Submission #33781

#	Time	Username	Problem	Language	Result	Execution time	Memory
33781		ztrong	Split the sequence (APIO14_sequence)	C++14	71 / 100	2000 ms	86944 KiB

sequence

#include <bits/stdc++.h>
using namespace std;

#define llint long long

void openFile() {
    ios_base :: sync_with_stdio(false);
    cin.tie(NULL);
#ifdef Tr___
    freopen("test.inp", "r", stdin);
    freopen("test.out", "w", stdout);
#endif
}

const int maxN = 1e5 + 5;
const int maxM = 2e2 + 5;
const llint INF = 1e9 + 7;

int N, K;
llint a[maxN];
llint f[maxN][2];
struct line {
    llint a, b;
    int id;
    line() {}
    line(llint a, llint b, int id): a(a), b(b), id(id) {}
} l[maxN];
int nLines = 0;
int last = 0;

void enter() {
    cin >> N >> K;
    for (int i = 1; i <= N; ++i) {
        cin >> a[i];
        a[i] += a[i - 1];
    }
}

void clear() {
    for (int i = 1; i <= nLines; ++i) {
        l[i].id = 0;
    }
    nLines = 0;
    last = 1;
}

void update(int id, llint a, llint b) {
    while (nLines >= 2 && last < nLines) {
        line lef = l[nLines - 1];
        line rig = l[nLines];

        if ((b - lef.b) * (lef.a - rig.a) <= (lef.a - a) * (rig.b - lef.b)) {
            --nLines;
        }
        else {
            break;
        }
    }
    last = min(last, nLines);
    l[++nLines] = line(a, b, id);
}

inline llint get(int id, llint x) {
    return l[id].a * x + l[id].b;
}

inline int query(llint x) {
    //so important!!!
    if (last > nLines) 
        last = nLines;
    last = max(last, 1);
    if (nLines == 0) return 0;
    while (last < nLines && get(last, x) <= get(last + 1, x)) ++last;
    return last;
}

int t[maxN][maxM];

void solve() {
    for (int k = 1; k <= K; ++k) {
        clear();
        for (int i = k; i <= N; ++i) {
            int la = query(a[i]);
            f[i][k&1] = get(la, a[i]);
            t[i][k] = l[la].id;

            update(i, a[i], f[i][!(k&1)] - a[i] * a[i]);
        }
    }

    printf("%lld\n", f[N][K&1]);
    int trace = t[N][K];
    vector<int> res;
    res.clear();
    while (trace) {
        res.push_back(trace);
        trace = t[trace][--K];
    }
    reverse(res.begin(), res.end());
    for (int x : res) {
        printf("%d ", x);
    }
}

int main() {
    openFile();
    enter();
    solve();
    return 0;
}

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