Submission #1085084

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
1085084	2024-09-07T13:31:16 Z	ZeroCool	Split the sequence (APIO14_sequence)	C++14	33 / 100	57 ms	131072 KB

sequence

#include <bits/stdc++.h>
using namespace std;
//#define int long long
#define ll long long
#define ld long double
#define ar array

const int LOG = 20;
const int MOD = 1e9 + 7;
const ll INF = 1e18;

const int N = 1e5 + 20;
struct LINE {
    ll a, b, id ;
 
    LINE (ll a, ll b, ll id ) : a(a), b(b), id(id) {}
 
    ll operator() (const ll &x) {
        return a * x + b;
    }
};
 
struct convex_hull_trick {
    vector<LINE> op;
    void init () {
        vector<LINE> ().swap(op);
    }
    bool bad (LINE ln1, LINE ln2, LINE ln3) {
        __int128 hi = 1;
        return hi * (ln3.b - ln1.b) * (ln1.a - ln2.a) <= hi * (ln2.b - ln1.b) * (ln1.a - ln3.a);
    }
 
    void add (LINE ln) {
        while (op.size() >= 2 && bad(op[op.size() - 2], op[op.size() - 1], ln)) {
            op.pop_back();
        }
        op.push_back(ln);
    }
 
    ar<ll,2> get (int x) {
        if (op.empty()) return ar<ll,2>{INF, -1l};
        int lf = 0, rt = op.size() - 1;
        while (lf < rt) {
            int mid = (lf + rt) >> 1;
            if (op[mid](x) <= op[mid + 1](x)) rt = mid;
            else lf = mid + 1;
        }
        return ar<ll,2>{op[lf](x), op[lf].id};
 
    }
}CHT;

ll pref[N];
ll dp[N][202];
int prv[N][202];
ll A[N];

signed main() {
    int n, k;
    cin>>n>>k;
   // ll A[n];
    for(int i = 0;i < n;i++)cin>>A[i];
    //ll pref[n];
    //int prv[k][n];
    pref[0] = A[0];
    for(int i= 1;i < n;i++)pref[i] = pref[i - 1] + A[i];
    //ll dp[n][k + 1];
    for(int i = 0;i < n;i++)dp[i][0] = 0;

    for(int j = 1;j < k;j++){
        CHT.init();
        for(int i = 0;i < n;i++){
            ar<ll, 2> c = CHT.get(pref[i]);
            dp[i][j] = -c[0];
            prv[j][i] = c[1]; 
            CHT.add(LINE{-pref[i], -(dp[i][j - 1] - pref[i] * pref[i]), i});
        }
    }
    for(int j = 1;j < k;j++){
        for(int i = 1;i < n;i++){
            //cout<<prv[j][i]<<" ";
        }
            //cout<<'\n';
    }
    ll res = -1;
    int opt = -1;
    for(int i = 0;i < n;i++){
        if(res < dp[i][k - 1] + (pref[n - 1] - pref[i]) * pref[i]){
            res = dp[i][k - 1] + (pref[n - 1] - pref[i]) * pref[i];
            opt = i;

        }
    }
    cout<<res<<'\n';
    vector<int> ans;
    for(int j = k - 1;j >= 0;j--){
        ans.push_back(opt);
        opt = prv[j][opt];
    }
    for(auto u:ans)cout<<u + 1<<" ";
}

Subtask #1
11.0 / 11.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	344 KB	contestant found the optimal answer: 108 == 108
2	Correct	0 ms	344 KB	contestant found the optimal answer: 999 == 999
3	Correct	0 ms	348 KB	contestant found the optimal answer: 0 == 0
4	Correct	1 ms	348 KB	contestant found the optimal answer: 1542524 == 1542524
5	Correct	0 ms	348 KB	contestant found the optimal answer: 4500000000 == 4500000000
6	Correct	1 ms	348 KB	contestant found the optimal answer: 1 == 1
7	Correct	1 ms	348 KB	contestant found the optimal answer: 1 == 1
8	Correct	0 ms	348 KB	contestant found the optimal answer: 1 == 1
9	Correct	0 ms	348 KB	contestant found the optimal answer: 100400096 == 100400096
10	Correct	0 ms	348 KB	contestant found the optimal answer: 900320000 == 900320000
11	Correct	0 ms	348 KB	contestant found the optimal answer: 3698080248 == 3698080248
12	Correct	0 ms	348 KB	contestant found the optimal answer: 3200320000 == 3200320000
13	Correct	0 ms	348 KB	contestant found the optimal answer: 140072 == 140072
14	Correct	0 ms	348 KB	contestant found the optimal answer: 376041456 == 376041456
15	Correct	0 ms	348 KB	contestant found the optimal answer: 805 == 805
16	Correct	0 ms	348 KB	contestant found the optimal answer: 900189994 == 900189994
17	Correct	0 ms	348 KB	contestant found the optimal answer: 999919994 == 999919994

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	1 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	1 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	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
11.0 / 11.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	1 ms	604 KB	contestant found the optimal answer: 610590000 == 610590000
2	Correct	1 ms	604 KB	contestant found the optimal answer: 311760000 == 311760000
3	Correct	1 ms	860 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	860 KB	contestant found the optimal answer: 1019625819 == 1019625819
6	Correct	1 ms	860 KB	contestant found the optimal answer: 107630884 == 107630884
7	Correct	2 ms	920 KB	contestant found the optimal answer: 475357671774 == 475357671774
8	Correct	1 ms	604 KB	contestant found the optimal answer: 193556962 == 193556962
9	Correct	1 ms	604 KB	contestant found the optimal answer: 482389919803 == 482389919803
10	Correct	1 ms	604 KB	contestant found the optimal answer: 490686959791 == 490686959791