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Submission #1000734

# Submission time Handle Problem Language Result Execution time Memory
1000734 2024-06-18T07:53:50 Z vjudge1 Split the sequence (APIO14_sequence) C++17
39 / 100
 956 ms 93888 KB 
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int  N = 1e5 + 30, MOD = 1e9 + 7;
int n,k;
int a[N];
ll pref[N],sf[N];
int p[N][203];
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;
        }
    }
    return {st[r].get(x),st[r].pos};
}
set<int> St;
void test(){
    cin >> n >> k;
    for(int i = 1;i <= n;i++){
        cin >> a[i];
        St.insert(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});
        int it = 1;
        for(int j = 1;j <= n;j++){
            while(it >= 0 && (it == (int)st.size() - 1 || (st[it].b - st[it + 1].b) * 1.0 >= sf[j + 1] * 1.0 * (st[it + 1].k - st[it].k))){
                it--;
            }
            pair<ll,ll> G = {st[it + 1].get(sf[j + 1]),st[it + 1].pos};
            dp[j] = G.first+ pref[j] * sf[j + 1];
            p[j][i] = G.second;
            if(!p[j][i] && i != 1){
                p[j][i] = j - 1;
            }
            line nv = {-pref[j],tdp[j],j};
            add(st,nv);
            it = min(it,(int)st.size() - 1);
            it+=5;
            it = min(it,(int)st.size() - 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(ps){
        f.push_back(ps);
        St.erase(ps);
        ps = p[ps][k--];
    }
    for(int i = 1;i <= n - 1;i++){
        if(St.find(i) != St.end()&&(int)f.size() < k1){
            f.push_back(i);
        }
    }
    sort(f.begin(),f.end());
    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
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 2396 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 2396 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 2396 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 2396 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 2396 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 2396 KB contestant found the optimal answer: 1 == 1
9 Correct 0 ms 2396 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 2396 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 2652 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 2396 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 2396 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 2396 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 2396 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 2396 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 2396 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 2648 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 2396 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 2396 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 2396 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 2392 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 2396 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 0 ms 2396 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 2392 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 2396 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
0 / 11.0

# Verdict Execution time Memory Grader output
1 Incorrect 1 ms 2396 KB contestant didn't find the optimal answer: 412301079 < 610590000
2 Halted 0 ms 0 KB -

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4696 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 4696 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 6 ms 4700 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 4700 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 7 ms 4700 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 6 ms 4700 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 4716 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 5 ms 4700 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 4700 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 4700 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
0 / 21.0

# Verdict Execution time Memory Grader output
1 Incorrect 4 ms 11876 KB contestant didn't find the optimal answer: 1594033848 < 1818678304
2 Halted 0 ms 0 KB -

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 50 ms 92824 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 45 ms 92784 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 768 ms 93888 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 45 ms 93576 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Incorrect 956 ms 93056 KB contestant didn't find the optimal answer: 36173624234 < 36183271951
6 Halted 0 ms 0 KB -