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Submission #329227

# Submission time Handle Problem Language Result Execution time Memory
329227 2020-11-19T23:46:32 Z jovan_b Split the sequence (APIO14_sequence) C++17
28 / 100
 142 ms 106916 KB 
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

ll pre[100005];
ll a[100005];
ll dp[100005];
ll dpp[100005];
int prosli[100005][205];

struct line{
    ll a, b;
    int ind;
    ll eval(ll x){
        return a*x+b;
    }
};

line seg[400005];

void upd(int node, int l, int r, line g){
    int mid = (l+r)/2;
    if(g.eval(pre[l]) >= seg[node].eval(pre[l]) && g.eval(pre[r]) >= seg[node].eval(pre[r])){
        seg[node] = g;
        return;
    }
    if(g.eval(pre[l]) >= seg[node].eval(pre[l]) || g.eval(pre[mid]) >= seg[node].eval(pre[mid])) upd(node*2, l, mid, g);
    if(g.eval(pre[r]) >= seg[node].eval(pre[r]) || g.eval(pre[mid+1]) >= seg[node].eval(pre[mid+1])) upd(node*2+1, mid+1, r, g);
}

pair <int, ll> query(int node, int l, int r, int x){
    pair <int, ll> res1 = {seg[node].ind, seg[node].eval(pre[x])};
    if(l == r) return res1;
    int mid = (l+r)/2;
    pair <int, ll> res2;
    if(x <= mid) res2 = query(node*2, l, mid, x);
    else res2 = query(node*2+1, mid+1, r, x);
    if(res1.second >= res2.second) return res1;
    else return res2;
}

void init(int node, int l, int r){
    if(l == r){
        seg[node].a = 0;
        seg[node].b = -1000000000000000LL;
        return;
    }
    int mid = (l+r)/2;
    init(node*2, l, mid);
    init(node*2+1, mid+1, r);
}

int main(){
    ios_base::sync_with_stdio(false), cin.tie(0);

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

    for(int j=1; j<=k; j++){
        init(1, 1, n);
        for(int i=1; i<=n; i++){
            pair <int, ll> d = query(1, 1, n, i);
            dp[i] = d.second;
            prosli[i][j] = d.first;
            line nline;
            nline.a = pre[i];
            nline.b = -pre[i]*pre[i] + dpp[i];
            nline.ind = i;
            upd(1, 1, n, nline);
        }
        for(int i=1; i<=n; i++){
            dpp[i] = dp[i];
        }
    }
    cout << dp[n] << "\n";
    int t = n;
    for(int i=k; i>=1; i--){
        cout << prosli[t][i] << " ";
        t = prosli[t][i];
    }
    return 0;
}

/*
7 3
4 1 3 4 0 2 3
*/

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 492 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 364 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 364 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 364 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 364 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 384 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 364 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 492 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 364 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 364 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 364 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 364 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 364 KB contestant found the optimal answer: 140072 == 140072
14 Correct 1 ms 364 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 364 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 400 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 364 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 364 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 364 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 364 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 364 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Runtime error 7 ms 1516 KB Execution killed with signal 11 (could be triggered by violating memory limits)
6 Halted 0 ms 0 KB -

Subtask #3
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 492 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 492 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 9 ms 620 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 492 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Runtime error 7 ms 1132 KB Execution killed with signal 11 (could be triggered by violating memory limits)
6 Halted 0 ms 0 KB -

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1260 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 2 ms 1260 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 60 ms 1388 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 1260 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 80 ms 1388 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 54 ms 1388 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 62 ms 1644 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 58 ms 1388 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 13 ms 1388 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 25 ms 1388 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
0 / 21.0

# Verdict Execution time Memory Grader output
1 Runtime error 21 ms 14828 KB Execution killed with signal 11 (could be triggered by violating memory limits)
2 Halted 0 ms 0 KB -

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Runtime error 142 ms 106916 KB Execution killed with signal 11 (could be triggered by violating memory limits)
2 Halted 0 ms 0 KB -