Submission #73069

#	Time	Username	Problem	Language	Result	Execution time	Memory
73069		polyfish	Split the sequence (APIO14_sequence)	C++14	22 / 100	1794 ms	88468 KiB

sequence

//I love armpit fetish
 
#include <bits/stdc++.h>
using namespace std;
 
#define debug(x) cerr << #x << " = " << x << '\n';
#define BP() cerr << "OK!\n";
#define PR(A, n) {cerr << #A << " = "; for (int _=1; _<=n; ++_) cerr << A[_] << ' '; cerr << '\n';}
#define PR0(A, n) {cerr << #A << " = "; for (int _=0; _<n; ++_) cerr << A[_] << ' '; cerr << '\n';}
#define FILE_NAME "data"
 
typedef pair<int64_t, int64_t> line;
 
const int MAX_N = 100007;
const int MAX_K = 107;
const int64_t INF = 1e9;
 
int n, k, a[MAX_N];
int64_t ps[MAX_N], f[MAX_N][MAX_K];
 
struct convex_hull {
    vector<line> d;
    int head;
 
    void reset() {
        d.clear();
        head = 0;
    }
 
    convex_hull() {
        reset();
    }
 
    bool bad(line l1, line l2, line l3) {
        return (l1.second - l3.second) * (l2.first - l1.first)
                <= (l1.second - l2.second) * (l3.first - l1.first);
    }
 
    void add_line(int64_t a, int64_t b) {
        d.push_back(line(a, b));
        while (d.size()>2 && bad(d[d.size()-3], d[d.size()-2], d.back()))
            d.erase(d.end() - 2);
    }
 
    int64_t get(int64_t x) {
        if (d.size()==0)
            return -INF;
        head = min(head, (int)d.size()-1);
        while (head+1<d.size() && d[head].first * x + d[head].second
                                < d[head+1].first * x + d[head+1].second)
            ++head;
        return d[head].first * x + d[head].second;
    }
};
 
void enter() {
    cin >> n >> k;
    ++k;
    for (int i=1; i<=n; ++i) {
        cin >> a[i];
        ps[i] = ps[i-1] + a[i];
    }
}
 
void trace(int pos, int nPart) {
    if (pos==0)
        return;
    for (int i=pos-1; i>=0; --i) {
        if (f[pos][nPart] == f[i][nPart-1] + ps[i] * (ps[pos] - ps[i])) {
            trace(i, nPart-1);
            break;
        }
    }
    if (pos!=n)
        cout << pos << ' ';
}
 
void dp() {
    f[0][0] = 0;
    convex_hull CH;
    for (int i=1; i<=k; ++i)
        f[0][i] = -INF;
    for (int i=1; i<=n; ++i)
        f[i][0] = -INF;
    for (int j=1; j<=k; ++j) {
        CH.reset();
        if (f[0][j-1]!=-INF)
            CH.add_line(ps[0], f[0][j-1] - 1LL * ps[0] * ps[0]);
        for (int i=1; i<=n; ++i) {
            f[i][j] = max(-INF, CH.get(ps[i]));
            // if (i==6 && j==7) {
            //     cerr << ps[i] << ' ' << f[i][j-1] - 1LL * ps[i] * ps[i] << '\n';
            // }
            // if (i==7 && j==7) {
            //     //cerr << CH.d[4].first << ' ' << CH.d[4].second << '\n';
            //     debug(CH.d[4].first * ps[7] + CH.d[4].second);
            //     debug(CH.d[5].first * ps[7] + CH.d[5].second);
            // }
            if (f[i][j-1]!=-INF)
                CH.add_line(ps[i], f[i][j-1] - 1LL * ps[i] * ps[i]);
        }
    }
    cout << f[n][k] << '\n';
    //debug(f[7][7]);
    trace(n, k);
}
 
int main() {
	#ifdef OFFLINE_JUDGE
		freopen(FILE_NAME".inp", "r", stdin);
		freopen(FILE_NAME".out", "w", stdout);
	#endif
	ios::sync_with_stdio(0); cin.tie(0);
	enter();
	dp();
}

Compilation message (stderr)

sequence.cpp: In member function 'int64_t convex_hull::get(int64_t)':
sequence.cpp:49:22: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         while (head+1<d.size() && d[head].first * x + d[head].second
                ~~~~~~^~~~~~~~~

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 0 / 11
• Subtask 4: 0 / 17
• Subtask 5: 0 / 21
• Subtask 6: 0 / 29