++i) cin >> A[i];
    vector<long long> ans = solve(N, A);
    for (int i = 0; i < N; ++i) {
        cout << ans[i] << '\n';
    }
    return 0;
}
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