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Submission #1055120

# Submission time Handle Problem Language Result Execution time Memory
1055120 2024-08-12T14:40:32 Z underwaterkillerwhale Split the sequence (APIO14_sequence) C++17
60 / 100
 2000 ms 81796 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 = 2e5 + 7;
const int Mod = 1e9 + 7;
const ll INF = 1e18;
const ll BASE = 137;
const int szBL = 320;

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

struct Line {
    #define ld long double
    ll a, b, id;
    ld rx;
    Line(ll aa = 0, ll bb = 0, ll _id = INF, ld _rx = INF) : a(aa), b(bb), id(_id), rx(_rx) {};
    ll eval(ll x) {
        return a * x + b;
    }
    ld isectx(const Line &other) {
        assert(a != other.a);
        return 1.0 * (other.b - b) / (a - other.a);
    }
    bool operator < (const Line &other) const {
        if (other.a != INF) return a < other.a;
        return rx < other.rx || (rx == other.rx && id < other.id);
    }
};

struct dynamicCHT {
    set<Line> hull;

    void init () {
        set<Line> ().swap(hull);
    }

    bool hasPrev(set<Line>::iterator it) { return it != hull.begin(); }
    bool hasNext(set<Line>::iterator it) { return it != hull.end() && next(it) != hull.end(); }

    bool bad(Line l1, Line l2, Line l3) {
        return l2.isectx(l3) <= l1.isectx(l2);
    }

    bool bad(set<Line>::iterator it) {
        return (hasPrev(it) && hasNext(it) && bad(*prev(it), *it, *next(it)));
    }

    void calcrx(set<Line>::iterator it) {
        Line l = *it;
        if (hasNext(it)) l.rx = l.isectx(*next(it));
        else l.rx = INF;
        hull.erase(it); hull.insert(l);
    }

    void insert_Line(Line newLine) {
        auto it = hull.lower_bound(newLine);
        if (it != hull.end() && it->a == newLine.a) {
            if (it->b > newLine.b) return;
            hull.erase(it);
        }
        it = hull.insert(newLine).first;
        if (bad(it)) {
            hull.erase(it);
            return;
        }
        while (hasPrev(it) && bad(prev(it))) hull.erase(prev(it));
        while (hasNext(it) && bad(next(it))) hull.erase(next(it));
        if (hasPrev(it)) calcrx(prev(it));
        calcrx(it);
    }

    pll get (ll x) {
        if (hull.empty())
            return MP(-INF, 0);
        Line it = *hull.lower_bound(Line(INF, 0, 0, x));
        return MP(it.eval(x), it.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;
            if (cur.fs < 1e16)
                trace[k][i] = cur.se;
//            cout << i <<" "<<k<<" "<<cur.fs<<" "<<cur.se <<"\n";
            cht.insert_Line(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:116:50: warning: suggest parentheses around arithmetic in operand of '^' [-Wparentheses]
  116 |             cht.insert_Line(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 0 ms 2392 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 2396 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 0 ms 2396 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 2396 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 0 ms 2396 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 0 ms 2396 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 2396 KB contestant found the optimal answer: 933702 == 933702
7 Correct 0 ms 2396 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 2396 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 2396 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 2396 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2396 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 2396 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 9 ms 3932 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 2396 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 10 ms 3616 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 8 ms 3792 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 9 ms 3928 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 2 ms 2652 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 2 ms 2652 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 3 ms 2908 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 2652 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 2652 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 57 ms 10416 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 2652 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 84 ms 10344 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 42 ms 9300 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 52 ms 10468 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 51 ms 10324 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 11 ms 3932 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 29 ms 5544 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 4188 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 6 ms 3792 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 746 ms 81796 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 9 ms 4188 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 454 ms 49976 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 469 ms 57600 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 549 ms 62032 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 491 ms 50992 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 515 ms 57972 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 672 ms 73800 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 84 ms 21676 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 79 ms 21388 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2101 ms 38556 KB Time limit exceeded
4 Halted 0 ms 0 KB -