Submission #546275

#	Time	Username	Problem	Language	Result	Execution time	Memory
546275		Jomnoi	Split the sequence (APIO14_sequence)	C++17	100 / 100	760 ms	81556 KiB

sequence

#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 (stderr)

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 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 21 / 21
• Subtask 6: 29 / 29