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Submission #655278

# Submission time Handle Problem Language Result Execution time Memory
655278 2022-11-03T17:29:56 Z benjaminkleyn Split the sequence (APIO14_sequence) C++17
0 / 100
 2000 ms 7020 KB 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

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

struct LineContainer : multiset<Line, less<>> {
	static const ll inf = LLONG_MAX;
	ll div(ll a, ll b) {
		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};
	}
};

int N, K, a[100001];
ll pref[100001] = {0};
ll dp[100001] = {0};
int last_split[100001];
int cnt[100001];

LineContainer cht;
int calc(int cost)
{
    cht.clear();
    cnt[0] = 0;
    for (int i = 1; i <= N; i++)
    {
        dp[i] = 0;
        cht.add(pref[i-1], dp[i-1] - pref[i-1] * pref[i-1], i-1);
        auto [val, idx] = cht.query(pref[i]);
        dp[i] = val - cost;
        last_split[i] = idx;
        cnt[i] = cnt[idx] + 1;
    }
    return cnt[N];
}

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

    int lo = 0, hi = 1e12;
    while (lo < hi)
    {
        int mid = (lo + hi) / 2;

        if (calc(mid) > K + 1)
            lo = mid + 1;
        else
            hi = mid;
    }

    calc(lo);
    cout << dp[N] + lo * cnt[N] << '\n';

    int i = N;
    do
    {
        i = last_split[i];
        cout << i << ' ';
    } while (--K);
    cout << '\n';

    return 0;
}

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:67:22: warning: overflow in conversion from 'double' to 'int' changes value from '1.0e+12' to '2147483647' [-Woverflow]
   67 |     int lo = 0, hi = 1e12;
      |                      ^~~~

Subtask #1
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 336 KB contestant found the optimal answer: 108 == 108
2 Correct 0 ms 212 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 212 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 212 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 212 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Incorrect 0 ms 212 KB Integer 0 violates the range [1, 9]
7 Halted 0 ms 0 KB -

Subtask #2
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 0 ms 212 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 328 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Execution timed out 2081 ms 212 KB Time limit exceeded
5 Halted 0 ms 0 KB -

Subtask #3
0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 340 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 340 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Execution timed out 2068 ms 212 KB Time limit exceeded
5 Halted 0 ms 0 KB -

Subtask #4
0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 340 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 4 ms 340 KB contestant found the optimal answer: 140412195 == 140412195
3 Incorrect 5 ms 340 KB declared answer doesn't correspond to the split scheme: declared = 49527810762549, real = 49729674225461
4 Halted 0 ms 0 KB -

Subtask #5
0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 29 ms 852 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 47 ms 1204 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Execution timed out 2076 ms 1364 KB Time limit exceeded
4 Halted 0 ms 0 KB -

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Execution timed out 2059 ms 7020 KB Time limit exceeded
2 Halted 0 ms 0 KB -