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답안 #922840

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
922840 2024-02-06T07:49:19 Z thangdz2k7 수열 (APIO14_sequence) C++17
100 / 100
 535 ms 83636 KB 
#include <bits/stdc++.h>
#define ll long long
#define line pair <ll, ll>
#define Point pair <double, double>
#define A first
#define B second
#define pb push_back

using namespace std;

const int N = 1e5 + 5;
const ll inf = 1e18;

int n, k, t;
int a[N], best[205][N];
ll dp[2][N], pre[N];

vector <int> idx;

Point giao(line l1, line l2){
    Point ans;
    double del = double (l1.A) - double(l2.A);
    ans.A = double (l2.B - l1.B) / del;
    ans.B = double (ans.A) + double(l1.B) / double(l1.A);
    return ans;
}

void add(int id){
    if (idx.empty()){
        idx.pb(id);
        return;
    }
    if (pre[id] == pre[idx.back()]) return;

    while (true){
        int sz = idx.size();
        if (sz <= 1) break;
        int id2 = idx[sz - 1];
        int id3 = idx[sz - 2];
        line l2 = line(pre[id2], dp[1 ^ t][id2] - pre[id2] * pre[id2]);
        line l3 = line(pre[id3], dp[1 ^ t][id3] - pre[id3] * pre[id3]);
        line p = line(pre[id], dp[1 ^ t][id] - pre[id] * pre[id]);
        Point k = giao(p, l3);
        if (k.A / double(p.A) > (k.B - double(l2.B) / double(p.A)) / double(l2.A)) break;
        idx.pop_back();

    }
    idx.pb(id);

}

int get(int &cur, int i){
    int sz = idx.size();
    cur = min(cur, sz - 1);
    int id = idx[cur];
    line p = line(pre[id], dp[1 ^ t][id] - pre[id] * pre[id]);
    dp[t][i] = p.A * pre[i] + p.B;
    while (cur < sz - 1){
        id = idx[cur + 1];
        p = line(pre[id], dp[1 ^ t][id] - pre[id] * pre[id]);
        ll val = p.A * pre[i] + p.B;
        if (dp[t][i] < val){
            dp[t][i] = val;
            ++ cur;
        }
        else return idx[cur];
    }
    return idx[cur];
}

void solve(){
    cin >> n >> k;
    for (int i = 1; i <= n; ++ i){
        cin >> a[i];
        pre[i] = pre[i - 1] + a[i];
    }

    for (int loops = 1; loops <= k; ++ loops){
        idx.clear();
        t = loops & 1;
        int cur = 0;
        for (int i = 1; i <= n; ++ i){
            if (i == loops){
                add(i);
                best[loops][i] = i;
            }
            if (i > loops){
                dp[t][i] = inf;
                best[loops][i] = get(cur, i);
                add(i);
                //cout << loops << ' ' << i << ' ' << dp[t][i] << endl;
            }
        }
    }

    //cout << inf * inf;

    ll ans = dp[k & 1][n];
    cout << ans << '\n';
    int cur = n;
    for (int i = k; i >= 1; -- i){
        cur = best[i][cur];
        cout << cur << ' ';
    }
}

signed main(){
    //freopen("split.inp", "r", stdin);
    //freopen("split.out", "w", stdout);
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    solve();
    return 0;
}

Subtask #1
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 4444 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 4444 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 4568 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 6492 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 6744 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 4444 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 4444 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 4444 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 4440 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 4444 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 4444 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 4444 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 4444 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 4444 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 4444 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 4444 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 4440 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 4444 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 4444 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 4 ms 22876 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 4444 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 6492 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 6488 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 12636 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 8540 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 6492 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 8536 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 4444 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 4444 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 19 ms 82448 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 4444 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 8 ms 57692 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 9 ms 74188 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 11 ms 82492 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 3 ms 20828 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 2 ms 14880 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 4 ms 24920 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 4444 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 4444 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 14 ms 82524 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 4444 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 14 ms 82532 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 12 ms 70236 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 14 ms 82524 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 14 ms 82524 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 18780 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 7 ms 35164 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# 결과 실행 시간 메모리 Grader output
1 Correct 2 ms 4700 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 4700 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 62 ms 82680 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 2 ms 4700 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 38 ms 49864 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 44 ms 58196 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 48 ms 62032 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 39 ms 51904 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 39 ms 58100 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 50 ms 74424 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# 결과 실행 시간 메모리 Grader output
1 Correct 12 ms 5596 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 12 ms 5600 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 420 ms 83636 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 18 ms 5856 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 535 ms 83504 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 345 ms 58908 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 428 ms 63192 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 307 ms 52764 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 331 ms 59108 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 417 ms 75280 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845