oj.uz

Submission #1000680

# Submission time Handle Problem Language Result Execution time Memory
1000680 2024-06-18T07:10:18 Z vjudge1 Split the sequence (APIO14_sequence) C++17
49 / 100
 2000 ms 88488 KB 
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int  N = 1e5 + 30, MOD = 1e9 + 7;
int n,k;
ll a[N];
ll pref[N],sf[N];
int p[N][201];
ll dp[N],tdp[N];
struct line{
    ll k,b;
    int pos = 0;
    ll get(ll x){
        return k * x + b;
    }
};

long double cross(line a,line b){
    return ((a.b - b.b) * 1.0 / ((b.k - a.k) * 1.0));
}
void add(vector<line> &st,line l){
    while((int)st.size() > 1 && cross(l,st[(int)st.size() - 2]) <= cross(l,st.back())){
        st.pop_back();
    }
    st.push_back(l);
}
pair<ll,ll> get(vector<line> &st,ll x){
    int l = -1,r = (int)st.size() - 1;
    while(r - l > 1){
        int mid = (l + r) >> 1;
        if(mid == (int)st.size() - 1 || (st[mid].b - st[mid + 1].b) * 1.0 >= x * 1.0 * (st[mid + 1].k - st[mid].k)){
            r = mid;
        }else{
            l = mid;
        }
    }
    // ll ret =0 ,pos = 0;
    // for(int i = 0;i < (int)st.size();i++){
    //     if(st[i].get(x) > ret){
    //         ret = st[i].get(x);
    //         pos = st[i].pos;
    //     }
    // }
    // cout << x << ' ' << st[0].k << ' ' << st[1].k<< ' ' << r << "x\n";
    return {st[r].get(x),st[r].pos};
}
void test(){
    cin >> n >> k;
    for(int i = 1;i <= n;i++){
        cin >> a[i];
    }
    for(int i = 1;i <= n;i++){
        pref[i] = pref[i - 1] + a[i];
    }
    for(int i = n;i >= 1;i--){
        sf[i] = sf[i + 1] + a[i];
    }
    for(int i = 1;i <= k;i++){
        vector<line> st;
        add(st,{0,0});
        for(int j = 1;j <= n;j++){
            pair<ll,ll> G = get(st,sf[j + 1]);
            dp[j] = G.first+ pref[j] * sf[j + 1];
            p[j][i] = G.second;
            line nv = {-pref[j],tdp[j],j};
            add(st,nv);
            // for(int prev = 0;prev < j;prev++){
            //     dp[j] = max(dp[j],tdp[prev] + pref[j] * sf[j + 1] - pref[prev] * sf[j + 1]);
            // }
        }
        for(int j = 1;j <= n;j++){
            tdp[j] = dp[j];
            dp[j] =0 ;
        }
    }
    ll res = 0;
    int ps = 0;
    for(int i = 1;i <= n;i++){
        if(tdp[i] > res){
            res = tdp[i];
            ps = i;
        }
    }
    vector<int> f;
    cout << res << '\n';
    int k1 = k;
    while(k){
        f.push_back(ps);
        ps = p[ps][k--];
    }
    reverse(f.begin(),f.end());
    assert((int)f.size() == k1);
    for(int j:f){
        cout << j << ' ';
    }
}
int main() {
    ios_base::sync_with_stdio(false);cin.tie(0);
    int t = 1;
    // cin >> t;
    while(t--){
        test();
    }
}

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 2396 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 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 348 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 348 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 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 1 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 2 ms 604 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 604 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 2 ms 604 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Incorrect 2 ms 604 KB Integer 0 violates the range [1, 199]
7 Halted 0 ms 0 KB -

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1368 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 1112 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 14 ms 1364 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 1116 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 15 ms 1364 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 13 ms 1364 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 15 ms 1112 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 15 ms 3164 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 4 ms 1116 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 6 ms 1368 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 9056 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 6 ms 9052 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 230 ms 9388 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 6 ms 9324 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 136 ms 9132 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 153 ms 9076 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 181 ms 9368 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 140 ms 9368 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 167 ms 9344 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 212 ms 9436 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 64 ms 87844 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 61 ms 87916 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2090 ms 88488 KB Time limit exceeded
4 Halted 0 ms 0 KB -