oj.uz

Submission #767529

# Submission time Handle Problem Language Result Execution time Memory
767529 2023-06-26T20:11:36 Z jeroenodb Split the sequence (APIO14_sequence) C++14
71 / 100
 58 ms 131072 KB 
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define INF (int)1e18
#define double long double
#define f first
#define s second
 
mt19937_64 RNG(chrono::steady_clock::now().time_since_epoch().count());
 
struct line{
    int m, c, i;
};
 
int eval(int x, line a){
    return a.m * x + a.c;
}
 
//(c2 - c1) / (m1 - m2) 
 
bool useless(line a, line b, line c){
    // return intersect(a, c) >= intersect(b, c);
    return (a.c - c.c) * (c.m - b.m) <= (b.c - c.c) * (c.m - a.m);
}
 
void Solve() 
{
    int n, k; cin >> n >> k;
    vector <int> a(n + 1);
    int sum = 0;
    for (int i = 1; i <= n; i++){
        cin >> a[i];
        sum += a[i];
        a[i] += a[i - 1];
    }
    k++;
    
    vector<vector<int>> dp(n + 1, vector<int>(k + 1, INF));
    vector<vector<int32_t>> par(n + 1, vector<int32_t>(k + 1, -1));
    deque<line> dq[k + 2];
    dp[0][0] = 0;
    line ok;
    ok.m = 0; ok.c = 0; ok.i = 0;
    dq[0].push_back(ok);
    
    //dp[i][j] = dp[i1][j - 1] + a[i1] ^ 2 - 2 * a[i1] * a[i] + a[i] ^ 2
    for (int i = 1; i <= n; i++){
        for (int j = k; j >= 1; j--){
            // for (int i1 = 0; i1 < i; i1++){
            //     int val = dp[i1][j - 1] + (a[i] - a[i1]) * (a[i] - a[i1]);
            //     if (val < dp[i][j]){
            //         dp[i][j] = val;
            //         par[i][j] = i1;
            //     }
            // }
            
            if (dq[j - 1].size() == 0) continue;
            
            int x = a[i];
            while (dq[j - 1].size() > 1 && eval(x, dq[j - 1][0]) >= eval(x, dq[j - 1][1])) dq[j - 1].pop_front();
            dp[i][j] = eval(x, dq[j - 1][0]) + a[i] * a[i];
            par[i][j] = dq[j - 1][0].i;
            
            ok.m = - 2 * a[i];
            ok.c = dp[i][j] + a[i] * a[i];
            ok.i = i;
            while (dq[j].size() > 1 && useless(ok, dq[j].back(), dq[j][dq[j].size() - 2])) dq[j].pop_back();
            dq[j].push_back(ok);
        }
    }
    
    int ans = (sum * sum) - (dp[n][k]);
    ans /= 2;
    cout << ans << "\n";
    
    vector <int> go;
    int i = n;
    while (par[i][k] != 0){
        i = par[i][k];
        k--;
        go.push_back(i);
    }
    
    reverse(go.begin(), go.end());
    for (auto x : go) cout << x << " ";
    cout << "\n";
}
 
int32_t main() 
{
    auto begin = std::chrono::high_resolution_clock::now();
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int t = 1;
//    cin >> t;
    for(int i = 1; i <= t; i++) 
    {
        //cout << "Case #" << i << ": ";
        Solve();
    }
    auto end = std::chrono::high_resolution_clock::now();
    auto elapsed = std::chrono::duration_cast<std::chrono::nanoseconds>(end - begin);
    cerr << "Time measured: " << elapsed.count() * 1e-9 << " seconds.\n"; 
    return 0;
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 212 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 212 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 212 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 212 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 212 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 212 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 212 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 212 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 212 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 212 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 212 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 212 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 212 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 212 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 340 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 340 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 340 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 340 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 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 212 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

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 340 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 852 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 340 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 724 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 852 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 ms 980 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 468 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 340 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 468 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 468 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 468 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 6 ms 3028 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 468 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 5 ms 3028 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 5 ms 2644 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 3056 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 5 ms 3228 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 980 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 1492 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 2004 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 2132 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 57 ms 26412 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 2132 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 47 ms 16760 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 45 ms 18676 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 52 ms 20408 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 42 ms 17356 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 47 ms 19012 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 58 ms 23888 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 25 ms 17588 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 24 ms 17876 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Runtime error 55 ms 131072 KB Execution killed with signal 9
4 Halted 0 ms 0 KB -