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Submission #999499

# Submission time Handle Problem Language Result Execution time Memory
999499 2024-06-15T16:04:25 Z fryingduc Split the sequence (APIO14_sequence) C++17
49 / 100
 864 ms 131072 KB 
#include "bits/stdc++.h"
using namespace std;

const int maxn = 1e5 + 5;
const long long inf = 1e16;
int n, a[maxn], k;
long long ps[maxn];
long long pref[maxn];
long long f[maxn], g[maxn];
int trace[maxn][205];

long long cost(int l, int r) {
    return (1ll * (ps[r] - ps[l - 1]) * (ps[r] - ps[l - 1]) - (pref[r] - pref[l - 1])) / 2;
}
void calc(int k, int l, int r, int optl, int optr) {
    if(l > r) return;
    long long res = inf;
    int pos = -1;
    int mid = (l + r) / 2;
    for(int i = optl; i <= min(mid, optr); ++i) {
        if(g[i - 1] + cost(i, mid) < res) {
            res = g[i - 1] + cost(i, mid);
            pos = i;
        }
    }
    f[mid] = res;
    trace[mid][k] = pos;
    calc(k, l, mid - 1, optl, pos);
    calc(k, mid + 1, r, pos, optr);
}
void solve() {
    cin >> n >> k;
    for(int i = 1; i <= n; ++i) {
        cin >> a[i];
        pref[i] = pref[i - 1] + a[i] * a[i];
        ps[i] = ps[i - 1] + a[i];
    }
    for(int i = 1; i <= n; ++i) {
        g[i] = cost(1, i);
    }
    for(int i = 2; i <= k + 1; ++i) {
        calc(i, 1, n, 1, n);
        for(int j = 1; j <= n; ++j) {
            g[j] = f[j];
            f[j] = 0;
        }
    }
    
    cout << cost(1, n) - g[n] << '\n';
    vector<int> vec;
    ++k;
    while(k > 1) {
        vec.push_back(trace[n][k] - 1);
        n = trace[n][k] - 1;
        --k;
    }
    reverse(vec.begin(), vec.end());
    for(auto i:vec) cout << i << " ";
}
signed main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    
    solve();
    return 0;
}

Subtask #1
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 348 KB contestant found the optimal answer: 999 == 999
3 Incorrect 0 ms 348 KB Integer 0 violates the range [1, 1]
4 Halted 0 ms 0 KB -

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 348 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 0 ms 348 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 348 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 348 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 348 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 600 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 348 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 348 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 348 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 604 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 604 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 604 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 604 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 604 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Runtime error 3 ms 860 KB Execution killed with signal 11
7 Halted 0 ms 0 KB -

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 2652 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 4 ms 2652 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 2652 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 5 ms 2756 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 4 ms 2652 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 5 ms 2760 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 4 ms 2652 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 2648 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 4 ms 2600 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 9052 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 9052 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 47 ms 9052 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 9052 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 54 ms 9224 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 50 ms 9052 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 48 ms 9048 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 33 ms 9048 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 45 ms 9048 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 58 ms 9052 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 27 ms 84060 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 29 ms 84064 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Runtime error 864 ms 131072 KB Execution killed with signal 9
4 Halted 0 ms 0 KB -