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Submission #1055198

# Submission time Handle Problem Language Result Execution time Memory
1055198 2024-08-12T15:18:37 Z underwaterkillerwhale Split the sequence (APIO14_sequence) C++17
78 / 100
 1661 ms 88460 KB 
#include <bits/stdc++.h>
#define ll long long
#define rep(i,m,n) for(int i=(m); i<=(n); i++)
#define reb(i,m,n) for(int i=(m); i>=(n); i--)
#define pii pair<int,int>
#define pll pair<ll,ll>
#define MP make_pair
#define fs first
#define se second
#define bit(msk, i) ((msk >> i) & 1)
#define iter(id, v) for(auto id : v)
#define pb push_back
#define SZ(v) (int)v.size()
#define ALL(v) v.begin(),v.end()

using namespace std;

mt19937_64 rd(chrono :: steady_clock :: now ().time_since_epoch().count());
ll Rand (ll l, ll r) { return uniform_int_distribution<ll> (l, r) (rd); }

const int N = 1e5 + 7;
const int Mod = 1e9 + 7;
const ll INF = 2e18;
const ll BASE = 137;
const int szBL = 320;

int n, K;
ll a[N];
ll dp[N][2];
int trace[202][N];
ll pre[N];

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) {
        return (long double)(ln3.b - ln1.b) / (ln1.a - ln3.a) <= (long double)(ln2.b - ln1.b) / (ln1.a - ln2.a);
    }

    void add (LINE ln) {
        while (SZ(op) >= 2 && bad(op[SZ(op) - 2], op[SZ(op) - 1], ln)) {
            op.pop_back();
        }
        op.push_back(ln);
    }

    pll get (ll x) {
        if (op.empty()) return MP(INF, 0);
        ll lf = 0, rt = SZ(op) - 1;
        while (lf < rt) {
            ll mid = (lf + rt) >> 1;
            if (op[mid](x) <= op[mid + 1](x)) rt = mid;
            else lf = mid + 1;
        }
        return MP(op[lf](x), op[lf].id);

    }
}cht;


void solution () {

    cin >> n >> K;
    rep (i, 1, n) cin >> a[i];
    rep (i, 1, n) pre[i] = pre[i - 1] + a[i];
    rep (i, 1, n) dp[i][1] = 0;
    rep (k, 2, K) {
        cht.init();
        rep (i, 1, n) {
            pll cur = cht.get(pre[i]);
            dp[i][k & 1] = -cur.fs;
            trace[k][i] = cur.se;
//            cout << i <<" "<<k<<" "<<cur.fs<<" "<<cur.se <<"\n";
//            if (dp[i][k & 1] != INF)
            cht.add(LINE(-pre[i], -(dp[i][k & 1 ^ 1] - pre[i] * pre[i]), i));
        }
    }
    ll res = 0;
    int opt = 0;
    rep (i, 1, n) {
        if (res < dp[i][K & 1] + (pre[n] - pre[i]) * pre[i]) {
            res = dp[i][K & 1] + (pre[n] - pre[i]) * pre[i];
            opt = i;
        }
    }
    vector<int> Ans;
    reb (k, K, 1) {
        Ans.push_back(opt);
        opt = trace[k][opt];
    }
    cout << res <<"\n";
    iter (&id, Ans) cout << id<<" ";
}

#define file(name) freopen(name".inp","r",stdin); \
freopen(name".out","w",stdout);
int main () {
//    file("TREEV");
    ios_base :: sync_with_stdio(false); cin.tie(0); cout.tie(0);
    int num_Test = 1;
//    cin >> num_Test;
    while (num_Test--)
        solution();
}
/*
no bug challenge +2
2 + 8 * 2 - 9
7 3
4 1 3 4 0 2 3

*/

Compilation message

sequence.cpp: In function 'void solution()':
sequence.cpp:87:45: warning: suggest parentheses around arithmetic in operand of '^' [-Wparentheses]
   87 |             cht.add(LINE(-pre[i], -(dp[i][k & 1 ^ 1] - pre[i] * pre[i]), i));
      |                                           ~~^~~

Subtask #1
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4444 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 4444 KB contestant found the optimal answer: 999 == 999
3 Incorrect 0 ms 2396 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 1 ms 4440 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 4444 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 2 ms 22876 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 4440 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 8540 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 6488 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 14680 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 8540 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 6492 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 8540 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 4696 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 4444 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 7 ms 80476 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 4444 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 5 ms 57692 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Incorrect 8 ms 74332 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 4444 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 4444 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 13 ms 80568 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 4444 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 14 ms 80504 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 12 ms 70232 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 13 ms 80476 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 13 ms 80420 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 18780 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 6 ms 35420 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 4960 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 4956 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 133 ms 81236 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 5228 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 77 ms 52132 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 84 ms 60312 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 100 ms 62736 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 82 ms 52340 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 96 ms 60584 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 121 ms 75056 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 21 ms 14200 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 21 ms 15012 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1487 ms 88140 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 25 ms 13984 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1661 ms 88460 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 957 ms 65064 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1201 ms 71304 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 984 ms 59836 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 1115 ms 67096 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1391 ms 82156 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845