Submission #921847

#	Time	Username	Problem	Language	Result	Execution time	Memory
921847		danikoynov	Shortcut (IOI16_shortcut)	C++14	0 / 100	1 ms	2396 KiB

shortcut

#include "shortcut.h"
#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

const int maxn = 1e5 + 10;
const ll inf = 1e18;
int n;
ll pref[maxn];
ll l[maxn], d[maxn], c;

ll dist[maxn];

ll get_dist(int l, int r)
{
    if (l > r)
        swap(l, r);
    return pref[r - 1] - pref[l - 1];
}

const int maxlog = 21;

struct sparse_table
{
    ll dpos[maxlog][maxn];
    int lg[maxn];

    void build(vector < ll > values)
    {
        int len = values.size();
        for (int i = 1; i <= len; i ++)
        {
            lg[i] = lg[i / 2]  + 1;
            dpos[0][i] = values[i - 1];
        }

        for (int j = 1; j < lg[len]; j ++)
        {
            for (int i = 1; i <= len - (1 << j) + 1; i ++)
            {
                dpos[j][i] = dpos[j - 1][i + (1 << (j - 1))];
                if (dpos[j - 1][i] > dpos[j][i])
                    dpos[j][i] = dpos[j - 1][i];
            }
        }
    }

    ll query(int l, int r)
    {
        if (l > r)
            return 0;
        int mlog = lg[r - l + 1] - 1;
        ll ans = dpos[mlog][r - (1 << mlog) + 1];
        if (dpos[mlog][l] > ans)
            ans = dpos[mlog][l];
        return ans;
    }
};



ll pos[maxn];

struct container
{
    map < ll, ll > mp;

    void add(pair < ll, ll > cur)
    {
        cur.second = - cur.second;
        map < ll, ll > :: iterator it = mp.lower_bound(cur.first);
        if (it != mp.end() && it -> second >= cur.second)
            return;
        it = mp.insert(it, cur);///mp[cur.first] = cur.second;
        /**cout << "add" << endl;
         for (pair <ll, ll > ch : st)
         {
             cout << ch.first << " " << ch.second << endl;
         }*/
        it -> second = cur.second;
        ///it = mp.find(cur.first);
        while(it != mp.begin() && prev(it) -> second <= cur.second)
        {
            it = prev(it);
            it -> second = cur.second;
            //mp.erase(prev(it));
        }

        /**cout << "result" << endl;
        for (pair <ll, ll > ch : st)
        {
        cout << ch.first << " " << ch.second << endl;
        }

        cout << "-----------" << endl;*/
    }

    ll query(ll x)
    {

        map < ll, ll > :: iterator it = mp.lower_bound(x);
        if (it == mp.end())
            return inf;
        return -it -> second;
    }

    void clear_container()
    {
        mp.clear();
    }
};

container opt[4];

bool check(ll x)
{

    ll ct[4] = {inf, inf, inf, inf};
    /**
    0 - up up
    1 - up down
    2 - down up
    3 - down down
    */


    for (int i = 0; i < 4; i ++)
        opt[i].clear_container();

    ll base, nec;
    for (int i = n; i > 0; i --)
    {
        /// key - pref[i - 1] + d[i] > x
        /// key >= x + pref[i - 1] - d[i] + 1
        base = x - d[i] - c;
        nec = x + pref[i - 1] - d[i] + 1;
        ct[0] = min(ct[0], base + pos[i] + opt[0].query(nec));
        ct[1] = min(ct[1], base + pos[i] + opt[1].query(nec));
        ct[2] = min(ct[2], base - pos[i] + opt[0].query(nec));
        ct[3] = min(ct[3], base - pos[i] + opt[2].query(nec));
        ///ct[0] = min(ct[0], x - d[i] - c + pos[i] + opt[0]);
        /**for (int j = i + 1; j <= n; j ++)
        {
            ll path = pref[j - 1] - pref[i - 1] + d[i] + d[j];
            if (path <= x)
                continue;

            /// |x[i] - x[l]| + |x[j] - x[r]| + d[i] + d[j] + c<= k
            /// |x[l] - x[i]| + |x[r] - x[j]| <= k - d[i] - d[j] - c

            ///ct[0] = min(ct[0], x - d[i] - d[j] - c + pos[i] + pos[j]);
            ///ct[1] = min(ct[1], x - d[i] - d[j] - c + pos[i] - pos[j]);
            ///ct[2] = min(ct[2], x - d[i] - d[j] - c - pos[i] + pos[j]);
            ///ct[3] = min(ct[3], x - d[i] - d[j] - c - pos[i] - pos[j]);
        }*/
        opt[0].add({pref[i - 1] + d[i], - d[i] + pos[i]});
        opt[1].add({pref[i - 1] + d[i], - d[i] - pos[i]});
       // opt[2].add({pref[i - 1] + d[i], - d[i] + pos[i]});
        //opt[3].add({pref[i - 1] + d[i], - d[i] - pos[i]});
        ///opt[0] = min(opt[0], - d[i] - pos[i]);
    }

    ///cout << "step " << ct[0] << endl;



    /**for (int i = 1; i <= n; i ++)
        for (int j = 1; j <= n; j ++)
        {
            if (pos[i] + pos[j] <= ct[0] &&
                    pos[i] - pos[j] <= ct[1] &&
                    - pos[i] + pos[j] <= ct[2] &&
                    - pos[i] - pos[j] <= ct[3])
                return true;
        }
    return false;*/

    for (int i = 1; i <= n; i ++)
    {
        ll top = inf, bot = -inf;
        /// pos[i] + pos[j] <= ct[0] ---- pos[j] <= ct[0] - pos[i]
        top = min(top, ct[0] - pos[i]);
        /// pos[i] - pos[j] <= ct[1] --- pos[j] >= pos[i] - ct[1]
        bot = max(bot, pos[i] - ct[1]);
        /// - pos[i] + pos[j] <= ct[2] --- pos[j] <= ct[2] + pos[i]
        top = min(top, ct[2] + pos[i]);
        /// -pos[i] - pos[j] <= ct[3] --- pos[j] >= - ct[3] - pos[i]
        bot = max(bot, - ct[3] - pos[i]);
        int lf = 1, rf = n;
        while(lf <= rf)
        {
            int mf = (lf + rf) / 2;
            if (pos[mf] < bot)
                lf = mf + 1;
            else
                rf = mf - 1;
        }

        if (lf > n)
            continue;

        if (pos[lf] <= top)
            return true;

    }

    return false;




}


ll find_shortcut(int N, vector<int> L, vector<int> D, int C)
{
    n = N;
    c = C;
    for (int i = 0; i < n - 1; i ++)
        l[i + 1] = L[i];
    for (int i = 0; i < n; i ++)
        d[i + 1] = D[i];

    pos[1] = 0;
    for (int i = 2; i <= n; i ++)
    {

        pos[i] = pos[i - 1] + l[i - 1];

    }

    for (int i = 1; i <= n; i ++)
    {
        pref[i] = pref[i - 1] + l[i];
    }


    ll lf = 0, rf = n * pref[n] + 2e9 + 10;
    while(lf <= rf)
    {
        ///cout << lf << " " << rf << endl;
        ll mf = (lf + rf) / 2;
        if (check(mf))
            rf = mf - 1;
        else
            lf = mf + 1;
    }


    return lf;
}

• Subtask 1: 0 / 9
• Subtask 2: 0 / 14
• Subtask 3: 0 / 8
• Subtask 4: 0 / 7
• Subtask 5: 0 / 33
• Subtask 6: 0 / 22
• Subtask 7: 0 / 4
• Subtask 8: 0 / 3