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Submission #131240

# Submission time Handle Problem Language Result Execution time Memory
131240 2019-07-16T20:49:01 Z Minnakhmetov Split the sequence (APIO14_sequence) C++14
100 / 100
 1314 ms 85624 KB 
#include<bits/stdc++.h>
using namespace std;

#define ll long long
#define all(aaa) aaa.begin(), aaa.end()

const ll INF = 1e18;
const int N = 1e5 + 5, K = 205;
ll dp[2][N], a[N], p[N];
int anc[K][N];

struct Line {
    ll k, b;

    int pos;

    bool q = false;
    double lx;

    bool operator < (const Line &oth) const {
        if (q)
            return k < oth.lx;
        if (oth.q)
            return lx < oth.k;
        return k > oth.k;
    }
};

struct CHT : vector<Line> {
    bool bad(iterator y) {
        iterator x, z;

        if (y != begin()) {
            x = prev(y);
            if (x->k == y->k)
                return x->b <= y->b;
        }
        if (next(y) != end()) {
            z = next(y);
            if (y->k == z->k)
                return y->k > z->k;
        }

        if (y == begin() || next(y) == end())
            return false;

        return (x->b - y->b) * 1.0 * (z->k - y->k) >= 
            (y->b - z->b) * 1.0 * (y->k - x->k);
    }

    void calcLx(iterator y) {
        if (y == begin()) {
            y->lx = -INF;
        }
        else {
            auto x = prev(y);
            y->lx = (x->b - y->b) / (double)(y->k - x->k);
        }
    }

    void add(Line a) {
        push_back(a);
        if (bad(prev(end()))) {
            pop_back();
            return;
        }
        while (size() > 1 && bad(end() - 2)) {
            erase(end() - 2);
        }
        calcLx(prev(end()));
    }

    int que(ll x) {
        auto it = upper_bound(begin(), end(), Line{x, -1, -1, 1});
        it--;
        return it->pos;
    }
} cht;

signed main() {
#ifdef HOME
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    int n, k;
    cin >> n >> k;

    for (int i = 0; i < n; i++) {
        cin >> a[i];
        p[i + 1] = a[i] + p[i];
    }

    k++;

    for (int i = 1; i <= n; i++) {
        dp[1][i] = p[i] * p[i];
    }

    for (int i = 2; i <= k; i++) {
        cht.clear();
        for (int j = i; j <= n; j++) {
            cht.add({-2 * p[j - 1], dp[(i & 1) ^ 1][j - 1] + p[j - 1] * p[j - 1], j - 1});

            int x = cht.que(p[j]);

            dp[i & 1][j] = dp[(i & 1) ^ 1][x] + (p[j] - p[x]) * (p[j] - p[x]);
            anc[i][j] = x;
        }
    }

    cout << p[n] * (p[n] - 1) / 2 - (dp[k & 1][n] - p[n]) / 2 << "\n";

    vector<int> v;
    while (anc[k][n] > 0) {
        n = anc[k][n];
        v.push_back(n);
        k--;
    }

    reverse(all(v));

    for (int i : v)
        cout << i << " ";

    return 0;
}

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB contestant found the optimal answer: 108 == 108
2 Correct 2 ms 376 KB contestant found the optimal answer: 999 == 999
3 Correct 2 ms 376 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 376 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 2 ms 376 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
7 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
8 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
9 Correct 2 ms 376 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 3 ms 376 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 2 ms 376 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 2 ms 376 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 2 ms 376 KB contestant found the optimal answer: 140072 == 140072
14 Correct 2 ms 376 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 376 KB contestant found the optimal answer: 805 == 805
16 Correct 2 ms 376 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 2 ms 376 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 2 ms 376 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 2 ms 636 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 2 ms 376 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 3 ms 376 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 2 ms 376 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 504 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 504 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 376 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 504 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 2 ms 376 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 4 ms 1400 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 2 ms 376 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 4 ms 1080 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 5 ms 1272 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 4 ms 1400 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 2 ms 632 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 2 ms 504 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 3 ms 632 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 504 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 2 ms 632 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 11 ms 2168 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 504 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 11 ms 2040 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 10 ms 1912 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 12 ms 2112 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 12 ms 2040 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 4 ms 760 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 6 ms 1144 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 1140 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 5 ms 1272 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 104 ms 9832 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 5 ms 1400 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 70 ms 6264 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 93 ms 7160 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 87 ms 7668 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 80 ms 6512 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 79 ms 7284 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 100 ms 8948 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 34 ms 7912 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 35 ms 7972 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1161 ms 85624 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 35 ms 8416 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1314 ms 84612 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 1127 ms 61152 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1053 ms 66076 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 950 ms 54880 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 875 ms 61628 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1111 ms 77372 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845