Submission #168790

#	Time	Username	Problem	Language	Result	Execution time	Memory
168790		popovicirobert	Shortcut (IOI16_shortcut)	C++14	97 / 100	2064 ms	39544 KiB

shortcut

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

using namespace std;

const int MAXN = (int) 1e6;

int dif_ord[MAXN], sum_ord[MAXN];
ll x[MAXN + 1], d[MAXN + 1];

inline bool check(ll k, int n, int c) {
    vector <int> sgn = {1, -1};
    int pos[2][2][2][2];
    ll vals[2][2][2][2];

    memset(pos, 0, sizeof(pos));
    for(int conf = 0; conf < 8; conf++) {
        vals[conf >> 2][(conf >> 1) & 1][0][conf & 1] = -1e18;
        vals[conf >> 2][(conf >> 1) & 1][1][conf & 1] = 1e18;
    }

    auto upd = [&](int p, int conf) {
        int a = (conf >> 2), b = (conf >> 1) % 2, c = conf % 2;
        ll v = x[p] * sgn[a] + d[p] * sgn[b];
        if(c == 0) { // mx
            if(vals[a][b][c][0] < v) {
                pos[a][b][c][1] = pos[a][b][c][0];
                vals[a][b][c][1] = vals[a][b][c][0];
                pos[a][b][c][0] = p;
                vals[a][b][c][0] = v;
            }
            else if(vals[a][b][c][1] < v) {
                pos[a][b][c][1] = p;
                vals[a][b][c][1] = v;
            }
        }
        else { // mn
            if(vals[a][b][c][0] > v) {
                pos[a][b][c][1] = pos[a][b][c][0];
                vals[a][b][c][1] = vals[a][b][c][0];
                pos[a][b][c][0] = p;
                vals[a][b][c][0] = v;
            }
            else if(vals[a][b][c][1] > v) {
                pos[a][b][c][1] = p;
                vals[a][b][c][1] = v;
            }
        }
    };

    int i = 0;
    ll A = -1e18, B = 1e18, a = -1e18, b = 1e18;

    auto get = [&](int a, int b, int c, int p) {
        if(pos[a][b][c][0] == p) {
            return vals[a][b][c][1];
        }
        return vals[a][b][c][0];
    };

    for(auto j : sum_ord) {
        if(j == 0) break;

        while(i < n && x[dif_ord[i]] - d[dif_ord[i]] < x[j] + d[j] - k) {
            upd(dif_ord[i], 3);
            upd(dif_ord[i], 0);
            i++;
        }

        B = min(B, (k - c) + x[j] - d[j] + get(0, 1, 1, j));
        A = max(A, x[j] + d[j] - (k - c) + get(0, 0, 0, j));
        b = min(b, (k - c) + x[j] - d[j] - get(0, 0, 0, j));
        a = max(a, x[j] + d[j] - (k - c) - get(0, 1, 1, j));
    }

    //cerr << k << " " << a << " " << b << " " << A << " " << B << "\n";

    // A <= y + z <= B
    // a <= z - y <= b

    if(A > B || a > b) {
        return 0;
    }

    int pa = 1, pb = 1;
    int pc = n, pd = n;

    for(i = 1; i <= n; i++) {
        while(pd > 0 && x[i] + x[pd] > B) {
            pd--;
        }
        pc = min(pc, n);
        while(pc > 0 && x[i] + x[pc] >= A) {
            pc--;
        }
        pc++;

        pa = max(pa, 1);
        while(pa <= n && x[i] - x[pa] >= a) {
            pa++;
        }
        pa--;
        while(pb <= n && x[i] - x[pb] > b) {
            pb++;
        }

        if(max(pc, pb) <= min(pa, pd) && max(pc, pb) <= i) {
            return 1;
        }
    }
    return 0;
}

long long find_shortcut(int n, vector<int> l, vector<int> D, int c) {

    int i;
    for(i = 2; i <= n; i++) {
        x[i] = x[i - 1] + l[i - 2];
    }
    for(i = n; i >= 1; i--) {
        d[i] = D[i - 1];
    }

    iota(dif_ord, dif_ord + n, 1);
    iota(sum_ord, sum_ord + n, 1);

    sort(dif_ord, dif_ord + n, [&](const int &a, const int &b) {
                return x[a] - d[a] < x[b] - d[b];
         });
    sort(sum_ord, sum_ord + n, [&](const int &a, const int &b) {
                return x[a] + d[a] < x[b] + d[b];
         });

    ll res = 0;
    for(ll step = 1LL << 50; step; step >>= 1) {
        if(check(res + step, n, c) == 0) {
            res += step;
        }
    }

    return res + 1;
}

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