Submission #918636

#	Time	Username	Problem	Language	Result	Execution time	Memory
918636		wii	Split the sequence (APIO14_sequence)	C++17	0 / 100	699 ms	83216 KiB

sequence

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

typedef double db;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;

#define lx (id << 1)
#define rx (lx  1)
#define gcd __gcd
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define bit(i, mask) ((mask) >> (i) & 1)
#define reset(x, val) memset(x, val, sizeof(x))
#define foru(i,a,b) for(int i = (a); i <= (b); ++i)
#define ford(i,a,b) for(int i = (a); i >= (b); --i)
#define FastIO ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);

template<typename T> bool maximize(T &res, const T &val) { if (res < val) { res = val; return true; } return false; }
template<typename T> bool minimize(T &res, const T &val) { if (val < res) { res = val; return true; } return false; }

const ll Linf = 0x3f3f3f3f3f3f3f3f;
const int Inf = 0x3f3f3f3f;
const ll Mod = 1e9 + 7;
const ll Mod2 = ll(1e9) + 9;
const int Lim = 1e6 + 5;
const int inv6 = 166666668;

// #define Sieve
#ifdef Sieve
    vector<int> pr;
    vector<int> lpf;
    void Linear_sieve(int n = Lim) {
        pr.assign(1, 2);
        lpf.assign(n + 1, 2);

        for (int x = 3; x <= n; x += 2) {
            if (lpf[x] == 2) pr.push_back(lpf[x] = x);
            for (int i = 1; i < pr.size() && pr[i] <= lpf[x] && pr[i] * x <= n; ++i)
                lpf[pr[i] * x] = pr[i];
        }
    }
#endif

/// ====*====*====*====*====*====*====*====*====*====*====*====*====*====*====*====*====

const int base = 3;
const int N = 1e5 + 5;
const int K = 200 + 1;
const int dx[] = {+1, -1, 0, 0};
const int dy[] = {0, 0, +1, -1};
const int block_size = sqrt(2e9) + 2;

struct Line {
    int a;
    ll b;
    int idx;

    Line() = default;
    Line(int a, ll b, int id):
        a(a), b(b), idx(id) {}

    bool operator< (const Line &x) const { return a < x.a; };
    ll operator() (ll x) const { return a * x + b; }
};

struct LineContainer {
    deque<Line> st;

    ld isect(const Line &x, const Line &y) {
        return ld(y.b - x.b) / (x.a - y.a);
    }

    int bad(const Line &a, const Line &b, const Line &c) {
        if (b.a == c.a) return true;
        return isect(a, b) < isect(b, c);
    }

    void add(int k, ll m, int id) {
        int top = st.size();
        Line l = Line(k, m, id);

        while (top >= 2 && bad(st[top - 2], st[top - 1], l))
            st.pop_back(), --top;

        st.push_back(l);
    }

    pair<ll, int> query(int x) {
        int l = 0, r = st.size() - 1;

        while (r >= 1 && isect(st[l], st[l + 1]) > x) {
            st.pop_front(); --r;
        }

        /*while (r >= 1 && isect(st[r - 1], st[r]) < x) {
            st.pop_back(); --r;
        }*/

        return make_pair(st[l](x), st[l].idx);
    }
};

int n, k;
int a[N], pref[N];
ll dp[N][2];
signed par[K][N];

LineContainer cht;
ll f(int l, int r) {
    return pref[r] - pref[l - 1];
}

/**
7 3
4 1 3 4 0 2 3
**/

void solve() {
    cin >> n >> k;
    foru(i, 1, n) cin >> a[i];
    foru(i, 1, n) pref[i] = pref[i - 1] + a[i];

    foru(i, 0, n) dp[i][0] = -Linf;

    dp[0][0] = 0;
	foru(z, 1, k) {
        int layer = z & 1;
        foru(i, 0, n) dp[i][layer] = -Linf;

		cht.st.clear();
		foru(i, 1, n - 1) {
			int j = i - 1;
			cht.add(-pref[j], dp[j][!layer], j);

            pair<ll, int> res = cht.query(f(i + 1, n));
			dp[i][layer] = res.first + f(i + 1, n) * pref[i];
            par[z][i] = res.second;
		}
	}

    ll ans = -Linf;
    int idx = -1;
    foru(i, 1, n - 1) if (maximize(ans, dp[i][k & 1]))
        idx = i;

    cout << ans << "\n";
    for (int z = k; z > 0; --z) {
        cout << idx << " ";
        idx = par[z][idx];
    }
}

signed main() {
    FastIO;

    #define task ""
    if (fopen(task".inp", "r")) {
        freopen(task".inp", "r", stdin);
        freopen(task".out", "w", stdout);
    }

    #define task "Test"
    if (fopen(task".inp", "r")) {
        freopen(task".inp", "r", stdin);
        freopen(task".out", "w", stdout);
    } else if (0) {
        ofstream fout(task".inp");
        fout.close();

        freopen(task".inp", "r", stdin);
        freopen(task".out", "w", stdout);
    }

    #ifdef Sieve
        Linear_sieve();
    #endif

    int ntest = 1;
    // cin >> ntest;
    while (ntest--) {
        //cout << "Case " << q << ": " << "\n";
        solve();
        cout << "\n";
    }

    return 0;
}

/**  /\_/\
 *  (= ._.)
 *  / >TL \>AC
**/

Compilation message (stderr)

sequence.cpp:164: warning: "task" redefined
  164 |     #define task "Test"
      | 
sequence.cpp:158: note: this is the location of the previous definition
  158 |     #define task ""
      | 
sequence.cpp: In function 'int main()':
sequence.cpp:160:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  160 |         freopen(task".inp", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:161:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  161 |         freopen(task".out", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:166:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  166 |         freopen(task".inp", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:167:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  167 |         freopen(task".out", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:172:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  172 |         freopen(task".inp", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:173:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  173 |         freopen(task".out", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

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