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답안 #682959

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
682959 2023-01-17T11:29:56 Z kusssso 수열 (APIO14_sequence) C++17
71 / 100
 139 ms 131072 KB 
#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
const int N = 1e5 + 5;

struct line {
    ll A, B;
    bool operator < (const line &oth) const {
        return make_pair(A, B) < make_pair(oth.A, oth.B);
    }
    ld ins (line oth) {
        return 1.0 * (oth.B - B) / (A - oth.A);
    }
    ll yy (ll x) {
        return A * x + B;
    }
};

struct convex_hull { // finding maximum
    vector<line> hull;
    bool ok (line l1, line l2, line l3) {
        return l1.ins(l3) < l1.ins(l2);
    }
    void add (line d) {
        while (hull.size() >= 2 && ok(hull[hull.size() - 2], hull[hull.size() - 1], d)) hull.pop_back();
        while (!hull.empty() && hull.back().A == d.A) hull.pop_back(); // hull.back().B < d.B
        hull.push_back(d);
    }
    ll query (ll x) {
        int lo = 0, hi = (int) hull.size() - 2, p = 0;
        while (lo <= hi) {
           int mid = (lo + hi) / 2;
           if (hull[mid].ins(hull[mid + 1]) <= x) {
               p = mid + 1;
               lo = mid + 1;
           }
           else {
               hi = mid - 1;
           }
        }
        return hull[p].yy(x);
    }
} H;

int n, k, a[N];
ll f[N], dp[N][205];

signed main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    
    cin >> n >> k;
    for (int i = 1; i <= n; i++) {
        cin >> a[i];
        f[i] = f[i - 1] + a[i];
    }
    for (int i = 1; i <= n; i++) {
        dp[i][1] = f[i] * (f[n] - f[i]);
    }
    k++;
    for (int t = 2; t <= k; t++) {
        convex_hull H;
        for (int i = 1; i <= n; i++) {
            H.add({f[i - 1], dp[i - 1][t - 1] - f[i - 1] * f[n]});
            dp[i][t] = max(dp[i][t], H.query(f[i]) + f[i] * (f[n] - f[i]));
            // for (int j = 1; j <= i; j++) {
                // // dp[i][t] = max(dp[i][t], dp[j - 1][t - 1] + (f[i] - f[j - 1]) * (f[n] - f[i])); 
                // dp[i][t] = max(dp[i][t], f[j - 1] * f[i] + (dp[j - 1][t - 1] - f[j - 1] * f[n]) + f[i] * (f[n] - f[i]));
                // //                           A       x                             B
            // }
        }
    }
    cout << dp[n][k] << '\n';
    vector<int> res;
    int i = n;
    for (int t = k; t >= 2; t--) {
        for (int j = i; j >= 1; j--) {
            if (dp[i][t] == dp[j - 1][t - 1] + (f[i] - f[j - 1]) * (f[n] - f[i])) {
                i = j - 1;
                res.push_back(i);
                break;
            }
        }
    }
    reverse(res.begin(), res.end());
    for (auto &e : res) cout << e << ' ';
    
    return 0;
}

Subtask #1
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 340 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 340 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 336 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 340 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 340 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 340 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 340 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 340 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 340 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 340 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 324 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 340 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 340 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 340 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 340 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 340 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 328 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 324 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 340 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 328 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 340 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 340 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 340 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 340 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 340 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 340 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 596 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 596 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 2 ms 596 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 596 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 2 ms 596 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 2 ms 596 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 580 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 596 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 596 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 2 ms 596 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 1876 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 1876 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 9 ms 1876 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 1876 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 14 ms 2112 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 12 ms 1876 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 10 ms 1988 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 8 ms 1876 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 1876 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 5 ms 1988 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 10 ms 16664 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 9 ms 16728 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 125 ms 16968 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 12 ms 16948 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 85 ms 16832 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 104 ms 16800 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 139 ms 16968 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 113 ms 16956 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 105 ms 17012 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 121 ms 16944 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Runtime error 58 ms 131072 KB Execution killed with signal 9
2 Halted 0 ms 0 KB -