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Submission #546275

# Submission time Handle Problem Language Result Execution time Memory
546275 2022-04-07T03:13:10 Z Jomnoi Split the sequence (APIO14_sequence) C++17
100 / 100
 760 ms 81556 KB 
#include <bits/stdc++.h>
#define DEBUG 0
using namespace std;
 
const int MAX_N = 1e5 + 10;
const int MAX_K = 2e2 + 10;
const long long INF = 9e18 + 7;
 
int A[MAX_N], pre[MAX_N];
int parent[MAX_K][MAX_N];
long long dp[2][MAX_N];

long long divide(const long long &a, const long long &b) {
    return a / b - ((a ^ b) < 0 and a % b != 0);
}

class Line {
public :
    long long m, c;
    int idx;
    Line() {}
    Line(const long long &m_, const long long &c_, const int &i) : m(m_), c(c_), idx(i) {}

    long long dot(const long long &x) const {
        return m * x + c;
    }

    long long intersectX(const Line &o) const {
        return divide(o.c - c, m - o.m);
    }
};

class LineContainer {
private :
    deque <Line> hull;
public :
    void init() {
        hull.clear();
    }

    void addline(const Line &f) {
        if(!hull.empty() and hull.back().m == f.m and hull.back().c == f.c) {
            hull.pop_back();
        }
        while(hull.size() >= 2 and f.intersectX(hull.back()) <= hull.back().intersectX(hull[hull.size() - 2])) {
            hull.pop_back();
        }
        hull.push_back(f);
    }

    pair <long long, int> query(const long long &x) {
        while(hull.size() >= 2 and hull[0].dot(x) <= hull[1].dot(x)) {
            hull.pop_front();
        }
        return make_pair(hull[0].dot(x), hull[0].idx);
    }
}cht;

int main() {
    int N, K;
    scanf(" %d %d", &N, &K);
    for(int i = 1; i <= N; i++) {
        scanf(" %d", &A[i]);
        pre[i] = pre[i - 1] + A[i];
    }
 
    for(int i = 1; i < N; i++) {
        dp[1][i] = 1ll*(pre[N] - pre[i]) * pre[i];
    }
    for(int i = 2; i <= K; i++) {
        int now = i % 2, prv = now ^ 1;
        cht.init();
        for(int j = i; j < N; j++) {
            cht.addline(Line(pre[j - 1], 1ll*-pre[j - 1] * pre[N] + dp[prv][j - 1], j - 1));
            auto [res, idx] = cht.query(pre[j]);
            dp[now][j] = res + 1ll*pre[j] * pre[N] - 1ll*pre[j] * pre[j];
            parent[i][j] = idx;
        }   
    }
 
    long long ans = -INF;
    int pos = N;
    for(int i = K; i < N; i++) {
        if(ans < dp[K % 2][i]) {
            ans = dp[K % 2][i];
            pos = i;
        }
    }
 
    stack <int> stk;
    while(K > 0) {
        stk.emplace(pos);
        pos = parent[K--][pos];
    }
 
    printf("%lld\n", ans);
    while(!stk.empty()) {
        printf("%d ", stk.top());
        stk.pop();
    }
    return 0;
}

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:61:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   61 |     scanf(" %d %d", &N, &K);
      |     ~~~~~^~~~~~~~~~~~~~~~~~
sequence.cpp:63:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   63 |         scanf(" %d", &A[i]);
      |         ~~~~~^~~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 212 KB contestant found the optimal answer: 999 == 999
3 Correct 1 ms 212 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 340 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 340 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 212 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 212 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 1 ms 212 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 340 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 0 ms 340 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 0 ms 340 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 340 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 0 ms 340 KB contestant found the optimal answer: 805 == 805
16 Correct 0 ms 212 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 340 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 340 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 468 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 340 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 340 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 308 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 340 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 340 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 340 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 340 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 340 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 340 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 1236 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 464 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 980 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 2 ms 1108 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 2 ms 1236 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 436 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 468 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 596 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 340 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 9 ms 1876 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 340 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 7 ms 1876 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 7 ms 1552 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 8 ms 1784 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 5 ms 1876 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 596 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 3 ms 980 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 724 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 724 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 65 ms 9292 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 724 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 46 ms 5844 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 55 ms 6644 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 54 ms 7244 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 47 ms 5852 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 66 ms 6648 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 61 ms 8360 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 16 ms 4336 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 17 ms 4328 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 726 ms 81556 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 17 ms 4396 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 760 ms 81344 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 518 ms 57928 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 627 ms 62268 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 468 ms 51316 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 489 ms 58296 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 626 ms 73964 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845