Submission #64330

#	Time	Username	Problem	Language	Result	Execution time	Memory
64330		qkxwsm	Split the sequence (APIO14_sequence)	C++17	22 / 100	2054 ms	3884 KiB

sequence

/*
PROG: source
LANG: C++11
    _____
  .'     '.
 /  0   0  \
|     ^     |
|  \     /  |
 \  '---'  /
  '._____.'
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;

struct chash
{
        int operator()(int x) const
        {
                x ^= (x >> 20) ^ (x >> 12);
                return x ^ (x >> 7) ^ (x >> 4);
        }
        int operator()(long long x) const
        {
                return x ^ (x >> 32);
        }
};

template<typename T> using orderedset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T, typename U> using hashtable = gp_hash_table<T, U, chash>;

template<class T>
void readi(T &x)
{
	T input = 0;
	bool negative = false;
	char c = ' ';
	while (c < '-')
        {
		c = getchar();
	}
	if (c == '-')
	{
		negative = true;
		c = getchar();
	}
	while (c >= '0')
	{
		input = input * 10 + (c - '0');
		c = getchar();
	}
	if (negative)
	{
		input = -input;
	}
	x = input;
}
template<class T>
void printi(T output)
{
	if (output == 0)
	{
		putchar('0');
		return;
	}
	if (output < 0)
	{
		putchar('-');
		output = -output;
	}
	int aout[20];
	int ilen = 0;
	while(output)
	{
		aout[ilen] = ((output % 10));
		output /= 10;
		ilen++;
	}
	for (int i = ilen - 1; i >= 0; i--)
	{
		putchar(aout[i] + '0');
	}
	return;
}
template<class T>
void ckmin(T &a, T b)
{
	a = min(a, b);
}
template<class T>
void ckmax(T &a, T b)
{
	a = max(a, b);
}
template<class T, class U>
T normalize(T x, U mod = 1000000007)
{
	return (((x % mod) + mod) % mod);
}
long long randomizell(long long mod)
{
	return ((1ll << 45) * rand() + (1ll << 30) * rand() + (1ll << 15) * rand() + rand()) % mod;
}
int randomize(int mod)
{
	return ((1ll << 15) * rand() + rand()) % mod;
}

#define y0 ___y0
#define y1 ___y1
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define PF push_front
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define debug(x) cerr << #x << " = " << x << endl;

const long double PI = 4.0 * atan(1.0);
const long double EPS = 1e-10;

#define MAGIC 347
#define SINF 10007
#define CO 1000007
#define INF 1000000007
#define BIG 1000000931
#define LARGE 1696969696967ll
#define GIANT 2564008813937411ll
#define LLINF 2696969696969696969ll
#define MAXN 100013
#define MAXK 213

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

int N, K;
ll arr[MAXN];
ll pref[MAXN], prodpref[MAXN];
// ll dp[MAXN][MAXK];
__int128_t dp[MAXN];
int taken[MAXN], parent[MAXN];
vector<int> takes;
int del = 0;
ll ans;
bool istaken[MAXN];

ll C(int L, int R)
{
        return prodpref[R] - prodpref[L] - (pref[L]) * (pref[R] - pref[L]);
}
void solve(ll c)
{
        dp[0] = 0;
        taken[0] = 0;
        for (int i = 1; i <= N; i++)
        {
                dp[i] = LLINF; dp[i] *= dp[i];
                for (int j = 0; j < i; j++)
                {
                        if (dp[i] >= dp[j] + C(j, i) + c)
                        {
                                dp[i] = dp[j] + C(j, i) + c;
                                taken[i] = taken[j] + 1;
                                parent[i] = j;
                        }
                }
        }
        return;
}

int32_t main()
{
	ios_base::sync_with_stdio(0);
	srand(time(0));
	//	cout << fixed << setprecision(10);
	//	cerr << fixed << setprecision(10);
	if (fopen("input.in", "r"))
	{
		freopen ("input.in", "r", stdin);
		freopen ("output.out", "w", stdout);
	}
        cin >> N >> K;
        K++;
        for (int i = 0; i < N; i++)
        {
                cin >> arr[i];
                pref[i + 1] = pref[i] + arr[i];
                prodpref[i + 1] = prodpref[i] + pref[i] * arr[i];
        }
        // for (int i = 1; i <= N; i++)
        // {
        //         for (int j = 0; j <= K; j++)
        //         {
        //                 dp[i][j] = LLINF;
        //         }
        // }
        // for (int i = 1; i <= N; i++)
        // {
        //         for (int j = 1; j <= K; j++)
        //         {
        //                 for (int k = 0; k < i; k++)
        //                 {
        //                         ckmin(dp[i][j], dp[k][j - 1] + C(k, i - 1));
        //                         // cerr << k << ' ' << i - 1 << ' ' << C(k, i - 1) << endl;
        //                 }
        //                 cerr << dp[i][j] << ' ';
        //         }
        //         cerr << endl;
        // }
        ll lo = 0, hi = LLINF;
        while(hi > lo)
        {
                ll mid = (lo + hi + 1) / 2;
                solve(mid);
                // cerr << mid << ' ' << taken[N] << endl;
                if (taken[N] >= K)
                {
                        lo = mid;
                }
                else
                {
                        hi = mid - 1;
                }
                // cerr << lo << ' ' << hi << endl;
        }
        solve(lo);
        del = taken[N] - K;
        dp[0] = 0; taken[0] = 0;
        for (int i = 1; i <= N; i++)
        {
                dp[i] = LLINF; dp[i] *= dp[i];
                int mx;
                for (int j = 0; j < i; j++)
                {
                        if (dp[i] >= dp[j] + C(j, i) + lo)
                        {
                                dp[i] = dp[j] + C(j, i) + lo;
                                mx = taken[j];
                        }
                }
                for (int j = i - 1; j >= 0; j--)
                {
                        if (dp[i] == dp[j] + C(j, i) + lo)
                        {
                                if (del >= mx - taken[j])
                                {
                                        del -= (mx - taken[j]);
                                        mx = taken[j];
                                        taken[i] = taken[j] + 1;
                                        parent[i] = j;
                                }
                        }
                }
        }
        ans = prodpref[N] - (dp[N] - K * lo);
        int u = N;
        while(u)
        {
                takes.PB(u);
                u = parent[u];
        }
        takes.erase(takes.begin());
        cout << ans << '\n';
        for (int i = 0; i < takes.size(); i++)
        {
                if (i) cout << ' ';
                cout << takes[i];
        }
        cout << '\n';
        //the order DOES NOT matter!
	//	cerr << "time elapsed = " << (clock() / (CLOCKS_PER_SEC / 1000)) << " ms" << endl;
	return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int32_t main()':
sequence.cpp:272:27: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         for (int i = 0; i < takes.size(); i++)
                         ~~^~~~~~~~~~~~~~
sequence.cpp:187:11: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
   freopen ("input.in", "r", stdin);
   ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:188:11: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
   freopen ("output.out", "w", stdout);
   ~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:253:47: warning: 'mx' may be used uninitialized in this function [-Wmaybe-uninitialized]
                                 if (del >= mx - taken[j])
                                            ~~~^~~~~~~~~~

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