Submission #701683

#	Time	Username	Problem	Language	Result	Execution time	Memory
701683		badont	Split the sequence (APIO14_sequence)	C++17	60 / 100	2089 ms	91012 KiB

sequence

#include<iostream>
#include<algorithm>
#include<vector>
#include<set>
#include<cassert>
#include<climits>
using namespace std;

#pragma GCC optimize("-funsafe-loop-optimizations")
#pragma GCC optimize("-funroll-loops")
#pragma GCC optimize("-fwhole-program")
#pragma GCC optimize("Ofast,no-stack-protector")
#pragma GCC optimize("-fthread-jumps")
#pragma GCC optimize("-falign-functions")
#pragma GCC optimize("-falign-jumps")
#pragma GCC optimize("-falign-loops")
#pragma GCC optimize("-falign-labels")
#pragma GCC optimize("-fcaller-saves")
#pragma GCC optimize("-fcrossjumping")
#pragma GCC optimize("-fcse-follow-jumps")
#pragma GCC optimize("-fcse-skip-blocks")
#pragma GCC optimize("-fdelete-null-pointer-checks")
#pragma GCC optimize("-fdevirtualize")
#pragma GCC optimize("-fexpensive-optimizations")
#pragma GCC optimize("-fgcse")
#pragma GCC optimize("-fgcse-lm")
#pragma GCC optimize("-fhoist-adjacent-loads")
#pragma GCC optimize("-finline-small-functions")
#pragma GCC optimize("-findirect-inlining")
#pragma GCC optimize("-fipa-sra")
#pragma GCC optimize("-foptimize-sibling-calls")
#pragma GCC optimize("-fpartial-inlining")
#pragma GCC optimize("-fpeephole2")
#pragma GCC optimize("-freorder-blocks")
#pragma GCC optimize("-freorder-functions")
#pragma GCC optimize("-frerun-cse-after-loop")
#pragma GCC optimize("-fsched-interblock")
#pragma GCC optimize("-fsched-spec")
#pragma GCC optimize("-fschedule-insns")
#pragma GCC optimize("-fschedule-insns2")
#pragma GCC optimize("-fstrict-aliasing")
#pragma GCC optimize("-fstrict-overflow")
#pragma GCC optimize("-ftree-switch-conversion")
#pragma GCC optimize("-ftree-tail-merge")
#pragma GCC optimize("-ftree-pre")
#pragma GCC optimize("-ftree-vrp")

using ll = long long;
#define all(x) x.begin(),x.end()

struct Line {
	mutable ll k, m, p;
    mutable int idx;
	bool operator<(const Line& o) const { return k < o.k; }
	bool operator<(ll x) const { return p < x; }
};

struct LineContainer : multiset<Line, less<>> {
	// (for doubles, use inf = 1/.0, div(a,b) = a/b)
	static const ll inf = LLONG_MAX;
	ll div(ll a, ll b) { // floored division
		return a / b - ((a ^ b) < 0 && a % b); }
	bool isect(iterator x, iterator y) {
		if (y == end()) return x->p = inf, 0;
		if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
		else x->p = div(y->m - x->m, x->k - y->k);
		return x->p >= y->p;
	}
	void add(ll k, ll m, int idx) {
		auto z = insert({k, m, 0, idx}), y = z++, x = y;
		while (isect(y, z)) z = erase(z);
		if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
		while ((y = x) != begin() && (--x)->p >= y->p)
			isect(x, erase(y));
	}
	pair<ll, int> query(ll x) {
		assert(!empty());
		auto l = *lower_bound(x);
		return {l.k * x + l.m, l.idx};
	}
};

void solve() {
    ll n, k;
    cin >> n >> k;

    vector<ll> a(n);
    for (auto& u : a)
        cin >> u;

    const ll INF = 1e18;

    auto solve = [&](vector<ll> a) -> pair<ll, vector<ll>> {
        vector<ll> p = a;
        
        for (int i = 1; i < n; i++)
            p[i] += p[i - 1];

        auto prefix = [&p](ll g) -> ll {
            g--;
            return (g < 0 ? 0LL : p[g]);
        };

        vector parent(k + 1, vector<int>(n + 1, 0));
        vector<ll> dp(n + 1, -INF);
        dp[0] = 0;

        for (int i = 1; i <= k; i++) {
            vector<ll> ndp(n + 1, -INF);
            LineContainer lc;
            for (int j = i; j <= n; j++) {
                //cout << j - 1 << ' ' << dp[j - 1] << '\n';
                if (dp[j - 1] != -INF) {
                    //cout << "adding line at: " << i << ' ' << j - 1 << " " << prefix(j - 1) << ' ' << dp[j - 1] - prefix(j - 1) * prefix(n) << '\n';
                    lc.add(prefix(j - 1), dp[j - 1] - prefix(j - 1) * prefix(n), j - 1);
                }
                assert(!lc.empty());

                auto [value, transition] = lc.query(prefix(j));
                //cout << j << ' ' << prefix(j) << " " << prefix(n) << '\n';
                ndp[j] = value + prefix(j) * prefix(n) - prefix(j) * prefix(j);
                //cout << i << ' ' << j << ' ' << ndp[j] << ' ' << transition << '\n';
                parent[i][j] = transition;
            }

            swap(ndp, dp);
            ndp.clear();
        }

        ll cur_idx = 0, max_dp = 0;
        for (int i = 1; i <= n; i++) {
            if (dp[i] > max_dp) {
                max_dp = dp[i];
                cur_idx = i;
            }
        }

        vector<ll> ret_seq;
        for (int i = k; i > 0; i--) {
            assert(cur_idx > 0);
            //cout << cur_idx << '\n';
            ret_seq.emplace_back(cur_idx);
            cur_idx = parent[i][cur_idx];
        }

        reverse(all(ret_seq));
        return {max_dp, ret_seq};
    };

    auto [ans1, seq1] = solve(a);
    reverse(all(a));
    auto [ans2, seq2] = solve(a);
    if (ans2 > ans1) {
        ans1 = ans2;
        swap(seq1, seq2);
        for (auto& u : seq1) {
            u = n - u;
        }
    }

    cout << ans1 << '\n';
    for (auto u : seq1)
        cout << u << ' ';
}

int main() {
    cin.tie(0)->sync_with_stdio(0);
    solve();
    return 0;
}

Compilation message (stderr)

sequence.cpp:9:51: warning: bad option '-funsafe-loop-optimizations' to pragma 'optimize' [-Wpragmas]
    9 | #pragma GCC optimize("-funsafe-loop-optimizations")
      |                                                   ^
sequence.cpp:11:39: warning: bad option '-fwhole-program' to pragma 'optimize' [-Wpragmas]
   11 | #pragma GCC optimize("-fwhole-program")
      |                                       ^
sequence.cpp:21:41: warning: bad option '-fcse-skip-blocks' to pragma 'optimize' [-Wpragmas]
   21 | #pragma GCC optimize("-fcse-skip-blocks")
      |                                         ^
sequence.cpp:42:41: warning: bad option '-fstrict-overflow' to pragma 'optimize' [-Wpragmas]
   42 | #pragma GCC optimize("-fstrict-overflow")
      |                                         ^
sequence.cpp:54:32: warning: bad option '-funsafe-loop-optimizations' to attribute 'optimize' [-Wattributes]
   54 |  bool operator<(const Line& o) const { return k < o.k; }
      |                                ^~~~~
sequence.cpp:54:32: warning: bad option '-fwhole-program' to attribute 'optimize' [-Wattributes]
sequence.cpp:54:32: warning: bad option '-fcse-skip-blocks' to attribute 'optimize' [-Wattributes]
sequence.cpp:54:32: warning: bad option '-fstrict-overflow' to attribute 'optimize' [-Wattributes]
sequence.cpp:55:23: warning: bad option '-funsafe-loop-optimizations' to attribute 'optimize' [-Wattributes]
   55 |  bool operator<(ll x) const { return p < x; }
      |                       ^~~~~
sequence.cpp:55:23: warning: bad option '-fwhole-program' to attribute 'optimize' [-Wattributes]
sequence.cpp:55:23: warning: bad option '-fcse-skip-blocks' to attribute 'optimize' [-Wattributes]
sequence.cpp:55:23: warning: bad option '-fstrict-overflow' to attribute 'optimize' [-Wattributes]
sequence.cpp:61:19: warning: bad option '-funsafe-loop-optimizations' to attribute 'optimize' [-Wattributes]
   61 |  ll div(ll a, ll b) { // floored division
      |                   ^
sequence.cpp:61:19: warning: bad option '-fwhole-program' to attribute 'optimize' [-Wattributes]
sequence.cpp:61:19: warning: bad option '-fcse-skip-blocks' to attribute 'optimize' [-Wattributes]
sequence.cpp:61:19: warning: bad option '-fstrict-overflow' to attribute 'optimize' [-Wattributes]
sequence.cpp:63:35: warning: bad option '-funsafe-loop-optimizations' to attribute 'optimize' [-Wattributes]
   63 |  bool isect(iterator x, iterator y) {
      |                                   ^
sequence.cpp:63:35: warning: bad option '-fwhole-program' to attribute 'optimize' [-Wattributes]
sequence.cpp:63:35: warning: bad option '-fcse-skip-blocks' to attribute 'optimize' [-Wattributes]
sequence.cpp:63:35: warning: bad option '-fstrict-overflow' to attribute 'optimize' [-Wattributes]
sequence.cpp:69:30: warning: bad option '-funsafe-loop-optimizations' to attribute 'optimize' [-Wattributes]
   69 |  void add(ll k, ll m, int idx) {
      |                              ^
sequence.cpp:69:30: warning: bad option '-fwhole-program' to attribute 'optimize' [-Wattributes]
sequence.cpp:69:30: warning: bad option '-fcse-skip-blocks' to attribute 'optimize' [-Wattributes]
sequence.cpp:69:30: warning: bad option '-fstrict-overflow' to attribute 'optimize' [-Wattributes]
sequence.cpp:76:26: warning: bad option '-funsafe-loop-optimizations' to attribute 'optimize' [-Wattributes]
   76 |  pair<ll, int> query(ll x) {
      |                          ^
sequence.cpp:76:26: warning: bad option '-fwhole-program' to attribute 'optimize' [-Wattributes]
sequence.cpp:76:26: warning: bad option '-fcse-skip-blocks' to attribute 'optimize' [-Wattributes]
sequence.cpp:76:26: warning: bad option '-fstrict-overflow' to attribute 'optimize' [-Wattributes]
sequence.cpp:83:12: warning: bad option '-funsafe-loop-optimizations' to attribute 'optimize' [-Wattributes]
   83 | void solve() {
      |            ^
sequence.cpp:83:12: warning: bad option '-fwhole-program' to attribute 'optimize' [-Wattributes]
sequence.cpp:83:12: warning: bad option '-fcse-skip-blocks' to attribute 'optimize' [-Wattributes]
sequence.cpp:83:12: warning: bad option '-fstrict-overflow' to attribute 'optimize' [-Wattributes]
sequence.cpp: In function 'void solve()':
sequence.cpp:93:39: warning: bad option '-funsafe-loop-optimizations' to attribute 'optimize' [-Wattributes]
   93 |     auto solve = [&](vector<ll> a) -> pair<ll, vector<ll>> {
      |                                       ^~~~~~~~~~~~~~~~~~~~
sequence.cpp:93:39: warning: bad option '-fwhole-program' to attribute 'optimize' [-Wattributes]
sequence.cpp:93:39: warning: bad option '-fcse-skip-blocks' to attribute 'optimize' [-Wattributes]
sequence.cpp:93:39: warning: bad option '-fstrict-overflow' to attribute 'optimize' [-Wattributes]
sequence.cpp: In lambda function:
sequence.cpp:99:37: warning: bad option '-funsafe-loop-optimizations' to attribute 'optimize' [-Wattributes]
   99 |         auto prefix = [&p](ll g) -> ll {
      |                                     ^~
sequence.cpp:99:37: warning: bad option '-fwhole-program' to attribute 'optimize' [-Wattributes]
sequence.cpp:99:37: warning: bad option '-fcse-skip-blocks' to attribute 'optimize' [-Wattributes]
sequence.cpp:99:37: warning: bad option '-fstrict-overflow' to attribute 'optimize' [-Wattributes]
sequence.cpp: At global scope:
sequence.cpp:166:10: warning: bad option '-funsafe-loop-optimizations' to attribute 'optimize' [-Wattributes]
  166 | int main() {
      |          ^
sequence.cpp:166:10: warning: bad option '-fwhole-program' to attribute 'optimize' [-Wattributes]
sequence.cpp:166:10: warning: bad option '-fcse-skip-blocks' to attribute 'optimize' [-Wattributes]
sequence.cpp:166:10: warning: bad option '-fstrict-overflow' to attribute 'optimize' [-Wattributes]

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