Submission #921779

#	Time	Username	Problem	Language	Result	Execution time	Memory
921779		danikoynov	Shortcut (IOI16_shortcut)	C++14	71 / 100	619 ms	435284 KiB

shortcut

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

using namespace std;
typedef long long ll;

const int maxn = 3010;
const ll inf = 1e18;
int n;
ll cpos[maxn], cs[maxn], pref[maxn], bef[maxn], aft[maxn];
ll l[maxn], d[maxn], c;

ll dist[maxn];
struct edge
{
    int to;
    ll w;

    edge(int _to = 0, ll _w = 0)
    {
        to = _to;
        w = _w;
    }

    bool operator < (const edge &e) const
    {
        return w > e.w;
    }
};

int used[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;
    }
};


struct point
{
    ll x, y;

    point(ll _x = 0, ll _y = 0)
    {
        x = _x;
        y = _y;
    }
};
struct rectangle
{
    point centre;
    ll diagonal;

    rectangle(point _centre = point(), ll _diagonal = 0)
    {
        centre = _centre;
        diagonal = _diagonal;
    }
};

ll pos[maxn];


struct event
{
    int type;
};

ll up_bound[2][maxn * maxn];
ll dw_bound[2][maxn * maxn];
rectangle con[maxn * maxn];

bool check(ll x)
{

    ll ct[4] = {inf, inf, inf, inf};
    /**
    0 - up up
    1 - up down
    2 - down up
    3 - down down
    */
    int sz = 0;
    for (int i = 1; i <= n; i ++)
    {
        /**if (p[1] < 0)
        {
            cout << "step " << i << endl;
            exit(0);
        }*/
        con[sz ++] = (rectangle(point(pos[i], 0), inf));
        for (int j = i + 1; j <= n; j ++)
        {
            ll path = get_dist(i, j) + d[i] + d[j];
            if (path <= x)
                continue;
            //cout << "condition " << i << " " << j << endl;
            //cout << pos[i] << " " << pos[j] << " " << x - d[i] - d[j] << endl;
            /// |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
            con[sz ++] = (rectangle(point(pos[i], pos[j]), x - 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]);
        }
    }

    if (sz == 0)
        return true;

    /**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;
    ///pair < ll, ll > ans;


    dw_bound[0][0] = -inf;
    up_bound[0][0] = inf;
    for (int i = 0; i < sz; i ++)
    {
        up_bound[0][i + 1] = up_bound[0][i];
        up_bound[0][i + 1] = min(up_bound[0][i + 1], con[i].centre.y + con[i].diagonal + con[i].centre.x);
        dw_bound[0][i + 1] = dw_bound[0][i];
        dw_bound[0][i + 1] = max(dw_bound[0][i + 1], con[i].centre.y - con[i].diagonal - con[i].centre.x);
    }


    dw_bound[1][sz + 1] = -inf;
    up_bound[1][sz + 1] = inf;
    for (int i = sz - 1; i >= 0; i --)
    {
        up_bound[1][i + 1] = up_bound[1][i + 2];
        up_bound[1][i + 1] = min(up_bound[1][i + 1], con[i].centre.y + con[i].diagonal - con[i].centre.x);
        dw_bound[1][i + 1] = dw_bound[1][i + 2];
        dw_bound[1][i + 1] = max(dw_bound[1][i + 1], con[i].centre.y - con[i].diagonal + con[i].centre.x);
    }



    for (int i = 0; i < sz; i ++)
    {
        if (i != 0 && con[i].centre.x == con[i - 1].centre.x)
            continue;
        ll top = inf;
        ll bot = -inf;

        top = min(top, -con[i].centre.x + up_bound[0][i + 1]);
        bot = max(bot, con[i].centre.x + dw_bound[0][i + 1]);
        /***for (int j = 0; j <= i; j ++)
        {
            top = min(top, con[j].centre.y + con[j].diagonal - (con[i].centre.x - con[j].centre.x));
            bot = max(bot, con[j].centre.y - con[j].diagonal + (con[i].centre.x - con[j].centre.x));
        }*/

        top = min(top, con[i].centre.x + up_bound[1][i + 1]);
        bot = max(bot, -con[i].centre.x + dw_bound[1][i + 1]);
        /**for (int j = i + 1; j < con.size(); j ++)
        {
            top = min(top, con[j].centre.y + con[j].diagonal - (con[j].centre.x - con[i].centre.x));
            bot = max(bot, con[j].centre.y - con[j].diagonal + (con[j].centre.x - con[i].centre.x));
        }*/

        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;
    pair < ll, ll > ans = {-1, -1};
    for (int l = 1; l <= n; l ++)
        for (int r = l; r <= n; r ++)
        {
            bool tf = true;
            for (rectangle rec : con)
            {
                ll val = abs(pos[l] - rec.centre.x) + abs(pos[r] - rec.centre.y);
                if (val > rec.diagonal)
                {
                    //cout << "fuck " << l << " " << r << endl;
                    //cout << "rectangle " << rec.centre.x << " " << rec.centre.y << " " << rec.diagonal << endl;
                    tf = false;
                    break;
                }
            }
            if (tf)
            {
                ans = {pos[l], pos[r]};

            }
        }
    if (ans.first == -1)
        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];
    }

    for (int i = 1; i <= n; i ++)
    {
        cpos[i] = cpos[i - 1] + l[i - 1];
        cpos[i] = max(cpos[i], d[i]);
        bef[i] = bef[i - 1];
        for (int j = 1; j < i; j ++)
        {
            bef[i] = max(bef[i], get_dist(i, j) + d[i] + d[j]);
        }
    }

    for (int i = n; i > 0; i --)
    {
        cs[i] = cs[i + 1] + l[i];
        cs[i] = max(cs[i], d[i]);
        aft[i] = aft[i + 1];
        for (int j = i + 1; j <= n; j ++)
        {
            aft[i] = max(aft[i], get_dist(i, j) + d[i] + d[j]);
        }
    }




    ll lf = 0, rf = inf;
    while(lf <= rf)
    {
        ll mf = (lf + rf) / 2;
        if (check(mf))
            rf = mf - 1;
        else
            lf = mf + 1;
    }


    return lf;
}

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